Quantum Physics Paper Analysis

We investigate the limits of quantum error correction (QEC) in neutral-atom processors approaching high-fidelity gates and fast cycle times. We show that shorter QEC cycles amplify platform-specific errors, notably Rydberg excitation hopping, and hinder decay of residual Rydberg population, leading to non-Markovian correlated errors that degrade logical performance. To address this, we introduce loss biasing, where spurious Rydberg excitations are rapidly converted into atom loss via mid-circuit ionization, transforming errors into erasure-like noise and suppressing their propagation. Loss biasing restores the fault-tolerant logical error scaling for intra-cycle Pauli errors; furthermore, we argue that when supported with loss-aware decoding, it can achieve the optimal scaling of erasures while enabling shorter QEC cycles with reduced hardware overhead. We outline an implementation using fast autoionization in alkaline-earth(-like) atoms, establishing loss biasing as a practical route toward fault-tolerant quantum computing with sub-millisecond QEC cycles.

Execution of quantum algorithms on large-scale quantum computers will require extremely low logical error rates, which necessitates the development of scalable decoding architectures. Local decoders are promising candidates for this task, as they avoid the communication and data processing bottlenecks inherent in global decoding strategies. Cellular automaton (CA) decoders represent a distinct class of local decoders, offering a path toward the low-latency, real-time decoding required for practical applications. In this work, we present SCALA (Signaling CA with Local Attraction), a novel non-hierarchical cellular automaton decoder for quantum repetition and toric codes. By evaluating SCALA alongside the hierarchical CA decoder proposed by Harrington, we provide a direct comparison between non-hierarchical and renormalization-group-style local decoding strategies. We characterize SCALA across three key metrics: Performance, scalability, and robustness. Our results show that SCALA achieves a code-capacity threshold of approximately $p_c\approx 7.5\%$ and provides strong sub-threshold scaling of about $p_L\propto p^{d/4}$ on the toric code. In terms of scalability, our non-hierarchical design ensures that the local computational resources remain independent of system size, yielding a modular local architecture suitable for hardware implementation. Finally, SCALA demonstrates strong robustness to qubit measurement errors and noise within the decoder itself, a critical advantage for real-time decoding on noisy hardware. Our results establish SCALA as a high-performance, scalable, and robust local decoder for scalable quantum error correction.

Deep reinforcement learning (RL) for quantum circuit optimization faces three fundamental bottlenecks: replay buffers that ignore the reliability of temporal-difference (TD) targets, curriculum-based architecture search that triggers a full quantum-classical evaluation at every environment step, and the routine discard of noiseless trajectories when retraining under hardware noise. We address all three by treating the replay buffer as a primary algorithmic lever for quantum optimization. We introduce ReaPER$+$, an annealed replay rule that transitions from TD error-driven prioritization early in training to reliability-aware sampling as value estimates mature, achieving $4-32\times$ gains in sample efficiency over fixed PER, ReaPER, and uniform replay while consistently discovering more compact circuits across quantum compilation and QAS benchmarks; validation on LunarLander-v3 confirms the principle is domain-agnostic. Furthermore we eliminate the quantum-classical evaluation bottleneck in curriculum RL by introducing OptCRLQAS which amortizes expensive evaluations over multiple architectural edits, cutting wall-clock time per episode by up to $67.5\%$ on a 12-qubit optimization problem without degrading solution quality. Finally we introduce a lightweight replay-buffer transfer scheme that warm-starts noisy-setting learning by reusing noiseless trajectories, without network-weight transfer or $ε$-greedy pretraining. This reduces steps to chemical accuracy by up to $85-90\%$ and final energy error by up to $90\%$ over from-scratch baselines on 6-, 8-, and 12-qubit molecular tasks. Together, these results establish that experience storage, sampling, and transfer are decisive levers for scalable, noise-robust quantum circuit optimization.

Bosonic quantum error correction enables hardware-efficient protection of quantum information by encoding logical qubits in harmonic oscillators. Bosonic grid states, such as Gottesman-Kitaev-Preskill (GKP) states, are particularly promising due to their potential to correct small displacements and boson loss. However, their generation remains challenging, typically relying on probabilistic protocols or auxiliary qubit systems. Here, we propose deterministic protocols for generating bosonic grid states using programmable nonlinear bosonic circuits composed solely of squeezing, displacement, and Kerr operations. We show that aiming to enforce GKP symmetries in the output of these circuits yields states with competitive performance with respect to current realizations, but whose quality saturates with increasing circuit depth due to imperfect symmetry restoration. Instead, we find that these bosonic circuits naturally give rise to a distinct class of states, that we label as phased-comb states, which are unitarily related to standard grid states but feature an intrinsic phase structure. We demonstrate that these states define a scalable bosonic quantum error-correcting code with near-optimal performance under boson loss comparable to that of approximate GKP states. We further analyze their logical operations and show how to implement a universal gate set for them. Our results establish programmable nonlinear bosonic circuits as a viable route towards the generation of scalable bosonic quantum error-correcting states beyond standard GKP encodings.

Exact quantum codes detecting a prescribed set of Pauli errors are approached through algebraic constructions--stabilizer, codeword-stabilized, permutation-invariant, topological, and related families. Geometrically, exact Pauli detection is governed by joint higher-rank numerical ranges of these Pauli operators, whose structure for rank $\geq 2$ is largely uncharted. From this viewpoint, we show that such codes often form connected continuous families rather than collections of disjoint solution regions. These families are characterized by a single scalar derived from the Knill-Laflamme conditions: denoted $λ^*$, it is the Euclidean norm of the signature vector of Pauli expectation values on the maximally mixed code state, and provides a one-parameter summary of the code's joint Pauli variance profile. Within these continuous landscapes, stabilizer codes occupy only discrete, measure-zero subsets of the attainable $λ^*$-spectrum, exposing a largely unexplored continuum of genuinely nonadditive exact codes. We establish this picture by analyzing the geometry of higher-rank operator compressions, and extend it to symmetry-restricted settings where cyclic and permutation symmetries are imposed on both the error model and the code projector. Small-system cases reveal interval, singleton, and empty regimes through eigenvalue interlacing and symmetry-sector decompositions; larger systems are treated numerically via Stiefel-manifold optimization and symmetry-adapted parameterizations. In every unrestricted and symmetry-compatible case analyzed, the attainable $λ^*$-spectrum forms a single closed interval whenever nonempty--although a general proof remains open. These results place stabilizer, symmetric, and nonadditive code families within a unified higher-rank variance framework, suggesting a continuous geometric perspective on the landscape of exact quantum codes.

The partial oracles framework is a quantum search algorithm that has the potential to exceed the quadratic speedup of Grover's algorithm, up to a theoretical maximum of an exponential speedup. Until now, however, the framework has lacked an explicit method for constructing the operator that represents the search iteration. In this paper, we provide the missing construction, for the special case of an oracle function definable using only in-place operations (that is, where the calculated result of the oracle function can be read just from the qubits in the search index). The restriction to in-place operations means that the current work does not yet exhibit quantum advantage: oracle functions constructed using only in-place operations are always classically reversible. To demonstrate quantum advantage, it will be necessary to extend this construction method to include out-of-place operations (part II). As part of the construction of the search iteration operator, we define a new type of transform, the reciprocal transform, which is applied to the oracle function. We show that the reciprocal transform obeys a chain rule, which makes it possible to break down complex transforms into simple steps. To illustrate the practical application of this search method, we apply the reciprocal transform to elementary operations from the SHA-256 hash algorithm: addition modulo $2^n$, the $Maj(a, b, c)$ function, the $Ch(a, b, c)$ function, and the bit shift functions. We also introduce the QFrame python library, which is used to automate the construction of quantum circuits that represent reciprocal transforms.

High-quality photonic Bell state measurements (BSMs) enable scalable universal quantum computing and long distance quantum communication. However, when implemented with linear optics, BSMs are fundamentally probabilistic, introducing substantial hardware overheads and limiting noise tolerance in photonic quantum computing architectures. Nonlinear interactions at the single-photon level can overcome these limitations by enabling near-deterministic photon-photon gates. Here, we demonstrate a passive photon-sorting circuit based on the induced nonlinearity arising from photon scattering in a solid-state quantum emitter. The scattering is implemented in a directional waveguide-emitter coupling interface and embedded on-chip into a linear optical circuit, through which we demonstrate sorting of one- and two-photon components with a success probability of 62%. We find that the current system can enable BSMs with a 57% post-selected success probability without ancillary photons, exceeding the linear-optical limit of 50%, and can be readily improved to >65% with design optimisations.

Modular quantum computing architectures require error correction schemes that remain effective in the presence of noisy inter-processor operations. As such, minimizing the number of such operations on logical circuits partitioned across quantum processors is a primary objective of distributed quantum computing. In this work, we develop basic techniques for qubit allocation using an exemplar color code family and explore generalizations to other color codes. In particular, we show that a 10% reduction in processor-nonlocal gates is achievable in a setting where syndrome extraction occurs after every logical gate, as in today's devices, and that this scales to significantly greater advantages in the multi-qubit case. We also explore methods of achieving universal gate sets efficiently in this distributed logical setting and evaluate the trade-offs of multiple approaches such as magic state distillation, code switching, and a new method based on logical swaps. Finally, we discuss some considerations for an allocation algorithm for these architectures to perform scalably and connect it to existing work on quantum circuit partitions.

Systematic control errors remain a primary obstacle to realizing high-fidelity single-qubit gates. We introduce composite pulse sequences that implement X and Hadamard gates while simultaneously compensating amplitude (Rabi-frequency), detuning (frequency), and duration errors. Our construction uses two complementary strategies: (i) derivative-based cancellation of error terms in the full unitary (not just the transition probability), formulated via the Cayley-Klein parametrization, and (ii) direct minimization of the average gate infidelity over prescribed error ranges. We derive symmetric five-pulse solutions with closed-form phases that cancel all first-order terms (including the mixed derivative), and numerically optimize longer sequences -- up to 15 pulses -- to achieve higher-order suppression. We also show that standard ``universal'' five-pulse sequences (U5a/U5b) emerge as simple phase-shifted instances of our symmetric solutions, yielding broad robustness to both detuning and amplitude errors. Finally, we construct variable-area sequences for $R_x(π/2)$, which, up to virtual Z rotations, benchmark the Hadamard gate. Across all families we observe the expected trade-off between sequence length and robustness window, with substantial boosts in fidelity over large error domains.

High-fidelity control of superconducting qubits requires carefully shaped microwave pulses that account for multiple error channels. In this work, we present a pedagogical introduction to pulse-shaping techniques for transmon qubits, aiming to provide a unified, accessible framework that integrates physical intuition for pulse design, analytical understanding of gate-level descriptions, and practical considerations of hardware. This article further aims to serve as a guide for students and early researchers entering superconducting quantum computing. We begin by examining simple pulse envelopes and their spectral properties, highlighting how finite bandwidth leads to leakage outside the computational subspace. These observations motivate the introduction of the derivative removal by adiabatic gate (DRAG) technique, which uses a quadrature component proportional to the pulse's time derivative to suppress off-resonant excitations. We analyze the single-qubit case using the Magnus expansion, which provides a clear understanding of the order-by-order introduction of error channels. We discuss the practical hardware realities of control pulse generation, focusing on arbitrary waveform generators (AWG), local oscillators (LO), and IQ mixing. Common imperfections are discussed in terms of their impact on the effective pulse shape and qubit Hamiltonian. Finally, we extend the discussion to two-qubit operations, focusing on the cross-resonance gate and the emergence of effective interactions.

Photonic quantum computing provides a promising route toward quantum computation by naturally supporting the measurement-based quantum computation (MBQC) model. In MBQC, programs are executed through measurements on a pre-generated graph state, whose construction largely depends on probabilistic fusion operations. However, fusion operations in PQC are vulnerable to two major error sources: fusion failure and fusion erasure. As a result, MBQC compilation must account for both error mechanisms to generate reliable and efficient photonic executions. Prior state-of-the-art MBQC compilation, represented by OneAdapt, is designed for all-photonic architectures and mainly focuses on handling fusion failures. Nevertheless, it does not explicitly model fusion erasures induced by photon loss, which can be substantially more damaging than fusion failures. To mitigate fusion erasure errors, we introduce a new MBQC compilation scheme built upon the spin qubit quantum memory. We propose tree-encoded fusion, an encoding strategy that suppresses erasure errors during graph-state generation. We further incorporate this scheme into a compiler framework with algorithms that reduce the execution overhead of quantum programs. We evaluate the proposed framework using a realistic PQC simulator on six representative quantum algorithm benchmarks across multiple program scales. The results show that tree-encoded fusion achieves better robustness than alternative fusion-encoding strategies, and that our compiler provides exponential improvement over OneAdapt. In addition, we validate the feasibility of our approach through a proof-of-concept demonstration on real PQC hardware.

Fault-tolerant quantum computing increasingly demands rigorous, circuit-level evaluation of diverse quantum error correction (QEC) protocols and efficient prototyping of new ones. Such evaluation requires both the physical circuit and its Detector Error Model (DEM) to simulate end-to-end logical error rates. However, DEM construction today is performed by manual annotation, a tedious and error-prone process that effectively limits evaluation to simple memory experiments. We present LightStim, a framework that automates DEM construction concurrently with circuit compilation by maintaining a Pauli tableau augmented with measurement records, with no protocol-specific input required. We benchmark LightStim across protocols from memory experiments to end-to-end distillation circuits; cross-validation against public implementations confirms exact detector and observable counts and consistent logical error rates. LightStim additionally accelerates the exploration of new protocols, which we demonstrate through a novel heterogeneous cross-code lattice surgery design between surface and punctured quantum Reed-Muller codes. These capabilities together make LightStim a unified infrastructure for systematic QEC protocol evaluation and exploration.

We present pygridsynth, an open-source Python library for ancilla-free approximate Clifford+$T$ synthesis that runs in $O(\log(1/ε))$ for precision $ε$. For $n=1, 2$ qubits, the library builds upon established efficient and high-precision synthesis routines, such as nearly optimal $Z$-rotation synthesis and magnitude approximation. For $n\ge 3$ qubits, we introduce a partial-decomposition technique that generalizes the magnitude approximation, reducing constant factors in the $T$-count as $(\frac{21}{8}\cdot 4^n - \frac{9}{2}\cdot 2^n + 9)\log_2(1/ε) + o(\log(1/ε))$. The package also exposes a mixed-synthesis workflow that approximates target unitary channels by probabilistic mixtures of Clifford+$T$ circuits, for which we empirically find that the synthesis error is reduced from $ε$ to $ε^2/(2n)$. Taken together, these features make pygridsynth a Python-native platform for high-precision Clifford$+T$ synthesis and for benchmarking unitary and mixed synthesis strategies on multi-qubit instances.

As quantum hardware scales toward fault tolerant operation, the demand for correct quantum error correction (QEC) circuits far outpaces manual design capacity. AI agents offer a promising path to automating this synthesis, yet no benchmark exists to measure their progress on the specialized task of generating QEC circuits. We introduce StabilizerBench, a benchmark suite of 192 stabilizer codes spanning 12 families, 4-196 qubits, and distances 2-21, organized into three tasks of increasing difficulty: state preparation circuit generation, circuit optimization under semantic constraints, and fault tolerant circuit synthesis. Although motivated by QEC, stabilizer circuits exercise core competencies required for general quantum programming, including gate decomposition, qubit routing, and semantic preserving transformations, while admitting efficient verification via the Gottesman Knill theorem, enabling the benchmark to scale to large codes without the exponential cost of full unitary comparison. We define a unified generator weighted scoring system with two tiers: a capability score measuring breadth of success and a quality score capturing circuit merit. We also introduce continuous fault tolerance and optimization metrics that grade error resilience and circuit improvements beyond binary pass or fail. Following the design of classical benchmarks such as SWE-bench, StabilizerBench specifies inputs, verification oracles, and scoring but leaves prompts and agent strategies open. We evaluate three frontier AI agents and find the benchmark discriminates across models and tasks with substantial headroom for improvement.

We construct a quantum low-density parity-check code family from a length-512 Calderbank-Shor-Steane base matrix pair. The base pair is $(3,8)$-regular, both Tanner graphs have girth 8 , and the base code has parameters $[[512,174,8]]$. The construction uses affine cosets of six 3-dimensional subspaces of $\mathbb{F}_2^9$ as check supports, and then applies circulant permutation matrix (CPM) lifts. The main decoding experiment uses the CPM-lifted code with lift factor $P=32$, which has parameters $[[16384, 4142, \leq 40]]$, under the code-capacity depolarizing model. A belief-propagation decoder with post-processing achieved frame error rate about $10^{-8}$ at $p=$ 0.085 , and one observed logical residual of weight 40 gives a decoder-derived upper bound $d \leq 40$.

Dissipatively stabilized cat qubits are promising for fault-tolerant quantum information processing, yet their non-Hermitian (NH) spectral topology remains largely unexplored. We uncover rich Liouvillian exceptional structures in a cat-qubit mode stabilized by two-photon drive (TPD) and engineered two-photon loss, in the presence of single-photon drive (SPD) and single-photon loss. In the parameter space spanned by SPD strength and detuning, we identify both second- and third-order Liouvillian exceptional points (LEP2s and LEP3s). Remarkably, we show that the phase $θ$ of TPD provides coherent control over these exceptional points: the LEP3 diverges and vanishes at $θ=π/2$, while remaining stable and tunable elsewhere. We introduce a topological invariant based on the winding number of a resultant vector, which robustly identifies LEP3s with unit topological charge. Full master-equation simulations confirm that the system dynamics remains confined to the logical subspace with near-unity fidelity. Our results bridge dissipative stabilization, phase-coherent control, and NH topology, demonstrating controllable higher-order LEPs in open quantum systems.

Electron shuttling is emerging as a key mechanism for enabling long-range coupling in scalable spin-qubit architectures. Bringing shuttling waveform generation into the cryostat can improve scalability, but imposes strict area and power constraints on the control electronics. Concurrently, shuttling in Si/SiGe is further limited by a spatially varying valley splitting that induces spin--valley mixing and degrades coherence. Here, we make three contributions that address these limitations jointly: (i) an end-to-end co-simulation framework that combines disorder-informed valley maps with transistor-level cryogenic circuit simulations including electronic noise; (ii) a fully integrated cryogenic shuttling-signal generator tailored to velocity modulation, enabling period-wise waveform shaping through discrete circuit settings stored in on-chip memory; and (iii) a noise-aware optimization procedure that tunes only these implementable circuit controls, using one of four discrete resistor settings per period, to generate high-fidelity shuttling sequences. Across simulated valley and noise realizations in our co-simulation framework, the optimized velocity-modulation waveforms improve transport performance, achieving an average shuttling fidelity of $99.99 \pm 0.007\%$ at $v_{\mathrm{avg}} = 20~\mathrm{m\,s^{-1}}$ over a distance of $10~μ\mathrm{m}$, while maintaining active analog power consumption in the tens of $μ\mathrm{W}$ during shuttling. This validates on-chip storage and replay of optimized control settings as a practical strategy to mitigate valley disorder in scalable shuttling architectures.

We show how to directly and efficiently approximate arbitrary one-qubit unitaries, bypassing the Euler decomposition and the magnitude approximation problem, at the cost of one ancillary qubit. Our technique also applies to approximating unitaries with multi-qubit gate sets such as Clifford and CS, or Clifford and CCZ, as well as to approximating orthogonal matrices using multi-qubit gate sets such as Real Clifford and CCZ. The key tools are repeat-until-success circuits, lattice-based exact synthesis algorithms, integer point enumeration in convex sets, and relative norm equations.

Early modular fault tolerant quantum computers remain constrained by costly inter-module communication and limited magic state factory service. Understanding such bottlenecks and investigating compiler optimizations most close the gap between algorithm requirements and hardware capabilities is a concrete and practically urgent systems problem. We study the modular architectures based on Bivariate Bicycle codes and identify the dominant bottleneck: inter-module communication induced by non-Clifford operations. We build a compilation pipeline to fill the missing parts of prior works and propose compiler optimizations: synthesizing arbitrary-angle rotations at the factory (syn@fac), transvection based Clifford deferral, and Clifford insertion for critical path duration reduction. We extend the evaluation scope of the prior work to 40+ benchmark categories drawn from PennyLane and MQTBench, including quantum algorithms and Hamiltonian simulations with varying sizes. Under the present instruction cost, syn@fac reduces estimated circuit failure probability by a factor of 9.0 on average across non-Clifford benchmarks. The robustness persists across sweeps of instruction cost ratios, LPU count, and factory count. Besides, transvection reduces Clifford deferral compile time by 77.04\%, while Clifford insertion reduces end-to-end circuit duration by 11.54\% on average on MQTBench, with smaller gains on Hamiltonian simulations. We hope this work inspires the studies on compiler optimizations for early modular FTQC systems.

Higher-dimensional quantum systems, such as qudits, offer architectural and algorithmic advantages over qubits, but their increased spectral crowding and limited controllability render high-fidelity quantum gates particularly challenging. We propose a hybrid optimization framework that integrates optimal control theory methods with contextual deep reinforcement learning to achieve robust controlled-phase gates on two qutrits. Optimal control is first used to design high-fidelity control pulses for a nominal system model. Reinforcement learning is then employed as a calibration stage that learns small residual corrections to these pulses in the presence of static model mismatch, thereby preserving good gate performance under realistic parameter uncertainties. By learning structured, low-dimensional residual corrections conditioned on device-specific parameter variations, reinforcement learning enhances the transfer robustness of nominally optimal but parameter-sensitive control solutions across ensembles of devices. Crucially, the reinforcement learning step in our framework does not compete with the optimal control step but provides the adaptability required for realistic hardware, systematically reducing the sensitivity to parameter fluctuations. Our results establish reinforcement learning as a practical and scalable ingredient for robust calibration of quantum gates in high-dimensional systems.

Recent advancements in neutral atom platforms have enabled exploration of early fault-tolerant (FT) architectures for applications with quantum advantage, such as quantum dynamics simulations. An efficient fault-tolerant architecture has both spatially efficient quantum error correction codes (low qubit overhead), and efficient methodologies (transversal based gates, extractor based gates, etc.) for logical computation, to minimize overall execution time. Achieving the right balance between space and time can be critical for enabling early FT demonstrations of quantum advantage. In this work, we identify bottlenecks in existing spatially efficient schemes, which tend to be very serial, and do not take advantage of unutilized space. We introduce a teleportation-based scheme that leverages the reconfigurable connectivity of neutral atoms to parallelize logical operations. Our approach achieves up to \textbf{$\mathbf{\sim 3 \times}$ speedup} over extractor architectures at no extra space cost and achieves the best spacetime performance among other viable architectures before accounting for external \textit{resource-states}. To rigorously evaluate performance, we construct explicit quantum advantage benchmarks and \textit{simulate} compilation to a fault-tolerant instruction set, including low-level gate scheduling and shuttling patterns, and resource-state nondeterminism. We find that our speedups still apply and report exact space-time cost along with success probabilities, identifying architectures capable of achieving quantum advantage \textbf{with as little as $\mathbf{11,495}$ atoms and a runtime of $\mathbf{\sim 15}$ hours}.

In this paper, we give a mathematical proof that bounds the number of CNOT gates required to synthesize an $n$ qubit phase polynomial with $g$ terms to be at least $O(\frac{gn}{\max (\log g, 1)})$ and at most $O(gn)$. However, when targeting restricted hardware, not all CNOTs are allowed. If we were to use SWAP-based methods to route the qubits on the architecture such that the earlier synthesized gates are natively allowed, we increase the number of CNOTs by a routing overhead factor of $O(\log n) \leq α\leq O(n \log^2 n)$. However, if we only synthesize allowed gates, we do not need to route any qubits. Moreover, in that case the routing overhead factor is $1 \leq α\leq 4 \simeq O(1)$. Additionally, since phase polynomials and Hadamard gates together form a universal gate set, we get qubit routing for almost free.

Quantum Signal Processing (QSP) and Quantum Singular Value Transformation (QSVT) provide an efficient framework for implementing polynomials of block-encoded matrices, and thus offer a systematic approach to quantum algorithm design. However, despite a number of recent advances, important limitations remain. In particular, QSP can only transform unitary matrices, by applying a polynomial to their eigenvalues, while QSVT is a singular-value transformation and thus one can only obtain the polynomial of Hermitian matrices. As a consequence, these techniques do not directly apply to an arbitrary non-Hermitian matrix that is not diagonalizable. In this work, we propose a simple yet powerful method to extend these ideas to arbitrary square matrices by acting on their eigenvalues. To this end, we introduce the notion of an $n$-regular block encoding, namely, a block encoding whose $k$-th power reproduces the $k$-th power of the encoded matrix for every $0 < k < n$. We show that applying QSP to any unitary with this property is equivalent to applying a polynomial of degree at most $n$ to the block-encoded matrix, independently of its internal structure. Moreover, we provide a simple construction that transforms any block encoding into an $n$-regular one using only $O(\log n)$ ancillary qubits and operations. Finally, we show that this construction induces the desired transformation on the eigenvalues associated with the Jordan normal form of the matrix.

The use of noise-robust qubit encodings provides a way of extending the lifetime of quantum information at the hardware level. In this work, we introduce the spin Kerr-cat encoding, which leverages a clock transition in the spectrum of quadrupolar nuclei (having spin length $I\geq 1$) to achieve a first-order suppression of noise leading to qubit dephasing. The basis states of the spin Kerr-cat qubit are given by the two lowest levels of a $\mathbb{Z}_2$-symmetric nuclear-spin Hamiltonian and are well approximated by spin cat states. We compute the dephasing time of the spin Kerr-cat qubit under a model of $1/f$ noise, as well as relaxation of the qubit due to breaking of the $\mathbb{Z}_2$ symmetry by charge-noise-induced fluctuations of the quadrupolar tensor. Using measured parameters for antimony (${}^{123}\mathrm{Sb}$) donors in silicon, we estimate that a coherence time of $T_2^*=100$ s could be achieved with this encoding. We propose a two-qubit gate mediated by hopping electrons and estimate that with an enhancement of measured quadrupolar splittings by a factor of $\approx 4$, a gate fidelity of $99\%$ could be achieved for spin Kerr-cat qubits encoded in ${}^{123}\mathrm{Sb}$ nuclear spins, neglecting errors that impact the electron while it is being shuttled and read out.

We propose a fault-tolerant quantum computer architecture for trapped-ion devices, which we call the walking cat architecture. Our blueprint includes a compiler, a detailed description of all the quantum error-correction protocols, a micro-architecture, a sufficiently fast decoder, and thorough simulations. The backbone of the architecture is a cat factory, producing cat states distributed throughout the machine, which are consumed to perform logical operations. The walking cat architecture is based entirely on a modern quantum error-correction approach called low-density parity-check (LDPC) codes. We identify promising instances of the walking cat architecture, such as (1) a simple architecture based on a single LDPC code, (2) a fast architecture based on fast logical gates relying on a [[70, 6, 9]] code, equipped with Clifford-frame tracking for any 6-qubit Clifford gate, and (3) a dense architecture based on a [[102, 22, 9]]] code encoding 22 logical qubits per memory block. Our dense architecture provides a design with 110 logical qubits executing about one million T gates per day using only 2,514 physical qubits. We estimate that the quantum Hamiltonian simulation of a Heisenberg model on 100 sites can be executed within one month with 10,000 physical qubits, including all shots required to achieve chemical accuracy, suggesting that such a device could enter the regime of classically intractable physics simulations. Our design relies on hardware components that have been experimentally demonstrated on small devices. We emphasize simplicity over hypothetical performance to facilitate the practical realization of this machine. Based on this approach, we believe that a fault-tolerant quantum computer with hundreds of logical qubits capable of running millions of logical gates can be built in the near term, providing a platform to explore a broad range of applications.

We propose a cavity-based scheme that uses photonic chirality to control braiding and read out non-Abelian anyons in a fractional quantum Hall platform. Counter-propagating cavity modes interfere with a classical reference tone to create a rotating pinning landscape whose direction is set by photon circulation, so that opposite photonic branches drive opposite anyon loops. This realizes a branch-conditioned braid operation and maps the resulting braid response onto cavity intermode coherence. We derive the rotating pinning term and the readout relation at the effective-theory level, identify an operating window set by subgap driving, adiabatic transport, localization, and cavity coherence, and provide phenomenological diagnostics of transport locking. In the minimal four-anyon Ising realization, the leading signal reduces to a calibrated phase; more generally, the same readout structure becomes state dependent when the relative braid operator is non-scalar. The scheme provides a cavity route to braid-sensitive readout of non-Abelian anyons without relying on fragile electronic interference fringes.

As quantum computing matures into a practical paradigm, the need for secure and private quantum computation on untrusted hardware becomes increasingly urgent. While classical fully homomorphic encryption has enabled computation over encrypted data in untrusted environments, a fully homomorphic and practically implementable quantum counterpart remains elusive. In this work, we propose a universal quantum homomorphic encryption (QHE) framework developed from the Quantum One-Time Pad (QOTP) scheme. Our approach (QOTPH) maintains information-theoretic security and supports a broad class of quantum operations on encrypted quantum states through a systematic set of homomorphic gate decompositions and key update rules. By leveraging the symmetric structure of QOTP and exploiting the transformation properties of quantum gates under Pauli encryption, we enable non-interactive homomorphic evaluation of arbitrary circuits expressible in the Clifford+T gate set, as well as controlled and parameterized operations relevant to variational quantum algorithms and delegated computation. We provide a formal specification of the proposed encryption model, detail its implementation procedure, and report the results obtained from both simulated environments and real quantum processors. Experimental validation demonstrates the correctness of the homomorphic operations and the preservation of key secrecy under circuit-level noise and real-device constraints. This work takes a step toward bridging the gap between theoretical quantum homomorphic encryption and practical realization on near-term quantum hardware, offering a scalable and symmetric cryptographic primitive for privacy-preserving quantum computation.

Hybrid continuous-variable--discrete-variable (CV--DV) architectures process quantum information in bosonic modes and qubits, but noise limits their performance. To reduce the noise, existing DV error correction must be complemented by CV noise reduction. Existing CV noise-reduction schemes -- such as GKP-stabilizer codes -- can reduce CV noise, but only for Gaussian gates. Therefore, no current noise-reduction scheme can correct arbitrary CV--DV gates, including non-Gaussian ones. Here, we develop noise reduction for a universal CV--DV gate set, making it applicable to arbitrary CV--DV gates. We do so by introducing an ancilla qubit into a GKP-stabilizer code, allowing us to reduce the standard deviation of Gaussian displacement noise from $σ$ to $\tilde O(σ^2)$. To demonstrate the scheme, we show that it significantly reduces noise and improves fidelity in the preparation of non-Gaussian cat and Fock states.

Hamiltonian simulation is one of the most promising paths toward quantum advantage. Most prior approaches to Hamiltonian simulation circuit synthesis focus on local rewrite rules and low-level optimizations, and give limited attention to high-level scheduling of Pauli terms under varying constraints. In practice, different simulation algorithms require different orderings of the Pauli terms, yet many prior IR-based methods assume a fixed commutation structure, which limits their flexibility. We present MonteQ, a novel quantum circuit synthesis framework for Hamiltonian simulation. MonteQ leverages a two-level design that combines low-level synthesis heuristics with an upper-level tree structure to explore sequences of Pauli rotations. To avoid enumerating this factorially large tree, the Monte Carlo Tree Search algorithm serves as workhorse for judiciously exploring promising paths to leaf nodes. With this two-level design, MonteQ supports both logical-level and hardware-aware synthesis by selecting different low-level heuristics. It also supports different ordering constraints on the Pauli rotations by adjusting the high-level tree structure. For example, MonteQ can preserve the target unitary by using a directed acyclic graph that records the commutation relations among the Pauli rotations, or it can relax unitary preservation constraint to uncover additional optimization options. Our experimental results show that MonteQ can achieve an improvement, as measured in CNOT gate counts, of up to 53% (30% on average) against state-of-the-art compilers like Rustiq on a set of representative synthesis tasks.

Standard quantum error correction (QEC) models typically assume discrete, Markovian noise, obscuring the continuous quantum nature of physical environments. In this manuscript, we investigate the fundamental limits of an actively corrected surface code coupled to a continuous, un-reset quantum environment at zero and finite temperature. Using the generalized Caldeira-Leggett framework, we map the long-time evolution of the logical qubit to a boundary conformal field theory, establishing an exact equivalence to the anisotropic Kondo model. We evaluate computational times for a finite code distance $L$ for all spatial and temporal correlations. Our analysis reveals that a true thermodynamic threshold exists strictly for short-range environments ($z>1/(s+1)$). In critical or long-range regimes, the macroscopic footprint of the code weaponizes the continuous bath, hindering the topological protection.

The quantum instrument (QI) formalism is required to model mid-circuit measurements (MCMs) and the dependence of the post-measurement state on the measurement outcome. Correctly modeling QIs is essential for applications using MCMs, such as adaptive circuits and quantum error correction. Although QIs yield a joint quantum-classical state after measurement, errors in QIs can still be represented by a $d^2 \times d^2$ superoperator (e.g., process or transfer matrix) for each outcome, just as superoperators describe Markovian errors on unitary gates. However, because the joint quantum-classical system has a distinct error model for each outcome, this complicates the usual interpretation of process- or transfer-matrix error models. This Note offers practical guidance on understanding and interpreting QI error models.

We propose a broadband Purcell-protection scheme based on a single shared filter integrated directly into the feedline, enabling simultaneous protection of multiple qubits in a compact architecture with minimal hardware overhead. The filter consists of two open-ended stubs connected by an in-line transmission line, forming a $Π$ geometry, and operates via engineered passive microwave interference that suppresses the real part of the environmental admittance over a wide frequency window. Circuit simulations and finite-element modeling show strong suppression of transmission within the target band (the qubit's frequencies) while preserving the readout and reset modes of the multiplexed architecture. For realistic device parameters, the proposed design yields Purcell-limited relaxation times exceeding $1$ ms over a frequency span of approximately $1.5$ GHz, which can be further extended with straightforward modifications of the design. Our results establish the $Π$-filter as a compact and scalable solution for broadband impedance engineering in superconducting quantum circuits, compatible with standard dispersive readout protocols.

Block-encoding is a foundational technique in modern quantum algorithms, enabling the implementation of non-unitary operations by embedding them into larger unitary matrices. While theoretically powerful and essential for advanced protocols like Quantum Singular Value Transformation (QSVT) and Quantum Signal Processing (QSP), the generation of compilable implementations of block-encodings poses a formidable challenge. This work presents the BlockEncoding interface within the Eclipse Qrisp framework, establishing block-encodings as a high-level programming abstraction accessible to a broad scientific audience. Serving as both a technical framework introduction and a hands-on tutorial, this paper explicitly details key underlying concepts abstracted away by the interface, such as block-encoding construction and qubitization, and their practical integration into methods like the Childs-Kothari-Somma (CKS) algorithm. We outline the interface's software architecture, encompassing constructors, core utilities, arithmetic composition, and algorithmic applications such as matrix inversion, polynomial filtering, and Hamiltonian simulation. Through code examples, we demonstrate how this interface simplifies both the practical realization of advanced quantum algorithms and their associated resource estimation.

Tantalum is a promising platform for superconducting quantum circuits, yet coherence times remain limited by dielectric losses from interfacial two-level systems (TLS), exacerbated by native oxide regrowth. Here, we implement molecular surface passivation using self-assembled organic monolayers on freshly etched tantalum and silicon in coplanar waveguide resonators. Surface characterization by contact angle, XPS, FTIR and TEM confirm the formation of ordered, nanometer-thick films that suppress oxide formation. Microwave measurements in the ~5-9 GHz range reveal internal quality factors up to 1.8x10^6 in the single-photon regime at 100 mK, representing a ~140% improvement over untreated devices with native oxide. Power and temperature dependent measurements attribute this enhancement to reduced TLS-induced losses. These results demonstrate that molecular passivation effectively engineers low-loss interfaces and provides a scalable route toward high-coherence superconducting quantum devices.

Surface oxides contribute to losses in superconducting transmon devices resulting in degraded performance. We explore the use of the damascene process to replace the sidewall native oxide of a device with a metal/substrate interface. We simulate sidewall oxidation by burying an oxide layer during fabrication. We observe a modest improvement between the two types of devices, which is suggestive of a reduction in the surface participation ratio.

Measurement-only circuits provide a minimal setting in which repeated local projections can either generate or suppress many-body entanglement, giving rise to measurement-induced phase transitions and dynamical regimes, that might have no unitary counterpart. Here we investigate entanglement and information transitions in one-dimensional measurement-only Clifford circuits with long-range two-qubit parity checks. By tuning both the measurement range and density per layer, we uncover a broad set of phases whose classification requires probes beyond entanglement entropy, such as mutual information, tripartite mutual information, purification from an ancilla, and Bell-cluster statistics. We map phase diagrams using large-scale Clifford simulations for two protocols: a random-basis design in which each measurement is randomly chosen from $\lbrace XX,YY,ZZ \rbrace$, and a single-basis design in which the basis is fixed within each layer but varies between layers, hence introducing more structure to the circuit. We map the trajectory-averaged entanglement entropy to a two-dimensional statistical mechanics model by extending a replica-based method to random-basis measurement-only circuits, and show that a continuous-time limit yields an effective long-range XX hamiltonian in the steady state. This connection links the observed volume-law to sub-volume-law entanglement transition to the boundary between a continuous symmetry broken phase and a critical XY phase. Strikingly, in structured (single-basis) circuits we find a phase in which volume-law and long-range entanglement coexists with rapid, size-independent purification of an ancilla qubit, and the absence of scrambling, highlighting measurement-only circuits as a promising route to efficiently preparing highly entangled and technologically useful quantum states.

We explore the performance of the time-convolutionless (TCL) projection operator technique using the Fano-Anderson model as a test case. Comparing the exact TCL master equation with an expansion in powers of the strength of the system-environment coupling, we analyze the transient dynamics as well as the steady-state behavior. For a Lorentzian spectral density we demonstrate that the dimensionless expansion parameter corresponds to the ratio of the environmental correlation time to the relaxation time of the system, and we derive the convergence radius for the TCL expansion, which is seen to depend on the ratio of detuning and width of the spectral density. We further study the quantum non-Markovianity of the model based on the evolution of the Bures distance between quantum states and how it is represented by the second and fourth order of the expansion. Our results highlight both the strengths and the limitations of the TCL formalism in capturing key features of open quantum systems and, in particular, the challenges of accurately describing strongly coupled systems and non-Markovian dynamics.

We investigate the effect of a periodic electric field drive on the generalized Aubry-André model, also known as the Ganeshan-Pixley-Das Sarma (GPD) model, which is well known as a host of mobility edges. Our study of the Floquet spectrum of the driven GPD model uncovers the emergence of two distinct Floquet mobility edges, a delocalized--localized (DL) edge in the bounded regime, and a multifractal--localized (ML) edge in the unbounded regime. Using analytical results derived from Avila's global theory applied to the high frequency effective Hamiltonian, together with numerical diagnostics such as the fractal dimension and inverse participation ratio, we demonstrate that these mobility edges can be effectively controlled by the amplitude and frequency of the electric field drive. We also identify drive-induced localization at specific values of the driving parameters, corresponding to dynamical localization points in the absence of quasiperiodic potential. Furthermore, the dynamical study of the periodically driven GPD model demonstrates superdiffusive to almost ballistic transport in the bounded regime corresponding to the DL edges, whereas subdiffusive transport is observed in the unbounded regime associated with the ML edges. We also analyze deviations from the high-frequency effective description by explicitly examining the low-frequency driving regime, where significant and counterintuitive deviations in both spectral properties and transport behavior are observed. Our study highlights the interplay of a quasiperiodic potential and a periodically varying electric field drive as a powerful mechanism to engineer mobility edges and control transport in systems with rich spectral features.

We study random entanglement percolation in heterogeneous quantum networks, where the singlet-conversion probabilities (SCPs) of the edges are drawn from a probability distribution rather than being fixed. After briefly recalling random classical and random quantum entanglement percolation, we focus on polarization-dependent loss (PDL) as a physical source of random edge entanglement in photonic networks. In this setting, polarization imbalance induces a simple map from the PDL magnitude to the edge SCP. We illustrate this map for representative PDL models and discuss the resulting implications for entanglement percolation.

We study spectral properties of quantum many-body Hamiltonians through a subsystem-based framework. Given a Hamiltonian of the form $H = \sum_{X \subseteq Λ} Φ(X)$ acting on a tensor product Hilbert space, we associate to each subset $S \subseteq Λ$ a subsystem Hamiltonian $H_S$ and its spectrum $\mathcal{S}(S) = σ(H_S)$. This produces a family of spectra indexed by subsystems, allowing spectral data to be organized according to interaction structure. We show that subsystem Hamiltonians admit local approximations: $H_S$ can be approximated by operators supported on finite neighborhoods with an error bounded by $\|H_S - H_{S,r}\| \le |S| e^{-μr} \|Φ\|_μ$. As a consequence, subsystem spectra are stable under truncation in the sense that $d_H(\mathcal{S}(S), σ(H_{S,r})) \le |S| e^{-μr} \|Φ\|_μ.$ We then prove that for disjoint subsets $S_1, S_2 \subseteq Λ$, the subsystem spectrum is approximately additive: $d_H\big(\mathcal{S}(S_1 \cup S_2), \mathcal{S}(S_1) + \mathcal{S}(S_2)\big) \le (|S_1| + |S_2|) e^{-μD} \|Φ\|_μ,$ where $D = d(S_1, S_2)$. In the finite-range case, this relation becomes exact. The results show that spectral properties reflect the locality of interactions not only at the level of operators, but also at the level of spectra. The framework provides a way to study many-body systems in which interaction geometry directly shapes spectral behavior.

Belief propagation has recently emerged as a powerful framework for evaluating tensor networks in higher dimensions, combining computational efficiency with provable analytical guarantees. In this work, we develop the first end-to-end theory of tensor network belief propagation for a class of projected entangled pair states satisfying \emph{strong injectivity}. We show that when the injectivity parameter exceeds a constant threshold, BP fixed points can be found efficiently, and a cluster-corrected BP algorithm computes physical quantities to $1/\mathrm{poly}(N)$ error in $\mathrm{poly}(N)$ time for an $N$ qubit system. We identify a striking phenomenon we term \emph{algorithmic locality}: local perturbations of the tensor network affect the BP fixed point with an influence decaying rapidly with distance. As a result, updates to the fixed point after a local perturbation can be carried out using only local recomputation. Moreover, through the cluster expansion, this locality extends to observables, implying that local expectation values can be approximated from local data with controlled accuracy. Our results provide the first rigorous guarantee for the effectiveness of tensor-network belief propagation on a wide class of many-body states, bridging a gap between widely used numerical practice and provable algorithmic performance.

Quantum resources such as entanglement form the backbone of quantum technologies and their efficient generation is a central objective of modern quantum platforms. Independently, quantum batteries have emerged as nanoscale devices that utilize collective quantum effects to store energy with a charging advantage over classical strategies. Here, we show that these two pursuits can co-exist: protocols for fast generation of resourceful quantum states can simultaneously charge a quantum battery with a collective advantage, and conversely, a quantum battery protocol with a charging advantage can produce resource-rich states. Using this connection, we propose an integrated hardware protocol on superconducting circuits in which each experimental run can interchangeably accomplish either quantum battery charging, or quantum sensing through generation of metrologically useful states. Our results establish that quantum resources and stored energy are distinct yet co-producable quantities, opening the door to modular quantum architectures that dynamically switch between sensing and energy-storage functions, thereby producing additional functionalities without extra hardware cost.

Peaked quantum circuits, whose output distribution is sharply concentrated on a single bitstring, have emerged as a promising candidate for verifiable quantum advantage, as the correctness of the quantum output can be checked by simply comparing against the known peak. Recent work by Gharibyan et al. arXiv:2510.25838 claimed heuristic quantum advantage using peaked circuits executed on Quantinuum's 56-qubit H2 processor. These peaked circuits concentrate their output on a single hidden bitstring by training a shallow simulable circuit variationally and inserting an obfuscated permutation to increase the depth to a level that makes classical simulation intractable, with estimated runtimes of years for the largest instances. We show that these circuits can be efficiently simulated classically. We describe a method that efficiently performs a full tensor network contraction, allowing near-exact sampling and extraction of the peaked bitstring. The method exploits the mirrored structure of the circuit and iteratively cancels both halves into a Matrix Product Operator (MPO), and avoids the obfuscated permutation by greedily reducing the MPO bond dimension through a process we call unswapping. The method can fully contract and extract the peak of the largest circuit in approximately one hour on a single GPU, around half the time it took to run on the quantum hardware.

Quantum networks are a keystone of the quantum internet. However, existing implementations remain largely confined to static point-to-point links due to the absence of a switching paradigm capable of dynamically routing fragile quantum entanglement without introducing decoherence. Here, we propose the Universal Quantum Switch, a foundational building block allowing on-demand, non-blocking, and encoding-agnostic routing of quantum information, as well as seamless modality conversion between disparate quantum platforms. We develop a prototype in thin-film lithium niobate and experimentally demonstrate robust switching with $\le 4\%$ decoherence via thermo-optic modulation and high-speed electro-optic switching of arbitrary entangled states at 1 MHz. Moreover, we show that our platform can support reconfiguration speeds up to 1 GHz. To our knowledge, this work represents the first demonstration of multi-node dynamic entanglement distribution at these speeds. Complementing these experimental results, we project the architecture's scalability, showing dimension-independent decoherence, and provide a scalable, interoperable building block for heterogeneous quantum network fabrics.

Solid-state spin defects hold great promise as building blocks for various quantum technologies. Embedding spin centers in $p$-$n$ diodes under reverse bias has proved to be a powerful strategy to narrow the optical linewidth and increase spin coherence, while also enabling control of the photoluminescence wavelength via Stark shift. Given the multitude of parameters influencing spin centers in diodes (e.g., doping densities and profiles, temperature, bias voltage, spin center position), a question that has not yet been answered is: which set of these design parameters maximizes spin center coherence? In this work, we address this question by developing a scaled gradient descent optimization algorithm that minimizes the optical linewidth of spin centers by combining the numerical solution of a diode's Poisson equation with calculated charge noise from the non-depleted regions. Our optimization is performed for both single- and multiple-parameter cases for divacancies in SiC $p$-$i$-$n$ diodes, including reverse-bias voltage, doping density and profile, and diode total length. Importantly, the optimization is subject to realistic physical constraints, such as small operating bias voltages, avoidance of the dielectric breakdown regime and physical thresholds for doping density. Additionally, due to the leakage current at reverse bias voltages, we develop a new formalism to investigate its influence on coherence. We show that the corresponding noise can be mitigated by implanting spin defects away from the diode's surfaces. Our work provides guidance on experimentally relevant diodes for hosting spin centers with the narrowest optical linewidths and longest coherence times.

New sources of charge-parity (CP) violation beyond those described in the Standard Model (SM) are required to explain the observed matter--antimatter asymmetry of the Universe. The Standard Model Effective Field Theory (SMEFT) provides a framework to introduce additional electroweak sources of CP-odd physics in a model-independent manner. However, these CP-violating signatures are mostly degenerate to CP-even SMEFT operators in polarisation-blind observables, distinguishable only in the SM-New Physics (NP) interference using the azimuthal decay angle. Using Quantum Tomography techniques, we present a new approach to constraining these NP effects. Reconstructing the spin density matrix (SDM) of a diboson system, we go beyond `interference resurrection' to exploit the full signature of the Beyond-SM physics, including the pure quadratic NP terms. We show that this approach provides superior simultaneous sensitivity to characteristic features of CP-even and CP-odd contributions, including effects not fully captured by traditional angular observables.

We quantize a classically stable system of a harmonic oscillator polynomially coupled to a ghost with negative kinetic energy. We prove that due to an integral of motion with a positive discrete spectrum: i) the Hamiltonian has a pure point spectrum unbounded in both directions, ii) the evolution is manifestly unitary, iii) the vacuum is well-defined, iv) expectation values for squares of canonical variables are bounded. Numerical solutions of the Schrödinger equation confirm these results. We argue that the discrete spectrum of the integral of motion enforces stability for extended interactions.

The Dicke model (DM) serves as a paradigm for understanding collective light-matter interactions. We introduce the chiral Dicke model, a generalization where an atomic ensemble couples to a two-mode cavity via chiral interactions. Unlike the standard DM, the chiral DM is endowed with an inherent continuous $U(1)$ symmetry associated with angular momentum conservation. The ground-state phase diagram and the associated quantum phase transitions are charted out, revealing a $U(1)$-broken superradiant phase that spans a broad parameter space. We demonstrate that the spectrum of quantum fluctuations is highly tunable in both the symmetric and broken phases. Strikingly, our calculations reveal that the system exhibits `multiversality', where distinct universality classes govern the transition between the same two phases. In particular, along a special line in parameter space, the dynamical critical exponent for the normal-superradiant phase transition changes from $zν=1$ to $zν=1/2$. Our work establishes the chiral Dicke model as a powerful platform to realize novel quantum phases and multiversal critical phenomena in light-matter coupled systems.

Page and Wootters (1983) showed how time and dynamics can emerge in a stationary system containing a clock. Albrecht (1995) later showed, for discrete time, that within this framework any dynamical evolution can be obtained simply by choosing a different clock. Marletto and Vedral (2017) claimed that this ambiguity disappears assuming that the clock and the rest of the world do not interact. I show that their proof relies on an incorrect mathematical assumption. Also, eliminating the ambiguity completely would obstruct spacetime symmetries. Whereas the original clock ambiguity concerns all possible histories of a discrete-time system evolving under arbitrary Hamiltonians, but not the Hamiltonians themselves, I prove a stronger version for continuous and discrete unbounded time: the ambiguity extends to both histories and Hamiltonians, including noninteracting ones. Only the dimension of the Hilbert space remains. One might hope to dismiss the ambiguity as merely perspectival, but I show that this would predict incorrect correlations between outcomes and their records, making even knowledge impossible. Purely relational approaches therefore face both the stronger and the original clock ambiguity problems. The ambiguity is removed by taking into account the physical meaning of the operators.

This thesis is concerned with rigorous security analyses of practical Quantum Key Distribution (QKD) protocols, using a variety of modern proof techniques. The main results are as follows. First, we establish a security proof for variable-length QKD protocols against IID collective attacks, and extend this result to coherent attacks using the postselection technique. In doing so, we resolve a long-standing flaw in the application of the postselection technique to QKD, thereby placing it on a rigorous mathematical footing. Second, we develop a method to bound phase error rates in entropic uncertainty relation-based and phase error rate-based proofs, using only the observed statistics of the protocol, even when detectors are imperfect and only approximately characterized. This removes a key assumption of identical detector behaviour and enables these techniques to be applied in realistic settings. Third, we present a very general security analysis based on the marginal-constrained entropy accumulation theorem. The resulting framework can be readily adapted to practical imperfections and side channels, and is suitable for certification efforts. Finally, we show that the security of QKD protocols under realistic authentication assumptions can be reduced to the standard idealized setting, where authentication is assumed to behave honestly, with only minor protocol modifications. A distinctive feature of this thesis is its unified presentation of several major QKD security proof frameworks using consistent protocol descriptions and notation. Consequently, this thesis is intended not only as a collection of new technical results, but also as a useful reference for understanding rigorous security analysis in quantum key distribution.

We present a fast, memory-efficient, unitarity-preserving numerical method beyond the rotating-wave approximation for the closed Tavis-Cummings model in which a multilevel spin system interacts with a cavity mode. This model can describe the interaction of an ensemble of spins with a cavity mode in which the spin frequency and other parameters are time-dependent. The method exploits the fact that, while the Tavis-Cummings model is not tri-diagonal, it can be brought into tri-diagonal form by a change of basis that can be implemented purely by re-indexing (permuting basis elements), which is a fast operation. By truncating the Fock basis of the cavity mode, the computational complexity of the method is linear in the total dimension of the coupled system, both in time and memory. The method can be employed to simulate any closed quantum system whose Hamiltonian terms can be brought into tri-diagonal form.

In this work, we systematically investigate the quantum-information diagnostics of cosmological perturbations with a nontrivial sound speed, utilizing a normalized open two-mode squeezed-state framework. Rather than introducing new observables, our analysis focuses on how a modified sound speed dynamically reshapes the Schrödinger evolution of the squeezing parameters ($r_k$ and $φ_k$). We demonstrate how these dynamical changes are inherited by the reduced density matrix of the observable sector. By employing a sound-speed-resonance parametrization, we derive and evaluate the purity, von Neumann entropy, Rényi entropies, and logarithmic negativity. To overcome the intrinsic multiscale stiffness of the post-inflationary equations, we introduce a bounded variable $x = \tanh r_k$ as a partial regularization, which enables reliable numerical simulations exclusively within the inflationary regime. Our numerical results reveal that a nontrivial sound speed significantly suppresses the purity of the reduced state, indicating enhanced effective mixedness. Simultaneously, it strongly amplifies and modulates both the entropic and entanglement diagnostics. More precisely, a nontrivial sound speed postpones the onset of classicality by modulating the decoherence process. Ultimately, we show that a nontrivial sound speed leaves distinct and identifiable quantum-information signatures within the entanglement structure of the early universe.

Quantum technologies in the terahertz (THz) require a coherent interface between addressable qubits and THz quantum channels -- a capacity that so far, remains largely underdeveloped. Here, we propose and demonstrate the generation of steady-state entanglement between polar quantum emitters, mediated by THz photons. We exploit strong visible-light driving of the emitters to create Rabi-split dressed eigenstates whose energy separation can be optically tuned into the THz regime. The polar nature of the emitters activates THz transitions within these eigenstates, allowing them to couple to a THz photonic mode that induces collective dissipative dynamics. A coherent driving and control of these effective THz emitters is achieved by using a sideband optical drive with detuning close to the THz transition frequency. The resulting interplay of collective dissipation and driving activates a mechanism to generate steady-state entanglement with high values of the concurrence ($C>0.9$), attainable under experimentally feasible parameters. Crucially, both coherent manipulation and quantum state tomography are implemented entirely through optical means, avoiding direct THz control and detection. This establishes a hybrid visible-THz quantum interface in which a THz channel mediates qubit-qubit entanglement (a key operational requirement for THz quantum technologies) while remaining optically accessible.

We show that detecting steady-state Coulomb-mediated reduction in the thermal variance of the differential motional mode of two nanospheres can bound the Continuous Spontaneous Localization (CSL) parameter ($λ_{\text{CSL}}$). For realistic experimental parameters, the resulting bounds are comparable to those obtained from X-ray emission experiments and surpass those set by bulk-heating ones. Unlike these latter experiments, our bounds are robust against plausible coloured-noise extensions of collapse models. In the short-time regime, we find that a weak Coulomb-induced entanglement-based test between two charged nanospheres initialized in ground state can provide constraints on $λ_{\text{CSL}}$ comparable to limits set by early X-ray experiments.

We describe the design, implementation, and nine-month operational experience of the software management stack for Lagrange, an IQM Spark five-qubit superconducting quantum computer jointly acquired by LINKS Foundation, Politecnico di Torino and the Italian National Institute of Metrological Research (INRiM), and managed by LINKS. Lagrange is, to our knowledge, the first quantum computer in Italy that is fully operational and accessible to students and researchers from multiple institutions under formal service agreements, and to the general public under commercial agreements. When installed in mid-2025, the IQM Spark hardware was delivered by the vendor with authentication only: no billing, project management or fair usage enforcement were provided. We developed a modular middleware layer that filled that gap without modifying any vendor client software, by intercepting API calls through a proxy that enforces project-based budgets, reservation-aware authorisation, and per-user fairness policies. The middleware adopts a plugin architecture that cleanly separates vendor-specific logic from site-specific policies, enabling reuse across different quantum hardware backends and deployment contexts. Since entering production in September 2025, the system has processed over 240,000 quantum jobs totalling more than 1 week of QPU execution time, with greater than 98% uptime. Notably, students at Politecnico di Torino regularly use the machine during both lectures and formal examinations -- a practice we believe to be unique in Europe. We report on the system architecture, the operational lessons learned, and the infrastructure choices that made this deployment possible.

The creation of high-quality cluster states in superconducting microwave circuits is a relevant ingredient in continuous-variable quantum computing. Although large-scale cluster states have been established in optical systems, dissipation prevents their direct applicability to the microwave realm. Recent improvements in superconducting parametric circuits, in particular Josephson parametric amplifiers (JPA) and traveling wave parametric amplifiers (TWPA), have permitted substantial progress in producing entangled states using microwave photons. In this paper, we examine experimentally and theoretically the effects of numerous parametric pump tones on the degree of two-mode squeezing in a quantum circuit and apply it to the JPA. We find that additional pumps diminish the initial two-mode correlations achieved with a single pump by redistributing it among a larger network of modes and by introducing entanglement with additional idler frequencies. Taking into account the actual heterodyne measurement conditions, the experimental results are consistent with theoretical expectations.

The optical spectrum of a quantum system is jointly determined by the properties of the emitter and the driving field. All-optical spectral control can hence be a promising method to engineer the properties of single photon emitters for quantum technological applications. It was proposed that driving a two-level system with a periodic sequence of optical pi-pulses during the excited state lifetime shifts the emission and absorption maximum to an arbitrarily detuned pulse carrier frequency, enabling the mitigation of spectral diffusion in noisy emitters. In this article, we report on the first experimental observation of this effect. We implement the protocol on a solid-state emitter and reduce its inhomogeneously broadened optical linewidth close to the lifetime limit. By detuning the excitation laser, we are able to concentrate approximately half of the absorption to a freely selectable target frequency. Our approach is solely based on properties of coherently evolving quantum systems, rendering it applicable to a wide range of individual and ensembles of quantum emitters.

We present a new software package for efficient quantum circuit generation, designed to achieve optimal runtime performance. Despite being in an early stage of development, our implementation demonstrates significant advantages over existing tools. Using the quantum Fourier transform (QFT) as a benchmark, we show that our backend can generate circuits for systems with up to 2000 qubits faster than widely used frameworks such as Qiskit and Q#. This improvement is particularly relevant for applications where classical preprocessing time, including circuit generation, must be minimized to not diminish any potential quantum advantage - for example, in combinatorial optimization tasks. Additionally, our software provides high-level primitives for bit- and integer-level manipulations, offering a simplified interface for integration with high-level quantum programming languages.

We establish a relation between the exponential decay rates of quantum Markov semigroups with respect to different inner products. More precisely, it was conjectured by Fagnola, Poletti, Sasso and Umanità that for a Gaussian quantum Markov semigroup, the exponential decay rate with respect to the KMS inner product is bounded below by the exponential decay rate for the GNS inner product. We show that this is indeed the case and not limited to Gaussian quantum Markov semigroups, but holds for quantum Markov semigroups with a faithful normal invariant state on arbitrary von Neumann algebras. Additionally, the KMS inner product can be replaced by a whole class of inner products induced by operator monotone functions.

We propose a semiclassical framework for solving open quantum dynamics in driven-dissipative spin systems. Our method consists of generalized spin-wave approximations tailored to describing quantum trajectories unravelled from the master equation, and generically applies to regimes beyond the reach of conventional spin-wave theories, including short-range interactions and local quantum jumps, enabling the efficient simulation of large-scale interacting spins. We illustrate the versatility of our framework by studying a variable-range driven-dissipative Ising model on a 2D lattice. When the dissipation acts along the drive axis, we find a continuous phase transition breaking the $\mathbb{Z}_2$ symmetry, and demonstrate that the interaction range, when tuned from fully-connected to nearest-neighbour, profoundly alters the universality class of the criticality. With the dissipation along the interaction axis, we show the emergence of a first-order transition. Demonstrated with both state-diffusion and quantum-jump types of trajectory dynamics, our framework provides a powerful toolbox for the efficient semiclassical description of non-equilibrium dynamics and many-body phases in spin systems.

We construct mode-selective effective models describing the interaction of the quantum plasmon-polariton field supported by a finite dielectric medium and one or several quantum emitters. The construction of the effective model is based on the decomposition of the field into bright modes relevant to the interaction with the emitters and dark modes, which do not interact with the emitters. We show that the quantum plasmon-polariton field can be represented equivalently by a double-continuum spectrum or by a single hybrid continuum spectrum for each emitter. The system of the electromagnetic field coupled to a finite medium is composed of two families of continuum modes, each of them with an infinite degeneracy. The two families are deformations of the free electromagnetic field and the free medium, induced by the interaction between them, as described by the Lippmann-Schwinger equations. We show that if there are $N$ emitters interacting with this plasmon-polariton field, the effective interaction involves a much smaller set of bosonic continuum modes: the interacting part of the continuum can be described by $N$ non-degenerate one-dimensional continua, one for each emitter. The representation of the interaction in terms of a single hybrid continuum spectrum coincides with the one within the macroscopic Langevin model with bulk medium. This coincidence is explained by an exact compensation of two terms, one in the coupling term of the Hamiltonian and the other one in a Green tensor identity.

We characterize nonequilibrium phases in long-range dissipative spin systems through the statistical properties of quantum jump trajectories. While the average dynamics governed by the Lindblad master equation provides access to steady-state expectation values of order parameters, the quantum trajectory framework reveals features encoded in the spatial and temporal correlations of detection events. Focusing on a model exhibiting a paramagnetic-to-ferromagnetic phase transition, we investigate the full counting statistics of quantum jumps using a tilted Lindbladian approach. We combine this with cluster mean-field and cumulant expansion techniques, which allow us to capture, respectively, the short- and long-range structure of jump correlations. In addition, we study the waiting-time distributions of detection events. We show that quantum jump correlations display clear signatures of the underlying phases and reveal distinct dynamical features across the transition. Our results highlight the potential of trajectory-resolved observables as probes of collective behavior in open quantum many-body systems and provide new insights into the role of long-range interactions in shaping nonequilibrium dynamics.

The generalized second laws of quantum thermodynamics are usually formulated in terms of Rényi divergences and the associated family of generalized free energies. In catalytic thermal transformations, this framework typically certifies the existence of a suitable catalyst but does not make the catalytic contribution explicit in the resulting system-level inequalities. Here we develop a complementary formulation based on non-additive divergences, whose pseudo-additive structure yields a family of generalized free energies with an explicit catalyst-dependent correction term. For uncorrelated catalytic thermal transformations, we show that this leads to non-additive second-law relations that make the catalytic contribution explicit and provide nontrivial constraints on admissible catalysts when the catalyst is returned only approximately. We also analyze correlated catalytic thermal transformations and show, through explicit finite-dimensional examples, that reduced-state data are generally insufficient to characterize thermodynamic accessibility: the thermo-majorization behavior of the joint transformation can change while the system and catalyst marginals remain fixed, and even states with identical marginals and the same mutual information can exhibit different thermo-majorization accessibility. Our results show that non-additivity can be thermodynamically informative in uncorrelated catalysis, whereas correlated catalysis generally requires a genuinely joint-state-sensitive description beyond reduced-state monotones.

We investigate the reduced dynamics of two identical superconducting qubits capacitively coupled through a finite-length transmission line. Starting from circuit quantization, we derive a circuit Hamiltonian that naturally separates the line modes into even- and odd-parity sectors coupled to collective qubit operators. Depending on the hierarchy between the qubit frequency $ω_q$, the mode spacing $ω_{TL}$, and the coupling scale $ω_g$, the line acts either as a structured reservoir or as a discrete few-mode coupler. In the long-line continuum limit, each sector is described by a Drude--Lorentz spectral density and the dynamics is solved with the hierarchical equations of motion. Using the Breuer--Laine--Piilo measure, we identify the parameter region in which the reduced dynamics exhibits non-Markovian relaxation. In the short-line limit, the continuum description breaks down and the dynamics becomes respectively multimode or single-mode. This establishes a unified cQED picture of the dynamical regimes of finite-length transmission lines in superconducting-circuit architectures.

Closed-loop superconducting-qubit calibration has matured into DAG-orchestrated protocol chains, yet published frameworks treat the bath via a Markovian master equation or a phenomenological likelihood, absorbing bath structure into fit residuals instead of reporting it as a diagnostic. We integrate a QuTiP 5.x hierarchical-equations-of-motion (HEOM) solver driven by a Tier-1 1/f Burkard bath into a multi-protocol calibration DAG (Rabi -> {Ramsey || T1}) and benchmark it against sesolve and mesolve on a frozen platform in a pulse-level simulator (no hardware validation). The Ramsey channel carries the headline: the Markovian fit is censored by its exponential-family numerical ceiling, while HEOM recovers a physical revival envelope whose primary T2* separates from the Markovian reference by at least 13x at 95% independent-bootstrap confidence within the HEOM-feasible budget; the point-estimate ratio reaches >=28x on the 50-point primary-t1 grid and ~72x on the 30-point biexp-family tau_aw pivot at L=5. Rabi contrast falls 2.17% below mesolve on a noise-limited 30-point grid; the paired-bootstrap CI crosses zero, so this channel corroborates rather than independently establishes the non-Markovian signature. T1 decay shape matches across backends (beta=1.000), yet HEOM's initial occupation drops from 1.000 to 0.879 -- a bath-dressed contamination stable under a 16-point densification. The DAG adds 9.62 us average per-protocol scheduling overhead, no meaningful latency penalty at protocol granularity. HEOM-in-loop thereby changes what calibration reports: bath structure appears as a quantifiable residual rather than a hidden confound.

High-precision optical phase stabilization in quantum networks is fundamentally constrained by the strict photon-flux and duty-cycle limits required to avoid disturbing fragile quantum states. This challenge becomes especially critical when coordinating multiple independent light sources for multi-step quantum protocols. Here, we develop an integrated phase-stabilization framework that incorporates a Bayesian phase estimator to optimally extract information from sparse single-photon detection events. This approach outperforms conventional maximum-likelihood estimation and achieves the shot-noise limit under minimal photon flux. The framework enables real-time correction of combined phase noise from both nodal lasers and transmission fibers, facilitating a two-step excitation protocol for heralded entanglement generation between separate trapped-ion nodes via single-photon interference. Operating with a detected photon rate of approximately 1 MHz and a duty cycle less than or equal to 6.5%, the system maintains interferometric visibility greater than 97% over fiber links of 10 km and 100 km. This phase control yields deterministic ion-ion entanglement with parity contrast exceeding 85% at both distances, enabling device-independent quantum key distribution. Moreover, the resulting memory-memory entanglement at 10 km survives beyond the average time required to establish it -- a fundamental requirement for quantum repeaters. This work establishes a robust and scalable foundation for practical long-distance quantum networks.

We show in this article the improvements which can be obtained in the description of the luminescence properties of Pr3+ doped materials by using an extension of the Judd-Ofelt theory in order to relax some strong selection rules and approximations of the standard formalism and to better account for the influence of the 4f5d excited electronic configuration. The demonstration is made by re-examining the case of Pr3+:YAG, a well known luminescent and laser crystal with a very low energy 4f5d absorption band. Our extension thus provides a better agreement between calculated and measured absorption intensities, especially for the hypersensitive 3 H4 $\rightarrow$ 3 P2 transition. A comparison is made with the results obtained in the case of Pr3+:ZBLAN, a laser fluoride glass with much higher 4f5d absorption levels. Our investigation also gives the opportunity, in the case of Pr3+:YAG, to provide more complete and more reliable absorption and emission data than reported in the past literature and to exploit these data to better address the question of laser operation at various emission wavelengths. It is thus demonstrated that laser operation should be possible with improved laser performance at 488 nm, 616 nm and 744 nm, as it was already achieved in the past, but also at 566 nm and 931 nm by using appropriate laser cavities and laser mirrors.

We consider two-dimensional harmonic oscillator in the complex Bargmann-Fock-Segal representation with $T^*{\mathbb R}^{2}={\mathbb C}^2$ as classical phase space. We show that the eigenfunctions $ψ_n$ of the quantum Hamiltonian correspond to complex radial coordinates in the reduced phase space ${\mathbb C}^2/{\mathbb Z}_n\subset{\mathbb C}^2$. They describe ${\mathbb Z}_n$-invariant motion of particle along a circle $S^1$ in lens space $S^3/{\mathbb Z}_n\subset{\mathbb C}^2/{\mathbb Z}_n$, where ${\mathbb Z}_n$ is the cyclic group of rotation by an angle $2π/n$ on the circle $S^1$, $n=1,2,...\,$. Thus the general solution of the Schrödinger equation carries information about an infinite number of admissible classical states $ψ_n$ that can be mapped to other states after lifting into the quantum bundle. We show that in the Kepler/hydrogen atom problem there is a similar correspondence between classical and quantum states.

Several approximation procedures, such as the full or partial rotating-wave, time-averaging, and geometric-arithmetic approximations, have been proposed to derive Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) generators from the Born-Markov quantum master equation (e.g., the Redfield equation). Establishing rigorous error bounds for these approximations is of fundamental and practical importance. However, existing bounds face two major limitations: they are highly specific to individual methods, and, more critically, they diverge in the long-time limit, ensuring the accuracy of the derived GKSL generator only in short-time regimes. In this Letter, we resolve both issues by deriving a unified, rigorous error bound for a general class of approximation methods -- termed temporal coarse graining -- that encompasses all aforementioned schemes. Crucially, our error bound is time-uniform. This guarantees that GKSL generators obtained via temporal coarse graining remain accurate for arbitrarily long times, provided the dissipation timescale is significantly longer than the bath correlation timescale.

We investigate optimized vertical ion-shuttling protocols for trapped-ion applications across a range of ion-trap experiments, including three-dimensional gradient-measurement sensors, on-chip ion fluorescence collection and imaging, improved laser accessibility, and quantum information processing. In this work, we focus on minimizing motional energy gain during ion transport. Our findings indicate that anomalous heating becomes the dominant limiting factor only for shuttling durations exceeding $500~μ\mathrm{s}$, whereas the final motional excitation is strongly dependent on the selected transport protocol. Using a recently measured heating rate of $(3.1 \pm 0.35)$ quanta/ms at an ion--surface separation of $134 \pm 1.5~μ\mathrm{m}$, we demonstrate that the motional excitation can be restricted to fewer than eight quanta when the ion is vertically displaced by $86~μ\mathrm{m}$ from its initial position. These results enable adiabatic shuttling within $0.5~\mathrm{ms}$, thereby meeting the operational requirements for high-fidelity quantum sensing and coherent control.

We prove an exact quantum conservation law for a harmonic oscillator coupled to a ghost degree of freedom: a second classical conserved quantity lifts to a quantum operator that commutes with the Hamiltonian with no hbar corrections, yielding a rigorous, state-independent upper bound on the mean squared phase-space radius for all time and every quantum state with finite initial second moments. The proof uses only canonical commutation relations and the Leibniz rule; it requires no confining potential, no spectral assumptions, and no perturbative expansion. The interaction studied here is bounded and vanishes at large separations, the generic situation in effective field theory, yet this suffices to guarantee quantum stability in the sense of bounded second moments. Three independent numerical frameworks (Heisenberg picture, Schrodinger picture, and Fock-space diagonalization) confirm wavepacket confinement below the analytic bound, a real energy spectrum, and Poisson level statistics numerically consistent with an integrable structure. The absence of a confining potential means the proof is silent on spectral discreteness and the existence of a ground state; those questions, addressed for polynomial confining interactions in concurrent work, remain open for the interaction class studied here and represent the sharpest targets for future work. Ghost quantum instability is therefore not an inevitable consequence of a wrong-sign kinetic term but depends critically on the interaction structure.

Magnetic quantum sensors based on trapped ions utilize properties of quantum mechanics which have optimized precision and beat current limits in sensor technology. Trapped ions are highly sensitive in a large span of signal ranging from DC or static B-field to the radiofrequency range in 100s of MHz and can attain the sensitivity in the range of pT to sub pT . They are tuneable to frequencies of interest and can be used as a lock-in frequency detector. This modelling and simulation based study presents an innovative design of Surface Paul Traps, enabling the use of trapped ions as ultra-sensitive sensors for magnetic field detection and precise measurement of magnetic field gradients at a sub-millimeter spatial resolution. The novel design features multiple trapping regions, allowing for the mapping of magnetic fields across various ion-trapping zones. The study demonstrates groundbreaking advancements in ion manipulation and confinement through innovative chip architecture.

In quantum estimation for a $d$-parameter family of density operators on a finite-dimensional Hilbert space $\mathcal{H}$, an estimator is specified by a pair $\left(M,\hatθ\right)$, where $M$ is a POVM with a finite outcome set $Ω$ and $\hatθ:Ω\to\mathbb{R}^{d}$ is a classical estimator map. Since the number of outcomes $\left|Ω\right|$ is a priori unbounded, the space of admissible POVMs is vast, which makes the search for optimal estimators difficult. In this paper, for the minimization of the weighted trace of the mean squared error among locally unbiased estimators, we prove that it suffices to consider POVMs with at most $\left({\rm dim}\,\mathcal{H}\right)^{2}+d(d+1)/2-1$ outcomes, and that an optimal measurement can be chosen to be rank-one. For the minimization of the average weighted trace of the mean squared error in Bayesian estimation, we show that it suffices to consider POVMs with at most $\left( {\rm dim}\, \mathcal{H}\right)^{2}$outcomes, and again an optimal POVM can be taken to be rank-one. Furthermore, when the model admits a real sufficient subalgebra, we show that the $\left( {\rm dim}\, \mathcal{H} \right)^{2}$ term in the above support-size bounds can be reduced in both the locally unbiased and Bayesian settings. These bounds substantially reduce the search space for optimal measurements and justify restricting numerical optimization to rank-one POVMs with finitely many outcomes.

The quantum Mpemba effect (ME) in Markovian systems is conventionally explained by a smaller overlap between the initial state and the slowest decay mode (SDM). Such state, initially farther away from equilibrium or steady state, relaxes faster than closer ones, resulting to a crossing of their trajectories. This picture, by neglecting the transient dynamics, holds in the long-time limit. Here we experimentally observe multiple trajectory crossings (multi-ME) in the relaxation dynamics of a trapped ion. Such novel dynamics takes place in a unusual scenario where the initial state instead has a larger overlap with the SDM. We develop a theoretical framework based on relaxation speed to understand the multi-ME. We show that the initial relaxation speed is governed by the fastest decay mode, which together with the SDM overlap gives a phase diagram that reveals both the occurrence and the types of quantum ME observed in our experiment. Our study goes beyond the simple picture based on the long-time limit, tracks continuously the quantum ME dynamics, and establishes a comprehensive framework to describe the transient quantum relaxation.

We revisit the quantization of the order parameter, which we refer to as third quantization, from the perspective of the commutation relation between the phase operator of the order parameter and the particle-number operator. We show that this macroscopic commutation relation does not constitute an independent fundamental postulate added to quantum mechanics, but instead emerges naturally from second quantization in the thermodynamic limit for both bosonic and fermionic many-body systems. In this sense, both Bose-Einstein condensates (BECs) and Bardeen-Cooper-Schrieffer (BCS) states can be understood as macroscopic quantum states described by bosonic coherent states: in BEC, bosons condense into a single coherent mode with a well-defined phase, while in BCS systems, collective excitations of Cooper pairs can also acquire an effectively bosonic coherent description. On this basis, we propose a new macroscopic interpretation of the BCS-BEC crossover. To characterize this crossover, we model a conventional superconductor as an assembly of macroscopically separated superconducting segments. As the intra-segment coupling increases, the system evolves from a BCS-like regime toward a BEC-like regime, in which the segments collectively behave as macroscopic coherent states. Inter-segment tunneling then locks their phases, establishes global phase coherence, and gives rise to a bulk Bose-Einstein condensate. The phase diagram of the BCS-BEC crossover can thus be understood as a manifestation of a macroscopic quantum process governed by the coherent-state dynamics of the order parameter. Our results provide a unified perspective on BEC, BCS superconductivity, and the BCS-BEC crossover within the framework of third quantization.

We study the ground-state phase diagram of a spin-1 Heisenberg chain with staggered long-range (LR) interactions decaying as $\propto r^{-α}$ using a quantum Monte Carlo approach based on the split-spin representation. This formulation enables efficient large-scale simulations by mapping the spin-1 model onto spin-$1/2$ degrees of freedom with local projection constraints. We resolve the continuous quantum phase transition between the gapped Haldane phase at large $α$ (short-range regime) and a gapless antiferromagnetically ordered Néel phase at small $α$ (LR regime), where the continuous SU(2) symmetry is broken. From finite-size scaling and crossing point analyses, we determine the critical point to be at $α_c = 2.48(2)$ and extract the associated critical exponents, which indicate unconventional criticality. In particular, the transition is found to be nonconformal, characterized by a dynamic exponent $z \neq 1$. We further analyze the scaling of entanglement entropy and bipartite fluctuations across the transition, and determine the corresponding universal scalings in both phases and at criticality.

Measurement-induced phase transitions (MIPTs) in monitored quantum systems are typically diagnosed using entanglement-based measures. Here, we develop a complementary thermodynamic perspective based on the arrow of time (AoT), which arises from the intrinsic irreversibility of the quantum measurements driving these transitions. We study the AoT - defined as the logarithmic ratio of forward and backward trajectory probabilities - across a family of models exhibiting MIPTs. We find that, like entanglement entropy, the AoT is a nonlinear functional of the averaged density matrix; however, in contrast to entanglement, it is associated with a local operator. To determine whether the AoT exhibits critical behavior, we formulate and exactly solve a model of a random quantum circuit with non-projective measurements. This allows us to analytically demonstrate that the AoT displays nonanalytic behavior and identify its critical exponent. Our results establish the AoT as a novel diagnostic for phase transitions in monitored quantum systems.

We present a method for learning quantum hardware noise from a measurement distribution of a single device experiment. Each noise channel is represented by automatically differentiable Kraus operators obtained from a Stinespring-based parameterization that is completely positive and trace preserving by construction, and circuits are simulated with a matrix product density operator forward model. Independent channels are attached to each native gate type, to each nearest-neighbor crosstalk interaction, and to state preparation and measurement, and all channels are optimized end-to-end against a distance between the simulated and observed measurement distributions. On ibm_fez, a Heron-generation superconducting processor, training on a ripple-carry adder circuit reproduces the device output distribution, and the same learned parameters, applied without retraining, also track the device distribution of an unrelated multiplier circuit, indicating that the method captures intrinsic device characteristics rather than overfitting to the training circuit. A systematic evaluation across a range of benchmark circuits confirms that this generalization is consistent. We further use the learned model to perform an offline feasibility assessment of the quantum approximate optimization algorithm with an error detection scheme, demonstrating the kind of noise-aware prediction the framework is designed to enable.

When a quantum electronic device is coupled to an electrical resonator, admittance changes of the quantum subsystem may be detected. The effective reactance may include capacitive and inductive terms that incorporate geometric, quantum, and tunneling components; while the effective resistance may be composed of Sisyphus and Hermes terms linked to relaxation and decoherence, respectively. Such reflectometry is usually studied when all characteristic times of the quantum system are much shorter than the resonator's period, in which case only stationary quantum states are probed. We present a rigorous description of a driven-dissipative qudit-resonator system. Our approach demonstrates how to strictly introduce quantum and tunneling capacitances as well as Hermes and Sisyphus resistances, and how these values are modified when the dynamics of the subsystems becomes mutually dependent. We present the cases of a Cooper-pair box, a single-Cooper-pair transistor, a double quantum dot, and a single-electron box. Our approach can be applied to describe any quantum system coupled to any classical resonator.

We develop a path integral representation for the dynamics of quantum systems with a finite-dimensional Hilbert space, formulated entirely within a discrete phase space. Starting from the discrete Wigner function defined on $\mathbb{Z}_d \times \mathbb{Z}_d$ (with $d$ an odd prime), and the associated Weyl transform built from generalized displacement operators, we derive an exact evolution kernel that propagates the discrete Wigner function in time. By exploiting the composition law of the kernel and iterating the short-time approximation, we obtain a sum-over-paths expression for the propagator weighted by a discrete phase-space action that is the natural finite-dimensional counterpart of Marinov's functional. For Hamiltonians linear in the phase-space coordinates, we show that the fluctuation sum factorizes and, at times strictly commensurate with the lattice (the Clifford-covariant regime), collapses to a deterministic shift realizing the discrete analog of classical Hamiltonian flow. The formulation is applied to a single qutrit ($d=3$) under a diagonal Hamiltonian, and to two interacting qutrits, where we show explicitly that the full entanglement dynamics -- captured by a closed-form expression for the linear entropy valid for all times -- requires the coherent contribution of all fluctuation sectors of the action. The $\tildeμ= 0$ sector alone is non-real at finite time step and collapses to a trivial (uniform) kernel in the continuum limit, failing to reproduce the entanglement dynamics in either regime. We discuss the relevance of this construction for semiclassical simulation of many-body spin systems and the characterization of non-classicality through Wigner negativity.

The eigenstates of two test-masses (where each test-mass is placed inside of a harmonic trap) separated by a distance, can get entangled where gravity acts as the mediator of entanglement and it has been argued in \href{https://doi.org/10.48550/arXiv.2511.07348}{arXiv:2511.07348 [quant-ph]} that this entanglement of masses cannot be generated without the underlying quantum nature of gravity. In this work, we consider two non-relativistic Bose-Einstein condensates (formed inside of harmonic trap potentials with identical trapping frequencies) separated by a distance. We take a linearized quantum gravity model and investigate the generation of entanglement while gravitons serve as the mediator of entanglement. The entanglement is generated between the phonon modes of the two condensates, and we observe that for very low separation distance, the entanglement generated is significantly higher than that observed for the quantum gravity induced entanglement of masses or QGEM protocol; however, the fall of entanglement is faster than the two-particle case for two separated Bose-Einstein condensates. We observe that when the number of particles in the condensate is increased, the degree of entanglement for a smaller separation distance becomes substantially higher compared to the case discussed in \href{https://doi.org/10.1103/PhysRevD.105.106028}{Phys. Rev. D 105 (2022) 106028}, which allows for a more robust experimental proposal using this quantum gravity induced entanglement of phonons or QGEP protocol.

The main claim of arXiv:2206.08467 is that "functional (deterministic) no-signalling resources can be stronger than probabilistic ones" a certain nonlocal game on a Bell scenario with countably many parties. We disagree and argue that (i) under standard definitions, deterministic no-signalling resources are always probabilistic no-signalling resources; (ii) the deterministic strategy considered in arXiv:2206.08467 can be promoted to a genuinely probabilistic strategy with similar properties and (iii) a key step in the derivation in arXiv:2206.08467, claimed to hold for all no-signalling strategies, implicitly assumes measurability, leaving a gap in the argument. We propose measurability assumptions which we conjecture would make this derivation rigorous. Taken together, the phenomenon highlighted in arXiv:2206.08467 is best understood as a difference between measurable and non-measurable no-signalling resources.

We present a complete analysis of the angular momentum selection rules and electromagnetic backgrounds that constrain any spectroscopic search for the gravitomagnetic spin-quadrupole coupling in highly charged ions. A sequence of four barriers is identified: (i)~the Wigner-Eckart theorem mandates $j \geq 3/2$ electronic states for sensitivity to the rank-2 gravitomagnetic operator, excluding the deformation-immune $j=1/2$ states; (ii)~the nuclear electric quadrupole hyperfine interaction (HFS-E2) generates an $\sim 18$-orders-of-magnitude electromagnetic background in the required $j=3/2$ channel; (iii)~second-order HFS mixing between fine-structure levels leaves a residual $\sim 10^{-6}$ eV even after centroid extraction; (iv)~tensor nuclear polarizability (TNP), scaling with $B(E2)$ rather than $Q_s$, introduces an independent rank-2 background of $\sim 10^{-12}$ eV. We derive the algebraic conditions under which a multi-isotope, multi-transition Generalized King Plot can separate these backgrounds from the gravitational signal, and show that the minimum experimental topology requires three transitions and $N_{\text{odd}} \geq N_{\text{bkg}} + 1$ odd-spin isotopes with linearly independent nuclear parameters. For the molybdenum chain, this yields a first laboratory-derivable bound $|χ- 1| \lesssim 10^{8} - 10^9$ on the gyrogravitational ratio, limited by current precision on nuclear quadrupole moments and transition rates. We quantify the experimental milestones needed to improve this bound by each order of magnitude, providing a roadmap for future searches.

Sampling problems are promising candidates for demonstrating quantum advantage, and one approach known as quantum-enhanced Markov chain Monte Carlo [Layden, D. et al., Nature 619, 282-287 (2023)] uses quantum samples as a proposal distribution to accelerate convergence to a target distribution. On the other hand, many practical problems are large-scale and constrained, making it difficult to construct efficient proposal distributions in classical methods and slowing down MCMC mixing. In this work, we propose a divide-and-conquer neural network surrogate framework for quantum sampling to accelerate MCMC under fixed Hamming weight constraints. Our method divides the interaction graph for an Ising problem into subgraphs, generates samples using QAOA for those subproblems with an XY mixer, and trains neural network surrogates conditioned on the Hamming weight to provide proposal distributions for each subset while preserving the constraint. In numerical experiments of Boltzmann sampling on 3-regular graphs, our method consistently accelerated mixing as the system size $N$ increased, with average improvements in the autocorrelation decay rate constant by speedup factors of about $20.3$ and $7.6$ over classical pair-flip methods based on nearest-neighbor and non-nearest-neighbor exchanges, respectively. We also applied the method to an MNIST feature mask optimization problem with $N=784$, obtaining faster energy convergence and a $2.03\%$ higher classification accuracy. These results show that our method enables efficient and scalable MCMC and can outperform classical methods for practical applications on NISQ devices.

While the $^{229}$Th nuclear isomer has recently been observed and laser-excited, converting optical nuclear manipulation into a chip-scale solid-state frequency standard remains an open challenge. Here, we present a nanophotonic platform to realize an all-solid-state nuclear clock based on the low-energy isomeric transition of $^{229}$Th embedded in high-$Q$ fluoride photonic resonators. By coupling ensembles of thorium nuclei to confined optical modes, we show that resonant field build-up in the cavity can substantially enhance the nuclear excitation rate, enabling optical interrogation at practical laser intensities. We model the nuclei-photon interaction dynamics and outline a technological roadmap toward addressing this challenge, including resonator fabrication in fluoride crystals, thorium implantation, nuclear excitation with integrated lasers, and on-chip detection of vacuum-ultraviolet photons. As an initial proof of concept, we implant a crystalline fluoride whispering-gallery-mode resonator with $^{229}$Th and assess the impact of implantation-induced damage on resonator performance. Our platform leverages recent advances in materials integration and nanophotonics to chart a realistic route toward compact and scalable nuclear frequency standards.

Ultrafast strong-field laser--plasma physics is shown to offer a promising framework for relativistic nonlinear quantum electrodynamics (QED). As one of its key advantages, this approach to relativistic nonlinear QED does not require an external beam of relativistic particles. Instead, high-energy electrons are produced in this setting as a part of ultrafast strong-field laser--plasma interactions. An intense ultrashort laser pulse generates and accelerates dense electron bunches to relativistic energies, giving rise to photon-pair emission confined to the nanometer scale in space and the attosecond scale in time. As a lowest-order nonlinear QED process, relativistic electrons in laser-driven plasmas are shown to give rise to attosecond bursts of two-photon emission, providing an ultrabroadband source of correlated photon pairs. As a physically insightful estimate, the rate of this two-photon emission is expressed via a product $ α^2 γω_{turn}$, where $α$ is the fine-structure constant, $γ$ is the Lorentz factor, and $ ω_{turn}$ is the local relativistic curvature frequency. Photon pairs with strongest correlations, providing a resource for photon entanglement, are emitted at a much lower rate, estimated as $ α^2 γ^2 ω_{turn} E_{\perp} /E_S$, where $E_{\perp}$ is the laser electromagnetic field, determining the transverse Lorentz force, and $E_S$ is the Schwinger critical field. Our study offers a clear guidance on how quantum aspects of laser-driven relativistic plasma electrodynamics can be isolated from their classical counterparts, enabling a physically justifiable approach to the analysis of nonlinear QED phenomena in complex laser--plasma interactions driven by ultrashort high-intensity laser pulses.

Consider two parties who want to agree on a common frequency band for communication in the presence of independent jammers. Such jammers block a different subset of bands at each site, where each party can observe only its own set of unjammed bands. Yet, they must agree on a common band without communicating. We first establish the optimal classical strategy, maximizing the probability they output a common frequency band in a single shot. We proceed to show that sharing an entangled pair of local dimension d allows the parties to coordinate strictly better, provided both the number of safe bands d and the spectrum size n are sufficiently large. We study explicit quantum strategies offering a pathway to near-term demonstrations, including an explicit strategy for d = 2 that outperforms the classical optimum for all spectrum sizes, achieving a 5.4% advantage asymptotically (in n) with just one shared Bell pair. Our approach is based on a general framework for constructing quantum strategies from classical spreading sequences via symmetric orthonormalization that may be of independent interest, and opens the door to concrete applications of quantum networks for cognitive radio and spread-spectrum communication.

Optimization problems become fundamentally challenging as the number of variables increases. Because the volume of the search space grows exponentially, classical algorithms frequently fail to locate the global minimum of non-convex functions. While quantum optimization offers a potential alternative, mapping continuous problems onto near-term quantum hardware introduces severe scaling limits and barren plateaus. To bridge this gap, we propose the Distributed Quantum-Enhanced Optimization (D-QEO) framework. Instead of forcing the quantum processor to find the exact minimum, we use it simply as a topographical preconditioner. The QPU maps the landscape to locate the most promising basin of attraction, generating high-quality seed points for a classical GPU-accelerated solver to refine. To make this approach viable for utility-scale problems, we exploit the mathematical structure of separable functions. This allows us to cut a 50-qubit (i.e., $2^{50}$) global search space into independent and manageable sub-spaces using 5-qubit subcircuits. By executing these fragments concurrently with CUDA-Q, we completely bypass the overhead of cross-register entanglement and classical tensor knitting for separable functions. Benchmarks on the 10-dimensional Rastrigin and Ackley functions show that D-QEO prevents the exponential failure rates observed in purely classical algorithms. Furthermore, this quantum warm-start significantly reduces the number of classical BFGS iterations required to converge, providing a highly practical blueprint for utilizing near-term quantum resources in complex global search.

We propose a unified framework, dubbed topological word, for the complete non-Abelian bulk-boundary correspondence in multigap non-Abelian topological insulators. Composed by an ordered sequence of letters, each a non-Abelian charge depicting the gap-resolved topology, the topological word captures both the global non-Abelian topology corresponding to the homotopy classification, and the band-adjacency information. The latter, though crucial for the edge-state pattern across multiple gaps, is often overlooked in previous studies. We confirm our framework using both static models and periodically driven Floquet systems, and discuss its connection and distinction with existing descriptions, such as the phase-band singularities and braiding representations. Intriguingly, topological word continues to provide insight regarding topology and edge states, even as the global non-Abelian topology becomes ill-defined under broken parity-time symmetry.

Interconnecting heterogeneous quantum systems is an important step toward realizing the quantum internet. We propose a quantum network hub that interfaces local quantum devices with dense wavelength-division multiplexing (DWDM) networks in the telecom band via quantum frequency conversion (QFC) with frequency-channel selectivity. We show that standard periodically poled lithium niobate waveguides used for QFC exhibit a dispersion sweet spot, for example around the 780 nm band, enabling wide tunability of the pump wavelength while maintaining phase matching. Experimentally, we demonstrate the network hub by implementing a channel-selective and polarization-insensitive QFC from 780 nm to telecom wavelengths around 1540 nm. We achieve a pump tuning range of 2 THz and successfully distribute polarization-encoded single photons into 16 frequency channels on the ITU-T DWDM grid with 25 GHz channel spacing, while preserving the quantum information. These results position the QFC-based hub as a versatile backbone for connecting a wide range of quantum devices, spanning both photonic and matter-based systems, across frequency-multiplexed telecom networks.

In closed quantum systems, Krylov complexity admits a geometric description; operator growth is equivalent to Hamiltonian flow in an emergent phase space whose structure is fixed by the Lanczos coefficients. We show that this picture survives, albeit in a fundamentally altered form, once the system is coupled to an environment.Using a Schwinger-Keldysh formulation of the full counting statistics of the Krylov position, we derive an effective action for operator growth under Lindblad dynamics. Even for the minimal case of dephasing, the phase-space dynamics ceases to be Hamiltonian; environmental coupling generates diffusion in the variable conjugate to Krylov depth, converting deterministic trajectories in to stochastic ones. The hyperbolic mechanism underlying exponential complexity growth is therefore broadened and, beyond a parametrically controlled scale, destroyed.This identifies dissipation as a relevant perturbation of the chaotic Krylov fixed point and reveals operator growth in open systems as a problem of stochastic dynamics in an emergent phase space.

We present a theoretical study of the two-particle spectrum $ω(K)$ for the chiral waveguide QED setup of an array of two-level atoms directionally interacting with photons propagating along the waveguide. We demonstrate that for each pair center-of-mass momentum $K$ there exist distinct solutions with $\Imω\le 0$ in the two-particle spectrum, corresponding to bound, antibound and resonance states, in addition to the continuum of scattering states. Contrary to previous studies, which showed the bound and resonance-state spectra only over a limited range of $K$, the calculated spectrum is consistent across all $K$ values. An interesting finding is that the real part of the spectrum $\Re ω(K)$ in the chiral model is gapless.

Many real-world problems are naturally formulated as higher-order optimization (HUBO) tasks involving dense, multi-variable interactions, which are challenging to solve with classical methods. Quantum optimization offers a promising route, but hardware constraints and limitations to quadratic formulations have hampered their practicality. Here, we develop a distributed quantum optimization framework (DQOF) for dense, large-scale HUBO problems. DQOF assigns quantum circuits a central role in directly capturing higher-order interactions, while high-performance computing orchestrates large-scale parallelism and coordination. A clustering strategy enables wide quantum circuits without increasing depth, allowing efficient execution on near-term quantum hardware. We demonstrate high-quality solutions for HUBOs up to 500 variables within 170 seconds, significantly outperforming conventional approaches in solution quality and scalability. Applied to optical metamaterial design, DQOF efficiently discovers high-performance structures and shows that higher-order interactions are important for practical optimization problems. These results establish DQOF as a practical and scalable computational paradigm for large-scale scientific optimization.

Device-independence is the gold standard of quantum cryptography. To meet this standard, a central assumption is that no information leakage occurs during protocol execution. We relax this assumption by analyzing CHSH-based randomness certification and key distribution with partial leakage of the inputs, modeled in terms of a noisy channel. Our results quantify the certifiable local randomness and the secret key rate as a function of the magnitude of the input leakage.

The fragility of quantum metrological advantages under loss remains a major barrier to practical quantum sensing. For a two-photon-driven (TPD) Kerr resonator (TPD-Kerr model) subject to unavoidable single-photon loss (SPL), both the quantum Fisher information gain and squeezing level exhibit hard-to-track long-lived damped oscillations, restricting useful sensing and squeezing to extremely short time windows. We show that adding engineered two-photon loss (ETPL) -- forming a TPD-Kerr-ETPL hybrid model -- significantly mitigates these oscillations and converts the decay into a smooth, monotonic drop. This extends the high-sensitivity windows by over an order of magnitude. Moreover, we reveal a temporal hierarchy of quantum resources: the initial boost in metrological sensitivity arises from Gaussian squeezing, while sustained high-precision sensing stems from dissipatively stabilized non-Gaussian even-parity cat states. Crucially, only in models that include ETPL -- such as the TPD-Kerr-ETPL and TPD-ETPL systems -- does the dynamics actively mitigate SPL's detrimental effects, transforming damped oscillation into a smooth, easily trackable trajectory and enabling a prolonged, usable metrological window. Our approach transcends encoding-based or feedback-controlled schemes, offering a fully autonomous route to high-precision measurement without real-time feedback control. This establishes a general design principle: engineered loss, combined with appropriate driving, can actively preserve metrologically useful non-Gaussian quantum resources even in the presence of SPL -- paving the way toward robust, scalable quantum sensors in superconducting circuits, optomechanics, and trapped-ion platforms.

We investigate the topology of the different phases of the extended Su-Schrieffer-Heeger (eSSH) model, which includes hopping processes between translationally inequivalent atoms beyond nearest neighbors. Exact analytical expressions for the edge states of a semi-infinite eSSH chain are derived, with wave functions that decay exponentially from the boundary with a unit-cell decay factor z. From the winding number of the bulk Hamiltonian under periodic boundary conditions, we determine the topological phase diagram and establish the bulk-boundary correspondence: changes in the winding number coincide with bulk gap closings and with the condition |z|=1 for the edge-state solutions. For finite chains, we further obtain analytical, approximate expressions for the low-energy edge states, which are shown to be highly accurate.

Quantum linear system solvers typically realize the inverse map as a polynomial transformation of the spectrum, so their practical cost hinges on implementing this transformation at a low polynomial degree. We introduce constrained optimal polynomials as a framework for this task, drawing on classical Krylov subspace theory. Within this framework, we develop three classes of polynomial solvers. Baseline quantum Chebyshev-type iterations provide general-purpose polynomials based on spectral bounds. Constrained Uniform Polynomial (CUP) solvers optimize the tradeoff between approximation accuracy and block encoding normalization under a uniform spectral model consistent with the available bounds. Constrained Adaptive Polynomial (CAP) solvers retain this structure but replace the uniform model with a probability measure reconstructed from spectral moments via a maximum entropy ansatz, where the moments are extracted from QSVT measurements. Numerical experiments under hardware and stochastic noise show that these methods achieve lower error than standard QSVT-based inversion at a comparable polynomial degree, up to an order of magnitude in noise-limited regimes. CUP offers robust performance under generic spectra, while CAP provides further improvement when the spectral structure can be exploited.

We study how strategic interaction can arise from controlled quantum dynamics rather than being imposed as an external mathematical structure. We introduce a class of interaction-defined quantum games in which players are represented by distinguishable quantum walkers, strategies correspond to local coin operations, and payoffs are defined as expectation values of physical observables. Using interacting discrete-time quantum walks as a concrete platform, we demonstrate numerically that competitive, cooperative, and asymmetric games admit stable stationary strategy profiles when the walkers are coupled, while no non-trivial equilibria exist in the absence of interaction. To clarify the game-theoretic structure, we derive an analytic perturbative decomposition of the payoff function in the weak-interaction regime, showing explicitly that strategic coupling originates from interaction-induced interference terms in the joint probability distribution. For a collision-based phase interaction, the payoff becomes non-separable at first order in the interaction strength and generically admits stationary points satisfying the Nash conditions. Our results provide a physically explicit realization of strategic interdependence in quantum transport processes and establish interacting quantum walks as a minimal platform for studying game-theoretic behavior emerging from unitary dynamics.

We study black-hole quasinormal modes by applying the complex scaling method (CSM) to the perturbation equations of Schwarzschild and Reissner--Nordström black holes. The method converts the outgoing-wave boundary condition into a non-Hermitian eigenvalue problem, allowing quasinormal-mode frequencies to be computed within a common spectral framework. We first benchmark the method for the Schwarzschild Regge--Wheeler equation and then extend it to the Reissner--Nordström family, including the extremal limit. Our results show that CSM provides a unified and flexible approach to the computation of black-hole quasinormal frequencies.

Accurate state-of-health (SOH) estimation for lithium-ion batteries remains a challenging problem due to complex electrochemical degradation mechanisms and long-range temporal dependencies. In this work, we propose a quantum-enhanced recurrent framework, termed QLSTM, in which variational quantum circuits are directly embedded into the gating mechanisms of long short-term memory networks. By replacing classical affine transformations with parameterized unitary operations, the proposed model introduces structured nonlinear transformations into the recurrent state-transition process. Extensive experiments on multiple benchmark battery datasets demonstrate that QLSTM consistently outperforms classical sequence models in both predictive accuracy and robustness, achieving significant reductions in mean absolute error (MAE), with improvements on the order of 20% compared with classical LSTM baselines. Ablation studies further confirm that these improvements arise primarily from quantum-enhanced gating rather than input-level transformations. Additional analyses on qubit scaling and noise robustness reveal that model performance is governed by a balance between expressive capacity and trainability. These results provide empirical evidence that embedding quantum computational primitives within recurrent architectures offers a structurally grounded approach to improving sequence modeling capability. The proposed framework establishes a new design paradigm for integrating quantum operators into temporal learning models, with potential applications in complex dynamical system prediction tasks.

We introduce a quantum analogue of a classical synchronizing automaton. In classical case the state of a system evolves according to a set of rules forming an alphabet, and sequences of these rules, called words, govern its evolution. Certain special words, known as synchronizing words, drive the automaton into a predetermined state regardless of its initial configuration. Although such an apparently irreversible process seems incompatible with the unitarity of quantum mechanics, we present a resetting protocol based on quantum synchronizing words by incorporating auxiliary qubits whose states encode the rules of the automaton's alphabet. These qubits interact with the quantum automaton, whose state is encoded in a qudit, via a global unitary operation. When the qubit register is initially prepared in a state corresponding to a synchronizing word, the automaton evolves into a predetermined pure state independent of its initial state, while the qubit register is transformed into a complex, often entangled, state that encodes information about the automaton's original configuration. The resulting entanglement depends on both the rule set and the automaton's initial state, and we show how specific entangled states can be generated within this framework.

We study an Ising model with long-range interactions undergoing a time-periodic kicking. For different initial states we observe persistent period doubling. When there is period doubling we find that the initial state has relevant overlap with Floquet states showing time-translation symmetry breaking, organized in doublets displaying $π$-spectral pairing (as highlighted by the $π$-spectral gap) and long-range order (as shown by the eigenvalues of the magnetization in the doublet). We observe period doubling for initial states with domain walls and tilted spins, and for the latter ones a finite-size scaling of the relevant $π$-shifted gap and magnetization eigenvalues suggests period-doubling oscillations persisting for larger system sizes and lasting a time exponential in the system size. We find that just a minority of Floquet states displays time-translation symmetry breaking while the rest is thermal, a weak-ergodicity breaking situation typical of systems with quantum scars. Although the time-translation symmetry breaking eigenstates are the minority, their number is exponential in the system size and this motivates the period doubling observed for many different initial states.

We investigate the effects of finite-range interatomic interactions on the equation of state (EoS) of a weakly interacting Bose gas. Within the Cornwall-Jackiw-Tomboulis effective action approach, we show that finite-range effects influence not only the EoS but also the thermodynamic properties of the system at zero temperature, leading to nonuniversal behavior.

Optimizing tensor networks with standard first-order methods often leads to slow convergence and entrapment in local minima. Although second-order optimization offers enhanced robustness, explicitly constructing the full Hessian matrix is computationally prohibitive for large-scale systems. In this work, we bypass this bottleneck by introducing an analytical Hessian-vector product kernel designed for arbitrary compositions of linear maps. This two-pass algorithm leverages recursive tangent-state propagation with a bounded virtual bond dimension to guarantee scalability. We demonstrate the practical utility of this kernel by integrating it into a Riemannian trust-region framework for quantum circuit compression. Evaluated on time-evolution circuits for various spin chains, our second-order approach achieves up to a four-order-of-magnitude improvement in fidelity over naive Trotterization, while delivering significantly smoother, faster convergence than conventional first-order methods such as Riemannian ADAM.

A two-qutrit extension of the quantum Rabi model is studied. Despite its increased complexity, the model results to be integrable under specific, physically relevant conditions. This feature allows for the emergence of analytically tractable subdynamics. In this framework, the ground-state phase diagram can be derived, and the analysis reveals critical phenomena linked to both level crossings and quantum phase transitions.

The present work focuses on the strong/weak interaction of many-body spin-systems with a cavity mode. It introduces the necessity of redefining the physical conditions determining the strong/weak coupling regime in those systems. In more complex systems, the effective coupling emerging from the collective dynamics may differ indeed from the actual coupling of each individual subsystem with the bosonic field. This is shown by highlighting some counter-intuitive dynamical effects properly related to the coupling regime: a Jaynes-Cummings dynamics emerging although a strong interaction is present. The universality of this result is demonstrated through the analysis of three distinct systems: a two-qubit, a two-qutrit, and an $N$-qubit chain quantum Rabi models.

We show that the construction of the linear interferometer in the Supplemental Material of arXiv:1909.09581 is flawed, leading to a generally suboptimal solution. We then provide the correct derivation of the optimal interferometric configuration that achieves the quantum Fisher information limit for imaging N weak incoherent emitters.

Efficient resource allocation and optical switching promise high key rates, network adaptability, and cost reduction in repeaterless quantum communication networks. However, identifying optimal switching configurations remains a significant challenge due to the combinatorial complexity. We introduce a novel graph formulation to model the physical and logical structure of repeaterless quantum networks, enabling the systematic optimization of switching strategies. The problem is posed as a linear program and solved using a column generation approach. This method enables scalable computation despite the exponential number of possible network configurations. Our results not only provide a formal foundation but also a practical algorithm for the optimization of switching. Empirical tests confirm the solver's scalability with network size, demonstrating the framework's effectiveness and laying the groundwork for future optimization of quantum network control.

We study a class of quantum dynamical maps for d-level systems that interpolate between positive, Schwarz, and completely positive evolutions. Our approach is based on a geometric analysis of the parameter space, which reveals the structure of regions corresponding to different positivity classes and their boundaries. We show that dynamical trajectories naturally move across these regions, providing a clear geometric interpretation of transitions between Markovian and non-Markovian regimes. It is shown that within presented class the evolution becomes eventually entanglement breaking. This analysis highlights the role of divisibility and eternally non-Markovian evolution.

The Traveling Salesman Problem is a classical NP-hard combinatorial optimization problem that has been extensively studied in operations research. A major challenge in Traveling Salesman Problem formulations is the large number of subtour elimination constraints required to ensure a valid tour. To address this issue, we adopt an iterative approach grounded in well-established operations research techniques, in which subtour elimination constraints are generated dynamically. In addition, we integrate a preprocessing phase to reduce the number of candidate arcs. In this work, we investigate both classical and quantum optimization approaches for solving the problem using the proposed framework. In particular, for quantum optimization we analyze quantum annealing techniques within the D-Wave framework, considering both direct quantum execution on the QPU and hybrid quantum classical solvers. Computational experiments show that the proposed strategies significantly reduce the model size and lead to positive improvements in computational performance across classical, direct quantum, and hybrid optimization approaches.

We introduce an operational criterion to identify Wigner function (WF) negativity for an arbitrary quantum state within the framework of quantum non-demolition measurements. This criterion corresponds to experimentally accessible schemes that enable a direct measurement of the WF, and establishes the coherent-state basis as a privileged basis for determining when the WF exhibits negative regions. We show that the absence (presence) of coherent superpositions in the coherent-state basis provides direct information about the positivity (negativity) of the WF. In particular, the absence of such superpositions constitutes a sufficient condition for WF positivity. Although a general proof of necessity remains elusive, we demonstrate that this condition is also necessary in two relevant cases: Schrödinger-cat states and higher-order cat states on a circle. More precisely, for Schrödinger-cat states we establish a necessary and sufficient condition for the positivity of the WF in full generality, whereas for high-order cat states on a circle we derive an analogous condition in the limit of a large number of densely packed coherent states.

We present an explicit quantum circuit construction for Hamiltonian simulation of a first-order velocity--stress formulation of the three-dimensional elastic wave equation in homogeneous isotropic media. Previous studies have shown how elastic wave equations can be cast into forms amenable to Hamiltonian simulation, but they typically rely on black box Hamiltonian access assumptions, making gate complexity estimation difficult. Starting from the first-order velocity--stress formulation, we discretize the system by finite differences, transform it into Schrödinger form, and exploit the separation between the component register and the spatial register to decompose the Hamiltonian into structured tensor product terms. This yields explicit implementations of first-order and second-order Trotter formulas for the resulting time evolution operator. We derive corresponding error bounds and constant sensitive qubit and CNOT complexity estimates in terms of the discretization parameter, simulation time, target accuracy, and material parameters. Numerical experiments validate the proposed framework through comparisons with the exact time evolution and reconstructed physical fields.

We adopt a two-dimensional tensor-network (TN) ansatz to simulate variational quantum algorithms on two-dimensional qubit architectures, demonstrating its capability to accurately simulate deep circuits through the Quantum Approximate Optimization Algorithm (QAOA) applied to Ising spin-glass problems on heavy-hexagonal and square lattices. For heavy-hexagonal problems with up to three-body interactions, parameters trained on small instances and transferred to systems an order of magnitude larger improve the sampled energy distribution only up to intermediate depths, indicating a fundamental limit of parameter concentration as a transfer strategy. By extending the training itself with TN simulations on larger system sizes, we avoid local minima and obtain lower-energy samples. Analyses of entanglement growth and importance sampling show that the simulation remains classically feasible with moderate bond dimension. We find that parameter concentration also persists on square lattices, albeit at substantially higher computational cost to perform reliable sampling. Overall, our TN framework not only provides an efficient and controlled framework for benchmarking variational quantum algorithms on two-dimensional lattices, but also serves as an effective surrogate model for training variational algorithms.

Quantum coherence is an important quantum resource which plays a pivotal role in the field of quantum information. Based on metric adjusted skew information, we define a measure of quantum uncertainty to study average coherence under conical 2-designs generalized equiangular measurements, and prove the equivalence of this measure to the scaled average coherence based on metric adjusted skew information under a set of unitary groups, operator orthonormal bases, and mutually unbiased bases. We also derive two trade-off relations by this measure and solve a conjecture. Furthermore, we give two entanglement criteria by this measure and conical 2-designs generalized equiangular measurement, respectively, and illustrate the effectiveness of them by explicit examples.

We initiate an investigation into a notion of state complexity for discrete-variable quantum systems. Specifically, we propose an information-theoretic quantifier for the complexity of quantum states within the stabilizer formalism of quantum computation. This is achieved by leveraging the symmetric Jordan product (associated with classicality) and the skew-symmetric Lie product (linked to quantumness) between the square root of the quantum state and the Heisenberg-Weyl displacement operators. We establish the fundamental properties of this quantifier and demonstrate that state complexity is closely related to the nonstabilizerness of quantum states via the $L^4$-norm of their characteristic functions.

Higher-order networks with multiway interactions can exhibit collective dynamical phenomena that are absent in traditional pairwise network models. However, analyzing such dynamics becomes computationally prohibitive as their state space grows combinatorially in the multiway interaction order. Here we develop quantum algorithms for two central tasks -- synchronization estimation and certification of the no-phase-locking regime -- in the simplicial Kuramoto model. This model is a higher-order generalization of the celebrated Kuramoto model for coupled oscillators on graph-based networks. Under explicit assumptions on data access and types, and simplicial structure, we derive end-to-end quantum gate complexities and identify regimes with polynomial quantum advantage for synchronization estimation and super-polynomial quantum advantage for no-phase-locking certification over classical methods. More broadly, these results extend quantum algorithms for higher-order networks from structural analysis to nonlinear dynamical diagnostics, easing a major computational bottleneck and opening a route to quantum methods for probing higher-order phenomena beyond the reach of direct classical approaches.

Continuous-variable (CV) quantum teleportation is usually benchmarked by average fidelity, but when the teleportation is repeatedly used within optical networks or measurement-based architectures, uniformity across the input ensemble becomes equally important. We analyze this issue using two complementary figures of merit: the average fidelity and the fidelity deviation, which quantifies the input dependence of the single-shot teleportation fidelity. We prove that any deterministic unity-gain teleportation channel that is displacement covariant has vanishing fidelity deviation for coherent-state benchmarking, irrespective of whether the shared entangled resource is Gaussian or non-Gaussian. Nonzero deviation therefore diagnoses covariance breaking rather than non-Gaussianity. We then show that when a protocol raises the average fidelity through input-selective conditioning, the deviation generically increases in tandem, giving a quantitative universality cost. As a concrete example, we study teleportation enhanced by the so-called measurement-based noiseless linear amplification, where a heralded filter acts on the Bell-measurement record. The resulting trade-off among average fidelity, fidelity deviation, and success probability shows that stronger filtering can improve the conditional fidelity only by concentrating the successful events in favored regions of phase space, thereby suppressing the success probability and reducing input uniformity. Our results provide an operational framework for distinguishing genuine channel improvement from selectivity-driven post-selected advantage and suggest that the probabilistic CV teleportation should be assessed with average quality, universality, and heralding rate treated on an equal footing.

Constrained combinatorial optimization problems are frequently reformulated as quadratic unconstrained binary optimization (QUBO) models in order to leverage emerging quantum optimization algorithms such as the Variational Quantum Eigensolver (VQE) and the Quantum Approximate Optimization Algorithm (QAOA). However, standard QUBO formulations enforce inequality constraints through slack variables and quadratic penalties, which can significantly increase the problem size and distort the optimization landscape. In this work, we propose a slack-free penalty formulation for constrained binary optimization that eliminates auxiliary slack variables and preserves the feasibility structure of the original problem. The proposed approach introduces a nonlinear custom penalty function to enforce inequality constraints directly in the objective function. To address the computational challenges associated with evaluating nonlinear penalties in variational quantum algorithms, we employ the finite-sampling method that avoids the exponential complexity required by exact expectation computation. Furthermore, we integrate the Conditional Value-at-Risk (CVaR) objective to improve optimization robustness and guide the search toward high-quality solutions. The proposed framework is evaluated on instances of the multi-dimensional knapsack problem, a classical benchmark in combinatorial optimization. We showcase that the proposed custom-penalty formulation combined with CVaR sampling achieves improved optimality gaps and more consistent performance compared with conventional slack-based QUBO formulations. The results suggest that careful penalty design can play a critical role in enabling quantum and hybrid quantum-classical algorithms for constrained optimization problems that arise in operations research.

We analyze the quantum dynamics of the fractional-time Jaynes-Cummings model using a recent unitary framework for the fractional-time Schrödinger equation. We examine how the fractional derivative order $α$ influences non-classical features under different initial conditions. For an initial Fock state, fractional evolution introduces transient dynamics and heightened sensitivity to coupling strength. Through an inverse problem approach, we interpret these effects as arising from an effective time-dependent coupling with a strong initial pulse. For an initial coherent state, the fractional order tunes the system between dynamical regimes, with a transition at $α= 0.50 $ where standard collapse-and-revival is replaced by stable, periodic evolution. This regime enhances non-classical field properties, including stronger sub-Poissonian statistics, periodic quadrature squeezing, and the formation of Schrödinger cat states.

A recent paper published on Nature [Nature,646,813(2025)] by Aziz and Howl, claims that quantum particles become entangled when they interact gravitationally, even if the gravitational potential is treated classically. We show that the entanglement found by the authors stems from discarding some of the transition amplitudes, which, when kept, guarantee that an initially factorized state remains so over time. Therefore, no entanglement is generated by the classical gravitational interaction in the scenario considered by the authors.

The concept of cavity funneling has emerged recently as a promising route towards creating indistinguishable photons from highly dephased emitters. So far, all suggested solutions are solely based on dielectric cavities that require extremely high quality factors that are difficult to reach at visible wavelengths. Here we suggest a hybrid funneling architecture where a dephased emitter is coupled to a plasmonic nanoresonator that is enclosed by an outer dielectric cavity. The estimated lower limit of the outer cavity quality factor is found to be $\sim2$ orders of magnitude lower compared to a cascaded cavity system. Furthermore, the surrounding topology of our approach allows for a partial direct coupling between the emitter and the outer cavity which in turn can increase the overall system extraction efficiency $\left(β\right)$ by a factor of 12, boosting the probability of photon collection.

We introduce coherent-state propagation, a computational framework for simulating bosonic systems. We focus on bosonic circuits composed of displaced linear optics augmented by Kerr nonlinearities, a universal model of bosonic quantum computation that is also physically motivated by driven Bose-Hubbard dynamics. The method works in the Schrödinger picture representing the evolving state as a sparse superposition of coherent states. We develop approximation strategies that keep the simulation cost tractable in physically relevant regimes, notably when the number of Kerr gates is small or the Kerr nonlinearities are weak, and prove rigorous guarantees for both observable estimation and sampling. In particular, bosonic circuits with logarithmically many Kerr gates admit quasi-polynomial-time classical simulation at exponentially small error in trace distance. We further identify a weak-nonlinearity regime in which the runtime is polynomial for arbitrarily small constant precision. We complement these results with numerical benchmarks on the Bose-Hubbard model with all-to-all connectivity. The method reproduces Fock-basis and matrix-product-state reference data, suggesting that it offers a useful route to the classical simulation of bosonic systems.

Achieving high-fidelity control in the presence of strong non-Markovian noise is critical for the optimization of emergent solid-state quantum devices. We present a highly efficient optimization framework that combines automatic differentiation with the non-Markovian uniTEMPO algorithm, enabling direct gradient-based optimization of complex objective functions. We apply this method to semiconductor quantum dots, optimizing multi-pulse excitation schemes: specifically Swing-UP of a Quantum EmmiteR (SUPER) and Floquet-engineered Two-Photon Excitation (FTPE) for single- and bi-exciton generation. Our approach yields high preparation fidelities within experimentally accessible parameter regimes. By integrating adiabatic rapid passage (ARP), we systematically enhance both SUPER and FTPE, demonstrating that these optimized protocols consistently outperform standard resonant pi-pulses and two-photon excitation. Notably, this performance gap widens at elevated temperatures, establishing the superior thermal robustness of our optimized multi-pulse strategies for real-world quantum hardware.

Among the possible types of magnetic dipole interactions in molecular systems, couplings between nuclear motion and the nuclear spin have probably received the least attention in molecular spectroscopy. Although very small in comparison to effects related to electron spin, this type of hyperfine interaction plays an important role in the NMR spectroscopy of molecular systems. While measurement and prediction of spin-rotation tensors are a common place, vibrationally induced effects still lack a comprehensive description. In this article we develop a generic, theoretical framework that is well embedded in modern electronic structure theory and inspired by the Breit-Pauli Hamiltonian for electronic interactions, distinguishing between nuclear spin-orbit and spin-other-orbit contributions. We show that the interaction of nuclear spins with pseudorotational excitations of highly symmetric molecules may lead to experimentally accessible hyperfine splittings in NMR spectra, triggered by infrared light.

We develop a compact theory of time-reversed Young (TRY) interference beyond the symmetric two-slit geometry by considering equally spaced three-slit, finite $N$-slit, and infinite periodic slit arrays. In the TRY configuration, a point emitter illuminates the aperture, a position-fixed detector records the signal, and the response is reconstructed in source space by correlating the detector record with the source-coordinate label. We show that the three-slit case already reveals the essential new physics beyond two slits: a quadratic Fresnel phase survives, modifies the reconstructed interference law, and lifts the nominal dark fringes in the generic case. For a general equally spaced $N$-slit array, we identify the exact reconstructed response and show that the familiar textbook grating factor is recovered only when the quadratic phase is negligible, compensated, or reduced to a common phase across the array. In that ideal limit, the reconstructed peaks are source-space analogues of classical grating orders rather than outgoing diffraction beams. For an infinite periodic TRY array, we further show that the same discrete quadratic phase generates full and fractional Talbot-like revivals in source space, governed by a reciprocal-distance condition rather than the conventional Talbot propagation law. These results show that the symmetric two-slit TRY geometry is exceptional, while multi-slit TRY systems naturally combine source-space discrimination with sensitivity to aperture-wide phase structure and periodic-array revival physics.

A single organic spin platform hosts both dimerized $S=\tfrac{1}{2}$ and effective Haldane $S=1$ sectors, linked by bond-texture inversion. At the junction, the fractional mode is controlled by termination parity: quenched by local fusion at one termination and released as an uncompensated spin-$\tfrac{1}{2}$-like degree of freedom at the parity-shifted one. Two such internal boundary modes of a finite embedded Haldane domain hybridize with an exponentially decaying splitting, establishing termination parity as a design principle for engineering and coupling fractional boundary modes.

Standard quantum mechanics employs complex Hilbert spaces, but whether complex numbers are fundamental or merely convenient has long been debated. For decades, real-valued equivalents were considered mathematically possible but cumbersome. However, a landmark 2021 result claimed that any quantum theory based on real numbers is experimentally falsifiable via network Bell experiments. Yet, it remains an open question whether this falsification applies to all real-valued theories. Here we show that this conclusion rests on an incomplete real formulation, and we present a rigorous real-valued framework that perfectly reproduces all predictions of standard quantum mechanics, i.e. standard quantum mechanics. We demonstrate that the standard real tensor product ($\otimes_{\mathbb{R}}$) used in previous no-go theorems is algebraically incompatible with the rich structure of standard quantum mechanics. We present a real framework based on \ka space and prove that it is exactly isomorphic to standard quantum mechanics via an explicit bijection $γ$. The isomorphism extends to composite systems through a symplectic composition rule $\otimes^{\ks}$ that replaces the Kronecker product. Consequently, our formulation achieves the maximal $\mathrm{CHSH}_{3}$ violation of $6\sqrt{2}$ using purely real variables, directly contradicting previous falsification claims. These results demonstrate that complex numbers are not fundamentally required by nature; rather, they encode a deeper real geometric structure that governs quantum interference and entanglement, settling this long debate.

Determining the exponentially scaled ground state wavefunction and the associated molecular properties remains one of the central challenges in quantum chemistry. Hybrid quantum-classical algorithms implemented on quantum computers offer a promising route toward addressing this problem. However, despite several successful demonstrations on small molecular systems, accurate simulations of large and chemically realistic molecules remain difficult due to the limited capability of noisy intermediate scale quantum (NISQ) hardware. To bypass the limitations of NISQ devices, while simultaneously retaining the accuracy of the ground state energy estimations, we propose a dynamic ansatz construction strategy based on operator commutativity and energy driven screening within density matrix embedding theory (DMET) framework. The partitioning of the full system allows us to dynamically construct the ansatz over individual embedded subsystems, allowing each embedding problem be solved individually to a desired accuracy. The embedding Hamiltonian is updated in a self-consistent manner with dynamically formulated wavefunction, and their coupled optimization leads to accurate and efficient description of the overall system. To assess the performance of this approach, we apply it to several molecular systems and chemical processes with up to 144 qubits. These simulations require at most 20 qubits at a time and demonstrate improved accuracy and significantly reduced quantum gate requirements compared with conventional ansatze. We further investigate the impact of various fragmentation strategies and demonstrate the adaptability of our approach at each step of the DMET self-consistency cycle that leads to significantly improved accuracy for strongly correlated system.

In many chemical reactions, short-lived radical intermediates play a crucial role, while detecting such short-lived species in-situ remains challenging. The optically readable electronic spin of nitrogen-vacancy (NV) centers in diamond is a nanoscale sensor for such radical species: its longitudinal spin relaxation time (T$_{1}$) reacts to magnetic fluctuations from the unpaired electrons of radical species in its local environment. In this setting, we demonstrate the successful in-situ detection of the nitroxide radical 2,2,6,6-Tetramethylpiperidinyloxyl (TEMPO) using NV center-based T$_1$ relaxometry after depositing nanodiamonds onto the inner wall of a glass cuvette. A significant concentration-dependent shortening of the relaxation time was observed, from $197\:μs \pm 21\:μs$ without radical to $66\:μs \pm 30\:μs$ at a concentration of 1 M TEMPO. The detection is sensitive in the nanomolar (nM) range and the determined signal-to-noise ratio is between 1.6 and 3.

We introduce and empirically validate Landscape Span Compression (LSC), a device-agnostic metric for quantifying how hardware noise distorts the variational energy landscape of the Quantum Approximate Optimization Algorithm (QAOA). Intuitively, LSC measures how much noise flattens the energy landscape, approaching 1 as the landscape collapses toward a barren plateau. We report an experience study of applying QAOA with LSC-based noise characterization on IBM's ibm_fez for three constrained QUBO portfolio instances, distilling practical lessons for parameter transfer, calibration-model fidelity, and error mitigation. Running p=1 QAOA on ibm_fez (Heron r2, 156 qubits) with up to 57,344 shots per grid point across three constrained binary optimization instances encoded as QUBO problems, we find: (i) hardware noise uniformly compresses the landscape span by 24-30% without displacing the global minimum, supporting classical-to-hardware parameter transfer; (ii) feasibility fractions at the optimal parameters remain 1.5-1.7 times above random sampling despite noise-induced degradation; (iii) the IBM calibration-based noise model achieves Pearson r=0.959 structural agreement with hardware but explains only approximately 42% of approximation-ratio degradation, with crosstalk and coherent errors as the leading unexplained contributors; (iv) a consistent noise cost of approximately 0.03 approximation-ratio units is observed across all instances; and (v) Zero-Noise Extrapolation yields mixed energy improvements of +7%/+9%/-4% per instance with 3-5 times uncertainty inflation. We compare LSC against four existing metrics and argue it is the most robust discriminator of noise severity for constrained QAOA on near-term devices.

We show that stochastic resetting may lead to finite entanglement between individual, spatially separated spins (pairwise entanglement) in the steady state of the spin chains driven periodically with frequency $ω_D$. We find the presence of a critical resetting rate $r_c$ below which the steady state pairwise entanglement, measured via concurrence $C$, vanishes. We also identify an optimal resetting rate $r_m$ at which $C$ becomes maximum. These critical and optimal rates exhibit a non-monotonic dependence on $ω_D$. Our analysis demonstrates the existence of special drive frequencies at which $r_c$ vanishes and $r_m$ attains minima. We compute $C$ in the presence of stochastic resetting using exact diagonalization for both the integrable XY model and non-integrable Rydberg spin chains, which demonstrate these features. Our numerical results match perturbative analytical expressions for the special drive frequencies in the large drive amplitude regime.

Recent experiments on a range of engineered quantum systems have highlighted the important role of interacting two-level systems (TLSs) in modifying device properties and generating fluctuations. Focusing on the case of an oscillator coupled to a single near-resonant TLS, we explore how interactions between the TLS and lower-frequency thermally activated two-level fluctuators (TLFs) degrade the oscillator's coherence. Depending on the strength of the couplings, a single TLF can give rise to coherence oscillations that appear alongside, or supplant, Rabi oscillations of the oscillator-TLS system. Bath-driven transitions in the TLF cause irreversible coherence decay at a rate that is highly sensitive to both the couplings and the transition rate. For an ensemble of TLFs, we identify and characterise the different regimes of non-exponential phase-averaging-driven coherence decay that the oscillator can display. Using numerical calculations, we examine the extent to which systems with just a few TLFs differ from the limit of a large (continuum) TLF ensemble. Our work provides a theoretical framework for understanding the interplay of coherent TLS interactions and TLF-induced dephasing in quantum devices such as superconducting and phononic resonators.

Quantum neural networks (QNNs) suffer from a fundamental sampling bottleneck since quantum measurements are probabilistic, requiring many circuit executions to estimate outputs with sufficient accuracy. Conventional Monte-Carlo (MC) inference exhibits an $\mathcal{O}(1/\sqrt{N})$ sampling error, rendering QNN inference and training costly on near-term quantum hardware, especially where each shot requires expensive qubit generation. This work introduces a "single-shot" QNN framework by integrating quantum amplitude estimation (AE) into the readout stage. By embedding a trained QNN as a state-preparation oracle within AE, outputs are estimated through coherent interference rather than repeated sampling. We demonstrate that AE-based QNN inference achieves an $\mathcal{O}(1/N)$ error even with a single shot. We further analyze noise robustness and training feasibility, showing that AE can be a powerful primitive for overcoming the sampling overhead of QNNs. This highlights that when the model itself is quantum, quantum algorithms can enhance the computation efficiency.

Quantum computation is an attractive front for many problems that are intractable for computers today. One such problem is nonadiabatic quantum molecular dynamics, where quantized internal states coupling to parameterized modes result in a Hamiltonian resistant to oracle-based models and spectral decomposition. This dissertation applies diabatic Hamiltonian operators directly to the computational basis as first-quantized split-operator propagators, validated with dynamic observables including absorption and recurrence spectra, scattering cross-sections, population dynamics, and quantum scars. Circuits are derived and specified, with focused circuit optimization in multi-mode and multi-channel extensions, including multivariate potential energy terms and graph theoretic optimization from molecular symmetry. Resource estimation shows circuit depth advantage against QROM-loading architectures on a fault-tolerant scale, and a quantitative comparison against quantum signal processing variants confirms that a Trotter-based architecture retains a scalable T-gate advantage. Expanding beyond electronic states demonstrates that duality between finite basis and discrete variable representations permits congruent structural decompositions into quantum circuits, expanding the use of multi-channel dynamics far beyond chemistry.

Magnetic domain walls have long been pursued as carriers of classical information for storage and processing. With the ability to create, control, and probe domain walls at the nanoscale, they are recently recognized as an ideal platform for studying macroscopic quantum effects and provide a natural blueprint for building scalable quantum computing architectures. In particular, the experimentally demonstrated high mobility of domain walls makes them not only suitable as stationary qubits but also as flying qubits, which may offer advantages over currently explored quantum computing platforms. In this Perspective, we outline our current understanding of the essential ingredients and key requirements for realizing universal quantum computation based on magnetic domain walls. We highlight promising concrete material platforms and identify the experiments that are still needed to advance this concept. We also discuss the potential challenges and point to new opportunities in this emerging research direction at the interface between magnetism and quantum information science.

Electron transport in graphene under a laser-modulated barrier is studied in the presence of an energy gap, a scalar potential, and a uniaxial zigzag strain. The transfer-matrix approach is used with the boundary conditions to derive the transmission probabilities as functions of different system parameters. Without strain, raising either the energy gap or the potential generally reduces transmission in the central and lower sidebands. Moderate zigzag strain generates pronounced Fano-type oscillations that vanish at large strain, while transmission increases for low potential and decreases for high values. In the upper sideband, the incidence energy shifts the resonance peaks to the right, and growing the barrier width generates characteristic oscillatory patterns. Furthermore, increasing the laser field amplitude enhances transmission, whereas higher laser frequencies tend to suppress it. These findings offer new perspectives on controlling electronic transport in gapped graphene via external fields, strain, and potential applications in optoelectronic devices.

In incompressible flow the viscous force is solenoidal, whereas the Madelung transform of a spinless Schrödinger equation produces only gradient forces. The two are orthogonal, so viscosity cannot arise from Hamiltonian quantum mechanics alone; an open quantum treatment is required. Reducing the $N$-body density matrix to its one-body component and closing the dynamics via Born-Markov yields Lindblad jump operators with $k^2$ scattering rates, which we unravel via quantum state diffusion (QSD) into a norm-preserving stochastic nonlinear Schrödinger equation. Dissipation and stochastic forcing are not separate ingredients: both come from the same Lindblad operators, and their amplitudes are locked by the QSD structure. The Madelung transform of this equation, under incompressibility, gives a stochastic Navier-Stokes equation whose viscosity is set by the mean free path and whose noise correlator satisfies the fluctuation-dissipation relation by construction, in agreement with the Landau-Lifshitz framework. The recovery is conditional: the viscous identification holds at the ensemble level via the vortex decomposition of the velocity field; the single-trajectory identification remains open. The zeros of the wavefunction carry quantised circulation; their codimension-2 topology yields the Migdal area law for circulation statistics under a Poisson assumption, here through a different mechanism than the loop-functional saddle point and verified numerically even in the quantum regime where the de~Broglie length exceeds the Kolmogorov scale.

This paper studies the search for a single arc in a graph using the Szegedy walk. Arc search can be interpreted as finding a quantum particle not only in its position but also with a specific internal state. The quantum walk employed in this study is essentially the model proposed by Segawa and Yoshie for the purpose of edge search. First, we investigate how the symmetry of a graph is reflected in its time evolution matrix, and provide a sufficient condition under which the success probability of the search is independent of the marked arc. In particular, we prove that if a graph is arc-transitive, the success probability is independent of the choice of the marked arc. Next, we analyze path and cycle graphs and show that the quantum search is ineffective for these graphs, whereas it performs well for complete bipartite graphs $K_{n,n}$. These results provide a theoretical foundation for studying arc and edge searches on various graphs, while also suggesting new problems concerning the eigenvalue analysis of edge-signed graphs in spectral graph theory.

Quantum sensing with undetected photons is a technique where photons of one wavelength probe a sample, but information is extracted by measuring photons of another wavelength that never interacts with the sample. This has seen significant experimental advances in applications such as spectroscopy, microscopy, and bio-sensing. However, a detailed theoretical analysis using the tools of quantum metrology is currently lacking. Thus it is unclear how far away current schemes are from fundamental limits, and what the optimal measurement strategies are. We apply a multiparameter quantum estimation framework to quantify the error when estimating the unknown transmission and phase shift of a sample. The optimal measurement scheme is shown to require only a single controllable phase shift, easily implementable in existing setups. We also study how to use multipass interactions to maximise information gain. In general the optimum number of passes scales inversely with the log of the transmission of the sample. This work clarifies the metrological power of quantum sensing with undetected photons, and provides guidance for the design of experiments requiring high sensitivity.

Wave--particle duality demonstrates the peculiar nature of quantum mechanics. In which-way experiments, depending on the measurement scheme, a particle exhibits either wave-like or particle-like properties, as summarized by Bohr's principle of complementarity. In this work, we implement Mach-Zehnder (MZ) interferometry on a two-dimensional (2D) superconducting quantum processor. With precise control of the which-way measurement strength, we demonstrate the transition of a photon from wave-like to particle-like behavior. Furthermore, by performing quantum state tomography on two qubits located in the two paths, we demonstrate that which-way measurements break the entanglement and coherence between the two paths and cause information leakage from the quantum system to the environment. To capture this behavior quantitatively, we derive complementarity relations between the entropy and the fringe visibility. By applying a continuous which-way measurement during the evolution, we also observe the quantum Zeno effect that partially obstructs the interferometer path, giving rise to nonmonotonic behavior of purity and von Neumann entropy. Our experiments provide a detailed characterization of the full interferometer dynamics, reveal the relation between wave--particle duality and quantum information, and demonstrate the potential of superconducting quantum processors for testing quantum foundations under high precision and controllability.

We investigate symmetry-resolved entanglement in non-relativistic quantum field theories, including complex Lifshitz scalar chains and Lifshitz fermionic models. Using charged moments and the correlator method, we compute symmetry-resolved Renyi and von Neumann entropies and analyze their dependence on subsystem size, charge, mass, and the dynamical exponent z. Our results reveal distinct features of non-relativistic entanglement. In Lifshitz scalar theories, approximate equipartition among charge sectors emerges in the large-z regime, with configurational entropy dominating, whereas Lifshitz fermionic models exhibit genuine equipartition only in the relativistic limit, with fluctuation entropy prevailing. These findings highlight a rich interplay between conserved charges, subsystem size, mass, and dynamical scaling, and provide a framework to explore operationally accessible entanglement in non-relativistic systems. Our study offers insights relevant to experimental platforms such as cold atom setups and mesoscopic systems, where particle-number-resolved measurements can probe symmetry-resolved entanglement.

In recent years, quantum kernel methods have shown promising applications on near-term quantum devices. However, selecting an appropriate encoding circuit for a given dataset requires costly evaluation of multiple candidates, formulated as a meta-learning problem. In this paper, we propose an automated recommender that utilizes the intrinsic characteristics of datasets to predict the optimal circuit without any quantum evaluation. Nine candidates are assessed alongside 24 classical complexity metrics serving as features, evaluated through two training approaches with four configurations, along with 14 machine learning models. Both approaches achieve Top-3 accuracy of up to 85.7% in identifying the best-performing encoding circuit, and demonstrate that classical data complexity metrics provide sufficient predictive signal for circuit selection.

In this work, we review the open quantum dynamics of the most known bipartite systems, such as the qubit-qubit system, the oscillator-oscillator system, and the qubit-oscillator system. First, we compare each system with and without rotating wave approximation. In this analysis, we observe the influence of the counter-rotating term in the system dynamics. Also, we compare and analyze the resulting dynamics of the three bipartite systems where, due to the nature of each system, different dynamics are observed, but some similarities are also observed between them. To obtain the system dynamics, we use the same platform, the Qutip Toolbox starting from the phenomenological master equation of each system. We made the latter have the same platform for comparison. We attach the codes to generate these dynamics.

We study quantum sensing with Floquet chaotic dynamics generated by Haar random unitary gates. The metrological resources consist of three ingredients: A given initial state, a set number of Haar random unitary gates and the sensing gates. There are two natural ways of organizing the resources: the first one is the "control" protocol, where the random unitary gates act as random controls and intertwine with the deterministic sensing gates and the second one is the "state-preparation" protocol, where random unitary gates play the role of preparing the metrological useful states. In each protocol, we consider both global Haar random unitary gates and a set of local two-site Haar random unitary gates that forms a Floquet random quantum circuit (RQC) respectively. We find linear, shot-noise scaling of the metrological precision, quantified by the quantum Fisher information (QFI), in the asymptotic limit when the Hilbert space dimension becomes large, and quantum advantages beyond linear scaling in the non-asymptotic regimes. We also bound the fluctuation of the QFI using concentration inequalities. Our analytical findings are corroborated by numerical simulations. Finally, along the way of analyzing the precision limit, we prove an empirical conjecture of RQC: In the asymptotic limit of large local Hilbert space dimension, the Floquet operator of a Floquet RQC essentially behaves like a global unitary operator.

We present a compact, automated, high-brightness entangled photon source capable of generating all four Bell states with high fidelity. The system utilizes a type-0 quasi-phase-matched PPKTP crystal embedded within a polarization Sagnac interferometer. We introduce a switching scheme based on the controlled, motorized translation of the nonlinear crystal. This device is capable of generating any one of the Bell states on-demand. Experimentally, we demonstrate that translating the crystal from the interferometer's balanced position repeatedly toggles the state between $|φ^+ \rangle$ and $|φ^- \rangle$ (as well as $|ψ^+ \rangle$ and $|ψ^- \rangle$) at regular intervals of $122 \pm 14 ~μm$. Subsequently, a half-wave plate (HWP) in the idler arm transitions between the quantum states $|φ^{\pm}\rangle$ and $|ψ^{\pm}\rangle$. While the non-collinear geometry imposes an upper limit on the translation range as verified via EMCCD imaging, the source however, displays very little change of intensity in the operational window. State purity and entanglement are certified through quantum state tomography (QST), visibility measurements, Bell state measurements (BSM), and CHSH inequality violations, confirming that the source is robust and provides a repeatable, high-fidelity output.

We investigate the spin resolved vortex properties of electron positron pairs created from vacuum in time delayed, two color electromagnetic fields. By treating the temporal delay G as a continuous tuning parameter, we reveal a dynamic transition from interference-dominated domain patterns at G=0 to the nucleation of quantized vortex lattices at G=0.5. These topological structures exhibit a staggered arrangement analogous to von Karman vortex streets in fluid dynamics. We demonstrate that the momentum-space morphology is strictly governed by spin orbit selection rules, i.e., parallel spin configurations enforce a dipole-like connectivity, while anti-parallel configurations resolve into distinct quadrupole structures. This difference originates from the conservation of total angular momentum Jz, where the spin projection determines the required orbital angular momentum Lz of the created pairs. At large delays (G greater than 1), macroscopic vortex coherence dissolves into a chaotic phase landscope due to multi-channel interference, yet the spin-dependent nodal geometries remain robust. Our findings suggest that these topological signatures provide a high-fidelity diagnostic for the quantum dynamics of vacuum excitations in strong field QED.

The fate of non-trivial many-body states subject to decoherence is of both fundamental and practical interest. Here, we demonstrate a new analytic technique that allows for an exact treatment of dynamics of observables in matchgate circuits subject to arbitrary Pauli noise. We use this to obtain new insights on how decoherence influences critical ground states, focusing on the 1D transverse field Ising model subject to local Markovian Pauli noise. While such noise cannot kill the critical behavior of spin correlation functions, we show that it does lead to a surprising non-equilibrium state, with experimental signatures that are measurable without requiring post-selection or multiple copies of the system. Despite the infinite-temperature nature of the dissipation, the decohered state is characterized by a thermal distribution of low-energy quasi-particles. This is the direct consequence of a noise-induced emergent length scale that manifests itself in fermionic correlators. We show how these phenomena are directly accessible in experiments using a single probe qubit, and that our results also hold for a different dephased critical state (that of an XX spin chain in the zero magnetization sector).

The non-Hermitian skin effect can lead to directional amplification of response, with the associated end-to-end Green's function generally exhibiting size dependence. Any deviation in length or local disorder can drastically alter the amplification factor, rendering the response fragile in practical implementations. In this work, we identify a new type of scale-free, topological, and directionally amplified response in a Hatano-Nelson model under perturbed open boundary conditions. The scale-free response can be attributed to the first order boundary effect and characterized by a winding number defined on a continuous generalization of the finite-size Brillouin zone-a concept introduced in this work. Such scale-free behavior endows the end-to-end Green's function with significant robustness and making it promising for practical applications.

Quantum entanglement in systems of identical particles is often obscured by the interplay between exchange-induced correlations and the operational framework used to define entanglement. To study the role of exchange statistics, we propose a scheme using two \textit{distinguishable} particles where an exchange symmetry is artificially engineered via a relative phase $θ$ in the initial state. This approach allows continuous tuning from bosonic ($θ= 0$) to fermionic ($θ= π$) statistics. By monitoring the interplay between purity and coherence, we uncover distinct dynamical regimes dictated by the interaction strength $U$ and the phase $θ$. For particles initially loaded in a bound state, strong $U$ suppresses coherence development by avoiding the scattering band, reducing the purity toward its minimum. For particles initially on neighboring sites, coherence grows linearly in time. While non-symmetric inputs feature a sharp purity reduction at intermediate $U$, due to the competition between bound and unbound states, symmetric initial conditions produce transient coherence bursts that significantly enhance the purity. More generally, tuning the phase $θ$ reveals a high-purity region over a range of $θ$ at intermediate interactions, with the purity collapsing to $1/2$ as $θ$ approaches the fermionic limit. Our results show that the imposed statistics, or lack thereof, reshapes the entanglement dynamics and its response to the interaction $U$.

The negatively charged nitrogen-vacancy center (NV$^-$) in diamond is a versatile platform for quantum magnetometry under ambient conditions. Recently, laser threshold magnetometry (LTM) has been proposed as a means to significantly enhance the sensitivity of NV-based magnetometers by incorporating a diamond hosting NV$^-$ centers within a laser cavity and operating near threshold. While demonstrations have validated the concept, practical implementations remain technically demanding, requiring high pump powers and precise alignment of free-space cavities. It remains unclear whether the benefits of operating near threshold will outpace increased laser noise. In this work, we integrate an NV-diamond with a high NV$^-$ content into a compact external cavity diode laser and demonstrate singlet infrared absorption optically detected magnetic resonance (ODMR). The system exhibits exceptional threshold current stability, enabling ODMR using the threshold current as the read-out parameter. We report a five-fold enhancement in the ODMR contrast by operating near threshold. The best magnetic field sensitivity of $7.6~\mathrm{nT/\sqrt{Hz}}$ (DC-500 Hz) is achieved well above threshold, while near threshold sensitivity is limited by increased probe laser noise. These results establish a compact and mechanically robust platform for singlet absorption-based NV$^-$ magnetometry and highlight key trade-offs between contrast enhancement and laser noise near threshold.

Quantum scientific computing is to solve engineering and science problems such as simulation and optimization on quantum computerss. Solving ordinary and partial differential equations (PDEs) is essential in simulations. However, existing quantum approaches to solve nonlinear PDEs suffer from the issues of curse of dimensionality and convergence during the linearization process. In this paper, a Lindbladian homotopy analysis method (LHAM) is proposed as a quantum differential equation solver to simulate nonunitary and nonlinear dynamics. The original nonlinear problem is first converted to a recursive sequence of linear PDEs with the homotopy analysis and reformulated as a higher-dimensional lower block triangular linear homogeneous system. The solution is then embedded in the density matrix and obtained through the Lindbladian dynamics simulation. Compared to other methods such as the Carleman linearization and Koopman-von Neumann approach where the dimension of Hilbert space increases polynomially with the inverse of truncation error, the Hilbert space in LHAM increases only logarithmically. LHAM is demonstrated nonlinear PDEs including Burgers' equation and magnetohydrodynamics equations.

Arrays of ultracold neutral atoms, also known as Rydberg atom arrays, are rapidly developing into a powerful and versatile platform for quantum simulation. However, theoretical predictions about the bulk quantum phases of matter present in these systems have often diverged from experimental realizations on finite-sized arrays due to the strong effects of the boundaries. Here we propose a general, experimentally straightforward strategy to mitigate the effects of the boundaries and thus enable finite-sized arrays to stabilize bulk-like quantum order. Our scheme makes use of the properties of the ubiquitous disordered phase in Rydberg systems, driving the boundaries into an unbiased set of configurations that depend on the bulk physics. We numerically demonstrate the efficacy of this protocol in one- and two-dimensional systems on both ordered and critical phases.

Light with complex structures in polarization, phase and amplitude, has attracted a lot of attention in a broad range of applications and fundamental studies in classical and quantum optics. Along with the increased interest in structured light comes a need for efficient modulation platforms operating simultaneously for many modes. Multi plane light conversions (MPLC), i.e., multiple consecutive phase modulations in combination with free space propagation, have enabled such unitary transformations, which are usually built by bulky optical components, limited to scalar modulation, or rely on advanced nanofabrication techniques. Here, we demonstrate an efficient, monolithic MPLC architecture through direct laser writing in standard fused silica glass, resulting in a device with a compact form factor of only a few cubic millimeters. Our scheme is based on volumetric engineering of the glass's birefringence through laser-written nanogratings, which enables spatial control over full vectorial light structures. To showcase the approach's potential for integrated multimode-multipath optical networks, we demonstrate multi-mode unitary transformations, mode conversions, and complex beam-splitting for scalar light. We further extend the MPLC operation to vectorial light and implement various polarization-controlled spatial mode operations as well as the transformation of the topology of an optical Skyrmion. Finally, we highlight our scheme's promise for optical communications and implement a miniaturized multiplexer for spatial modes and polarization operating at telecom wavelength.

Barren-plateau results have established exponential gradient suppression as a widely cited obstacle to the scalability of variational quantum algorithms. When and whether these results extend to a given objective has been addressed through loss-specific arguments, but a general structural characterization has remained open. We show that the objective itself admits a fixed-observable representation if and only if the loss is affine in the measured statistics, thereby identifying the exact boundary of the standard concentration-based proof template. Existing transfer results for non-affine losses achieve this reduction under additional assumptions; our characterization implies that such a reduction is not structurally available for a class of non-affine objectives, placing them outside the automatic reach of the existing proof template. Beyond the affine regime, a chain-rule decomposition reveals three governing factors -- model responsivity, loss-side signal, and transmittance -- and induces a loss-class dichotomy: bounded-gradient losses inherit suppression, while amplification-capable losses can in principle counteract it. In the exponentially wide setting, both classes fail, but for different structural reasons. When the interface is instead designed at polynomial width -- exposing coarse-grained statistics rather than individual bitstring probabilities -- the exponential-dimensional obstruction is relaxed and the dichotomy plays a genuine role. In a numerical demonstration on a charge-conserving quantum system, the amplification-capable objective produces resolved gradients several orders of magnitude larger than affine and inheriting baselines at comparable shot budgets. Over the tested interval, its scaling trend is statistically distinguished from the exponential trend of both alternatives. The boundary is affine; what lies beyond it is a representation-design problem.

We introduce QuIC, a training-free quantum graph embedding that maps graphs to sorted output distributions via a fixed parameterized circuit. In the ideal one-repetition setting, we prove that the resulting sorted distribution is permutation-invariant and injective on labeled graphs under an irrational-angle condition, yielding completeness on isomorphism classes for the ideal one-repetition exact-arithmetic embedding. We then use those ideal structural properties to motivate a practical embedding pipeline and study how much of that behavior survives under finite-shot estimation, truncation, realistic noise, transpilation, and hardware execution. The sorted distribution concentrates discriminative signal in a compact head, making fixed-length head truncation an effective practical operating point in the tested regimes. Under noise-model simulation, all tested graph pairs satisfied the study's operational separation criterion, including strongly regular graph pairs that are standard 2-WL stress tests and CFI families used as hard instances for fixed-k WL methods. A hardware study comprising 14,800 transpiled circuits across 37 CFI families on IBM Heron (ibm_fez, 156 qubits), including paired one- and two-repetition evaluations, reports empirical separation up to 66 qubits for the tested families under the reported execution protocol, identifies a device-dependent depth limit near 210-250 layers, and characterizes the current practical boundary of the method under the reported execution protocol.

This research investigates the performance and efficacy of machine learning models in stock prediction, comparing Artificial Neural Networks (ANNs), Quantum Qubit-based Neural Networks (QQBNs), and Quantum Qutrit-based Neural Networks (QQTNs). By outlining methodologies, architectures, and training procedures, the study highlights significant differences in training times and performance metrics across models. While all models demonstrate robust accuracies above 70%, the Quantum Qutrit-based Neural Network consistently outperforms with advantages in risk-adjusted returns, measured by the Sharpe ratio, greater consistency in prediction quality through the Information Coefficient, and enhanced robustness under varying market conditions. The QQTN not only surpasses its classical and qubit-based counterparts in multiple quantitative and qualitative metrics but also achieves comparable performance with significantly reduced training times. These results showcase the promising prospects of Quantum Qutrit-based Neural Networks in practical financial applications, where real-time processing is critical. By achieving superior accuracy, efficiency, and adaptability, the proposed models underscore the transformative potential of quantum-inspired approaches, paving the way for their integration into computationally intensive fields.

Quantum kernel methods have been proposed as a promising approach for leveraging near-term quantum computers for supervised learning, yet rigorous benchmarks against strong classical baselines remain scarce. We present a comprehensive empirical study of quantum kernel support vector machines (QSVMs) across nine binary classification datasets, four quantum feature maps, three classical kernels, and multiple noise models, totalling 970 experiments with strict nested cross-validation. Our analysis spans four phases: (i) statistical significance testing, revealing that none of 29 pairwise quantum-classical comparisons reach significance at $α= 0.05$; (ii) learning curve analysis over six training fractions, showing steeper quantum slopes on six of eight datasets that nonetheless fail to close the gap to the best classical baseline; (iii) hardware validation on IBM ibm_fez (Heron r2), demonstrating kernel fidelity $r \geq 0.976$ across six experiments; and (iv) seed sensitivity analysis confirming reproducibility (mean CV 1.4%). A Kruskal-Wallis factorial analysis reveals that dataset choice dominates performance variance ($\varepsilon^2 = 0.73$), while kernel type accounts for only 9%. Spectral analysis offers a mechanistic explanation: current quantum feature maps produce eigenspectra that are either too flat or too concentrated, missing the intermediate profile of the best classical kernel, the radial basis function (RBF). Quantum kernel training (QKT) via kernel-target alignment yields the single competitive result -- balanced accuracy 0.968 on breast cancer -- but with ~2,000x computational overhead. Our findings provide actionable guidelines for quantum kernel research. The complete benchmark suite is publicly available to facilitate reproduction and extension.

Considerable effort has been devoted to developing techniques for witnessing and characterizing quantum resources that emerge from collective properties of a set of states. In this context, Bargmann invariants play a central role: they witness coherence and related resources, and underpin important applications. In this work, we introduce a unified formalism that fully characterizes and organizes the capability of Bargmann invariants to witness different manifestations of coherence in sets of states. It is formulated around the construction of Bargmann scenarios, which specify relevant tuples of Bargmann invariants, and Bargmann polytopes, which describe the values that said invariants can have when the states are incoherent. We study their basic geometry, connect them to existing formalisms, and illustrate their physical relevance. Our construction opens new opportunities for the certification of quantum devices and lays the path toward a full quantum resource theory based entirely on multivariate traces of states.

Preparing correlated quantum states is essential for emerging technologies, but remains challenging in many-body systems. Here we propose a dissipative protocol that engineers nonreciprocal, energy-selective transitions to steer dipolar quantum systems toward desired many-body states. This is realized by introducing two types of controllable dissipative auxiliary atoms that act as nonreciprocal excitation and de-excitation channels, respectively, enabling a directional walk in Hilbert space. This approach enables stabilization of states across the many-body spectrum, not limited to the ground state and requiring no \textit{a priori} knowledge of the Hamiltonian. Our approach is designed for neutral atoms in dipolar Rydberg arrays, but applies broadly to setups with similar capabilities, providing a flexible and scalable framework for state preparation in programmable platforms.

The fundamental difference between closed and open quantum dynamics lies in their environmental interaction: closed systems are perfectly isolated and evolve reversibly under unitary Hamiltonian dynamics, whereas open systems continuously couple to an external bath, resulting in irreversible dissipation and information loss. In this work, we show internal Hamiltonian dynamics can be "faked`` via external pure dissipation, i.e., Lindbladians without a coherent Hamiltonian part. More concretely, we show that, in a GKSL representation with zero explicit Hamiltonian term but nontraceless jump operators, bounded-norm dissipative generators can approximate Hamiltonian dynamics within $ε$ error in diamond norm using $\mathcal{O}(t^2/ε)$ evolution time. We further prove that for time-independent dynamics this $\mathcal{O}(t^2/ε)$ scaling is in the worst case, necessary and optimal from a geometric perspective, which captures the fundamental decoherence cost for catching up with the speed of Hamiltonian dynamics. Our construction leads to various implications, including the BQP-completeness of purely dissipative dynamics even before reaching approximate equilibrium, a Zeno-adjacent state-independent freezing effect, the no super-quadratic fast-forwarding theorem of a class of purely dissipative dynamics, and reducing Lindbladian simulation cost via gauge changing.

AtomTwin.jl is an open-source Julia package for developing and simulating quantum protocols, hardware configurations and building digital twins for neutral-atom quantum processors and related atomic quantum devices. AtomTwin operates between mathematical models and physical devices; modeling atoms, optical tweezers, laser fields, atomic motion, interactions, and noise processes natively from physical geometry and parameters, without requiring users to define Hamiltonians manually. The package provides hardware-level instruction sequences, high-performance solvers for coupled quantum and classical dynamics, and a ready-to-use model for ytterbium-171 atoms in an extensible framework designed to accommodate a greater variety of atomic species and hardware components in the future. This paper describes the software architecture, performance benchmarks against existing toolboxes, and a demonstrated end-to-end application: preparation of a logical Bell state in the $[[4,2,2]]$ error-detecting code with four $^{171}$Yb atoms in moveable tweezers.

It is pointed out that the vertex operators of a chiral boson in 1+1 dimensions provide an explicit realization of dichotomic, bounded, Hermitian operators that saturate the Tsirelson bound of the Bell-CHSH inequality in the vacuum state.

Quantum Fisher Information (QFI) sets the ultimate precision limit for parameter estimation and is therefore a central quantity in quantum metrology. In time-dependent many-body systems, however, maximizing QFI is a highly non-trivial task due to the combined effects of non-commutativity, control complexity, and the exponential growth of the Hilbert space. In this work, we present a physics-informed neural network (PINN) framework to address this problem through the learning of counter-diabatic quantum dynamics. Our approach combines a variational PINN formulation with a Magnus-expansion treatment of time-ordered evolution, enabling the adiabatic gauge potential and the scheduling function to be inferred directly from the underlying physics while enforcing the Euler-Lagrange structure of the protocol. The method is applied to several families of driven spin Hamiltonians, including nearest-neighbor, dipolar, and trapped-ion-inspired interactions, for systems of up to six qubits. The numerical results show that the proposed framework systematically improves over reference solutions based only on the Euler-Lagrange condition, yielding high normalized QFI together with favorable fidelity and extremal-balance metrics while preserving small phsical residuals. The analysis further shows that learning the scheduling function provides a clear performance advantage in most cases, and reveals non-trivial finite-size effects, with $q=3$ emerging as a particularly challenging regime. Although scalability remains limited by the exponential growth of the operator space and by automatic-differentiation costs, the results demonstrate that PINNs constitute a viable and physically grounded route for learning metrologically optimal control strategies in interacting quantum systems.

We simulate a long-range extended Ising model in one dimension using a hybrid quantum algorithm, namely Variational Quantum Eigensolver (VQE). In this quantum simulation, we investigate how quantum resources scale with system size and interaction strength. Three structure-aware ansatze incorporating nearest-neighbor (NN), next-nearest-neighbor (NNN), and next-next-nearest-neighbor (NNNN) entangling blocks are constructed by mimicking the string operators in the Hamiltonian. We show that energy fidelity alone is not a good indicator for finding the ground state of our model. To overcome this problem, we introduce an additional criterion based on pairwise logarithmic negativity as a more reliable way to find the actual ground state by the VQE. We find that the interaction range parameter alpha primarily governs the minimum number of ansatz layers required, rather than proximity to the quantum critical point. In particular, we show that in the non-local regime (alpha <= 1), the NNN and NNNN ansatze reduce the layer scaling rate by factors of 2.5x and 3.8x relative to NN in all phases, including the critical point. The total number of two-qubit gates required for reliable simulation grows quadratically with system size for all three ansatze. This is consistent with the theoretical prediction, as the number of non-local terms in the Hamiltonian also grows quadratically with the system size. In the local regime, however, the number of required two-qubit gates grows linearly with system size. In contrast, in the quasi-local regime, the required number of two-qubit gates for the quantum simulation is more subtle and depends on the phase of the Hamiltonian.

Rydberg atom arrays are powerful platforms for studying quantum many-body systems. We consider the Rydberg-Ising Hamiltonian on periodic chains and numerically study ensembles of states generated by random global pulse sequences subject to hardware constraints and fixed evolution times. We compare the statistical properties of such states with those of Haar-random states within the relevant lattice symmetry sector. In the strong-interaction regime (short interatomic distance), the dynamics is governed by an effective blockade that restricts Hilbert-space exploration and limits entanglement growth. In this regime, level-spacing statistics of reduced density matrices are close to random-matrix predictions, while the distribution of measurement probabilities deviates from Porter-Thomas behavior. For weaker interactions (larger interatomic distance), the system approaches Haar-like statistics at long times, as reflected in entanglement entropy, entanglement spectrum statistics, and the distribution of measurement probabilities. At intermediate interactions, this behavior is observed on experimentally relevant timescales. Motivated by this observation, we investigate whether generic symmetric quantum states can be efficiently prepared using quantum optimal control in this regime. Employing target states drawn from an ensemble with a broad entropy distribution, we observe high fidelities (infidelities between $10^{-5}$ and $3\times 10^{-2}$ for 9 spins). The fidelity, however, decreases with the entanglement entropy of the target state, demonstrating that highly entangled states are intrinsically harder to prepare under realistic constraints.

We analyze vibrational dynamics in a toy model for polaritonic chemistry under collective electronic strong coupling. In a Holstein-Tavis-Cummings model, incoherently excited by a photon, we show that disorder leads to non-Gaussian states of vibrational modes on short time scales at the single-molecule level. Using exact matrix product state simulations, we demonstrate that this effect can remain robust for larger molecule numbers, implying that nuclear wave packets cannot be effectively described by thermal states. Furthermore, we compare simulations of the exact quantum dynamics with semiclassical approximations. We find that the Ehrenfest approximation can only well reproduce ensemble-averaged observables for very large system sizes. Also simulations in the truncated Wigner approximation fail to capture the non-Gaussian effects. Our work highlights the importance of disorder and genuine quantum effects in cavity-modified nuclear dynamics in polaritonic chemistry.

Observables of out-of-equilibrium quantum many-body systems display complex temporal behavior that encodes the underlying physical mechanisms but typically resists straightforward interpretations. We introduce recurrence analysis - a nonlinear time-series analysis framework long established for classical dynamical systems - to investigate correlated quantum many-body dynamics. Recurrence plots provide a qualitative fingerprint of simulated or experimental data, while recurrence quantification analysis extracts corresponding numerical descriptors. Applying this framework to quenches from the paramagnetic ground state in the one-dimensional transverse-field Ising model, we observe a clear progression in the recurrence plots of two-site correlations: nearly periodic patterns in the deeply ferromagnetic phase give way to multiscale temporal structures at criticality. Recurrence quantifiers further recover the critical field strength without prior knowledge of the model, establishing recurrence analysis as a versatile tool for characterizing quantum many-body dynamics, including unsupervised detection of quantum phase transitions.

Shortcuts to adiabaticity (STA) were first developed in quantum dynamics to realize rapid transformations with suppressed residual excitations. Here we show how the same idea can be implemented in classical nonlinear dissipative Lagrangian systems. Using a coupled $r$-$θ$ manipulator as an illustrative model, we perform inverse engineering on the Euler-Lagrange equations with Rayleigh dissipation by prescribing endpoint-stationary trajectories, obtaining the corresponding force and torque profiles and quantifying how geometric coupling amplifies errors and residual energy. We further compare smooth STA protocols with actuator-bounded time-optimal solutions and with proportional-integral-derivative tracking, which highlights a trade-off among smoothness, speed, and robustness. Finally, we introduce a single-shot correction based on one mid-course measurement to reduce the effect of early deviations while keeping the inputs nearly smooth. These results provide a practical bridge between quantum STA concepts and their classical counterparts.

Fiber-integrated micro-optical elements promise a scalable approach to photon collection and beam shaping for quantum information processing. Here, we demonstrate single-step fabrication of micro-spherical, micro-spiral, and micro-axicon structures directly on the core of single-mode optical fibers using focused ion beam (FIB) machining with nanometer-scale precision. Atomic force microscopy reveals that micro-concave and micro-convex spherical surfaces achieve shape accuracies of approximately $λ/80$ and $λ/50$ at $λ= 780$ nm, respectively. Optical characterization using a He-Ne laser at 633 nm confirms the expected far-field donut beam patterns for the micro-spiral and micro-axicon structures. Mach-Zehnder interferometry further verifies the corresponding azimuthal and radial phase profiles of the light emitted from the spiral and axicon fibers. Surface metrology shows that the optimized FIB process preserves optical-grade surface quality, introducing no measurable additional roughness at spatial scales relevant to visible and near-infrared operation. These monolithically integrated fiber micro-optical elements enable a broad range of applications in quantum technology, including fiber micro-cavities for cavity quantum electrodynamics, beam shaping for neutral atom trapping, and the generation of structured light for free-space quantum network links.

Integrated photonics is widely regarded as a key enabler for scalable quantum key distribution (QKD), offering compactness, stability, and compatibility with semiconductor fabrication. Despite rapid advances in chip-based QKD, the implementation security of integrated photonic components remains insufficiently understood. Here we present the first systematic study of an implementation-level security vulnerability associated with p-n junction-based variable optical attenuators (VOAs), a ubiquitous component in integrated QKD transmitters. We theoretically and experimentally demonstrate that electrically biased p-n junction VOAs emit spontaneous luminescence. Using a single-photon-sensitive spectral measurement technique, we identify the emission wavelength to be centered around 1107 nm, well separated from the C-band quantum signals. This spectral separation gives rise to a previously unrecognized wavelength-resolved side channel, enabling potential wavelength-splitting attacks without directly disturbing the encoded quantum states. By incorporating the measured luminescence into a quantitative security analysis, we show that even extremely weak emission can lead to non-negligible information leakage. Our findings reveal a fundamental and previously overlooked security risk in photonic integrated QKD systems and highlight the necessity of security-aware device design for future integrated quantum communication technologies.

Quantum computing is a new approach to computation that utilizes superposition, entanglement, interference, and tunneling to solve problems too complex for classical computers. This paper discusses the basic concepts and development of quantum computing, exploring its potential applications in the built environment and urban microclimate research. In buildings, quantum computing may help optimize energy management, control HVAC systems, and plan electric vehicle charging networks more efficiently. For urban microclimates, it could accelerate renewable energy planning and support multi-objective design, making it easier to balance urban building performance with climate conditions. Since current quantum hardware is still in the Noisy Intermediate-Scale Quantum (NISQ) stage, we propose the "BITE" principle to guide researchers in choosing suitable problems for quantum acceleration: B (Big search), I (Input-light), T (Tiny computation), and E (Evaluation polish). Although quantum computing still faces challenges such as noise and hardware limits, it offers great potential for developing more climate-resilient, sustainable, and energy-efficient cities of the future.

We experimentally demonstrate the detection of momentum transfers from individual collisions of Kr, Xe, and SF$_6$ with an optically levitated nanoparticle, finding good agreement with theoretical expectations. The observed event rates accurately measure the gas partial pressures, while the spectral shape provides a sensitive probe of the surface properties of the nanoparticle, including its temperature. The reconstruction of impulse signals as small as 200 keV/$c$ further establishes that levitated optomechanical sensors can reach the sensitivity required for precision measurements of fundamental particle interactions, and demonstrates a proof-of-principle for a primary pressure sensor based on the detection of individual gas particle collisions.

Variational Monte Carlo (VMC) combined with expressive neural network wavefunctions has become a powerful route to high-accuracy ground-state calculations, yet its practical success hinges on efficient and stable wavefunction optimization. While stochastic reconfiguration (SR) provides a geometry-aware preconditioner motivated by imaginary-time evolution, its Kaczmarz-inspired variant, subsampled projected-increment natural gradient descent (SPRING), achieves state-of-the-art empirical performance. However, the effectiveness of SPRING is highly sensitive to the choice of a momentum-like parameter $μ$. The original sensitivity of $μ$ and the instability observed at $μ=1$, have remained unclear. In this work, we clarify the distinct mechanisms governing the regimes $μ<1$ and $μ=1$. We establish convergence guarantees for $0\leμ<1$ under mild assumptions, and construct counterexamples showing that $μ=1$ can induce divergence via uncontrolled growth along kernel-related directions when the step-size is not summable. Motivated by these theoretical insights and numerical observations, we further propose \textit{Principal Range Informed MomEntum SR} (PRIME-SR), a tuning-free momentum-adaptive SR method based on effective spectral dimension and subspace overlap. PRIME-SR achieves performance comparable to optimally tuned SPRING while significantly improving robustness in VMC optimization.

Quantum magic rectangular games provide a natural setting for studying perfect quantum strategies and their underlying structure. However, existing analyses are largely case-specific and do not reveal a unifying characterization. In this work, we give a complete characterization of all perfect quantum strategies for quantum magic rectangular games, in the form of necessary and sufficient conditions on the shared state and measurement operators. Our approach identifies a structural set of constraints that any perfect strategy must satisfy, thereby providing a unified framework for understanding these games. As an illustration, our characterization shows that even in the $3 \times 3$ case, two pairs of bell states are not structurally enforced for perfect quantum strategies. More broadly, our results offer new insights into the structure of quantum correlations underlying perfect nonlocal strategies.

In this article we present a comprehensive theoretical investigation of phonon lasing with mixed-species trapped ions, as demonstrated in [T. Behrle, Phys. Rev. Lett. 131 (2023)], employing both a semi-classical mean-field description and a full quantum theory. We derive an analytic expression for the second-order coherence function, confirming the experimental observation of the system's lasing behaviour above threshold. Building on the successful implementation of the two-ion lasing scheme, we propose a novel approach for achieving phonon lasing with a single trapped ion, offering significant experimental advantages and making the implementation of multiple phonon lasers within a single setup feasible. Furthermore, we explore lasing in a squeezed basis and in different regimes of the Lamb-Dicke approximation, highlighting the potential to produce non-classical states with promising applications in precision sensing. Our analysis of a sensing protocol based on squeezed states, using experimentally feasible parameters, shows a sensitivity enhancement of up to two orders of magnitude.

The limited number of qubits is a major bottleneck in Quantum Approximate Optimization Algorithm (QAOA) for large-scale combinatorial optimization in the Noisy Intermediate-Scale Quantum (NISQ) era. To make progress, existing techniques rely on qubit reduction at the cost of information loss, hence leading to degraded computational performance. As a remedy, we propose the Equivalence-preserving Qubit Efficient QAOA (EQE-QAOA), which significantly reduces the required number of qubits without degrading the performance of QAOA. By exploiting intrinsic symmetries and conserved quantities, we first demonstrate that the QAOA dynamics are strictly confined to an invariant subspace of the Hilbert space. We subsequently prove that the evolution within this subspace is exactly equivalent to that of the full-scale system, achieving the same optimal solution as the original QAOA. Moreover, to reduce the number of qubits, we propose an isometric mapping that re-encodes the subspace into a space relying on fewer qubits. Furthermore, we derive the applicability conditions of EQE-QAOA and show that it is broadly applicable to large-scale combinatorial optimization problems, excluding only unconstrained problems with completely independent variables. Numerical simulations based on Max-Cut instances validate that EQE-QAOA significantly reduces qubit requirements and computational resources, while preserving exact optimization performance.

Upper and lower quantum functionals, introduced by Christandl, Vrana and Zuiddam (STOC 2018, J. Amer. Math. Soc. 2023), are families of monotone functions of tensors indexed by a weighting on the set of subsets of the tensor legs. Inspired by quantum information theory, they were crafted as obstructions to asymptotic tensor transformations, relevant in algebraic complexity theory. For tensors of order three, and more generally for weightings on singletons for higher-order tensors, the upper and lower quantum functionals coincide and are spectral points in Strassen's asymptotic spectrum. Moreover, the singleton quantum functionals characterize the asymptotic slice rank, whereas general weightings provide upper bounds on asymptotic partition rank. It has been an open question whether the upper and lower quantum functionals also coincide for other cases, or more generally, how to construct further spectral points, especially for higher-order tensors. In this work, we show that upper and lower quantum functionals generally do not coincide, but that they anchor new spectral points. With this we mean that there exist new spectral points, which equal the quantum functionals on the set of tensors on which upper and lower coincide. The set is shown to include embedded three-tensors and W-like states and concerns all laminar weightings, significantly extending the singleton case.

Quantum many-body scars are rare exceptions to thermalization: they sustain non-thermal stationary states without the protection of any local conservation law, and are generally expected to be fragile. Here we construct an analytically tractable random unitary circuit hosting a single scar, and derive from first principles the thermalization mechanism governing perturbations thereof - described by a picture of fluctuating interfaces. Surprisingly, despite being thermodynamically irrelevant for local observables, the scar leaves a sharp fingerprint in the entanglement dynamics, driving a transition as a function of perturbation strength that is not probed by any local measurement.

Physical intuition suggests that local dynamical evolution or measurement-induced disturbances of hidden variables might bypass Bell's theorem. We establish a generalized transition-kernel framework encompassing arbitrary local dynamics and rigorously prove that any strictly local dynamical model is mathematically equivalent to a static Bell model. We show that attempts to circumvent this equivalence -- including historical temporal models and recent macroscopic pilot-wave hydrodynamic analogs -- inevitably introduce explicit nonlocality (parameter dependence) or forfeit measurement independence. Our results establish a general boundary: nonlocal statistical correlations cannot be generated by purely local dynamical processes.

Satisfiability (SAT) is a central problem in computer science, and advances in SAT-solving algorithms have a far-reaching impact across many fields. Recent works have proposed quantum SAT solvers based on Grover's algorithm, a quantum search technique. However, Grover-based approaches face a key limitation: they typically require prior knowledge of the number of satisfying assignments of the target Boolean formula. This information is unavailable in most practical settings. Quantum counting can be used to estimate this quantity, but it incurs a computational overhead that is several orders of magnitude higher than Grover search. In this paper, we propose a novel quantum SAT solver based on entanglement and equivalence checking. Our method does not assume prior knowledge of the number of solutions and is computationally more efficient than quantum counting. Although the worst case time complexity is inevitably exponential, we prove that the expected time complexity of our approach is only constant time O(1) over random Boolean functions. Experimental results also support our theoretical claim.

Dark and subradiant states have emerged as a promising resource for stabilizing open quantum batteries against dissipation, but existing studies are largely limited to qubit ensembles and symmetry-based constructions. Here we introduce a systematic, thermodynamically consistent framework for identifying long-lived energy storage states in interacting multilevel quantum batteries, combining the Davies master equation with a Morris-Shore (MS)-type decomposition of dissipative coupling blocks. Focusing on a minimal model of two interacting qutrits coupled to a common bath, we analytically construct dark, bright, and funnel states-excited states that decay exclusively into protected manifolds. We also derive quantitative robustness conditions governed by the ratio of interaction strength to anharmonicity. We show that multilevel ladder structure and exchange interactions enable energetic storage states beyond the qubit case. Numerical simulations confirm that these states exhibit long-lived energy storage under realistic dissipation. Finally, we show that high-energy funnel states provide a natural design target for multilevel quantum batteries, as their decay pathways are highly structured and directed toward protected manifolds. Knowledge of these pathways offers a principled basis for developing future protection and control strategies in superconducting multilevel platforms.

Superconducting qubits, realized by incorporating Josephson junctions into superconducting circuits, behave as artificial atoms with anharmonic energy spectra and can be precisely controlled and measured using microwave cavities within the framework of circuit quantum electrodynamics (cQED). Since its emergence in the early 2000s, cQED has established superconducting qubits as leading candidates for scalable quantum devices and has enabled the exploration of hybrid quantum systems that integrate disparate physical platformsThis review surveys superconducting hybrid quantum electromechanical systems in which mechanical resonators are coupled to superconducting qubits, with a focus on two widely used qubit platforms: the transmon and the fluxonium. We provide an overview of the underlying coupling mechanisms arising from interactions through the phase and charge degrees of freedom of the qubit, and discuss how these mechanisms give rise to both longitudinal and transverse qubit-mechanical interactions. We further review extensions of electromechanical platforms to electro-optomechanical architectures, in which optical cavities are integrated to enable coherent interfacing between superconducting circuits and optical photons. This review aims to present a unified framework and perspective on qubit-mechanical and qubit-mechanical-optical hybrid systems in superconducting quantum technologies and applications related to sensors.

Large language models (LLMs) show strong capabilities in general reasoning but typically lack reliability in scientific domains like quantum mechanics, which demand strict adherence to physical constraints. This limitation arises from the scarcity of verifiable training resources and the inadequacy of coarse feedback signals in standard alignment paradigms. To address the data challenge, we introduce QuantumQA, a large-scale dataset constructed via a task-adaptive strategy and a hybrid verification protocol that combines deterministic solvers with semantic auditing to guarantee scientific rigor. Building on this foundation, we propose the verification-aware reward model (VRM) tailored for Reinforcement Learning with Verifiable Rewards (RLVR), which employs an adaptive reward fusion (ARF) mechanism to dynamically integrate deterministic signals from a scientific execution suite (SES) with multidimensional semantic evaluations for precise supervision. Experimental results demonstrate that our method consistently outperforms baselines and general-purpose preference models. Notably, our optimized 8B model achieves performance competitive with proprietary models, validating that incorporating verifiable, rule-based feedback into the reinforcement learning loop offers a parameter-efficient alternative to pure scaling.

Atmospheric turbulence makes free-space quantum polarization links intrinsically time varying, whereas receiver-side reduced interfaces are often treated as static. This paper develops a slow-time receiver interface by extending an aperture-conditioned static model to the temporal domain. The receiver-plane phase field, beam-centroid displacement, and scintillation are modeled as hidden slow-time stochastic processes, from which the reduced interface is generated at each instant. A leading-order closure maps coarse-grained phase roughness to an effective polarization-mixing variance while preserving the inherited local polarization-channel family. Aperture conditioning then yields time-dependent effective depolarization, coherence, and detection descriptors. In a representative weak-turbulence case, the polarization branch remains close to the near-ideal regime, with effective depolarization on the order of \(10^{-3}\) and effective coherence close to unity, whereas the detection branch exhibits visibly stronger fluctuations and a longer correlation time. These results show that a single static receiver-side parameterization is insufficient to characterize the temporal behavior of turbulent free-space quantum links. The resulting interface is intended for receiver-side characterization of time-varying quantum links, with MDI-QKD as one representative downstream application.

The interplay between many-body interactions and controlled dissipation provides a rich framework for exploring nonequilibrium quantum phases. In this work, we explore an open Dicke model including Rydberg-dressed interactions in a driven-dissipative cavity and unveil its unique nonequilibrium dynamics therein. We find that Rydberg-dressed interactions generate an additional critical coupling, which alters the stability of fixed points and hence determines fruitful dynamical phase transitions. Beyond the mean-field limit, we demonstrate that our system supports a superradiant continuous time crystal (CTC) phase, proving CTC can exist in an interacting spin-1/2 system. By bridging driven-dissipative quantum cavity and interacting atomic systems, our Rydberg-dressed Dicke system offers measurable signatures from the cavity emission photons, making it experimentally feasible as a versatile platform for exploring dynamical phase transitions and macroscopic temporal order in open quantum matter.

Multiphoton entangled states are pivotal resources for implementing optical quantum information protocols. Recently, energy-time-entangled triphotons have been observed in hot atomic ensembles. However, in these protocols, the complex fifth-order nonlinear susceptibility entailed by four- or five-level systems limits our understanding of triphoton generation. Here, to directly capture the generation mechanism of triphotons and their associated optical properties, we investigate the generation of energy-time-entangled triphotons in a six-level cold atomic ensemble. The fifth-order nonlinear susceptibility indicates the existence of two sets of spontaneous six-wave mixing in the system. Notably, triphoton generation in this system is subject to stringent timing constraints. Collectively, these characteristics give rise to threefold coincidence counts, which -- dominated by the fifth-order nonlinear susceptibility -- exhibit asymmetrically damped Rabi oscillations in the two-dimensional time domain. Furthermore, we analytically derive that the temporal correlation properties of conditional two-photon states are preserved -- a unique feature of $W$-class tripartite entanglement. These results not only lay the groundwork for the experimental preparation of triphotons using six-level systems but also provide key support for understanding the generation mechanism of triphotons involving more complex fifth-order nonlinear susceptibilities.

In this work, we investigate the reliability of information-theoretic measures based on the electron-density and shape-function, specifically Shannon and Rényi entropies, as descriptors of electronic correlation. By establishing a rigorous decomposition of these entropic measures into additive and nonadditive contributions, supported on a Mulliken-like atomic partition of molecules, we systematically analyze the asymptotic behavior of the entropies at the infinite-internuclear-distance limit to assess the problem of static correlation and extensivity. Our algebraic and numerical analysis reveals several flaws in the use of these density-based descriptors. We demonstrate that for minimal-basis and different theoretical levels, the Shannon and Rényi entropies fail to encode the amount of static correlation conveyed by the underlying wavefunction. Conversely, shape-function Shannon entropies and Rényi entropies (for $α\neq 1$) violate extensivity. In larger basis sets, uncorrelated Hartree-Fock densities consistently overestimate entropy compared to sufficiently correlated (e.g., full-valence-CAS) densities. Moreover, the entropies for insufficiently correlated methods violate extensivity. These findings indicate that electron-density-based measures are insufficient for capturing static correlation, suggesting that robust entropic descriptors should be constructed from higher-dimensional Hilbert-space objects.

We present a matrix product state (MPS) method for including decoherence processes in calculations involving waveguide quantum electrodynamics (waveguide QED) using density matrices. The approach is based on collision quantum optics, where the many-body state of the waveguide is represented as discrete time bins, which are efficiently represented using an MPS chain. Our method is a generalization of previous MPS methods, and we demonstrate how one can efficiently expand to density matrices, allowing for the inclusion of various loss processes in the form of Lindblad terms in the Liouvillian superoperator responsible for the relevant dissipation dynamics. As an application of the theory, we study various waveguide QED systems and the influence of emitter pure dephasing (which is one of the most important processes in real systems) on the light-matter interactions, including a two-level system (TLS) in a semi-infinite waveguide with time-delayed feedback, two spatially separated TLSs with finite delays, and finally the scattering of few-photon Fock pulses on a TLS. In addition to emitter pure dephasing, we also show how to include off-chip radiative decay, and show how it differs qualitatively from pure dephasing.

Near-term quantum devices with limited qubits motivate the study of space-bounded quantum computation in the data stream model. We show that Shannon entropy estimation exhibits an exponential separation between quantum and classical space complexity in this setting. Technically, we develop a two-stage quantum streaming algorithm based on a quantum procedure with an explicitly constructed oracle derived from the streaming input. This algorithm achieves logarithmic space complexity in the accuracy parameter, whereas any classical streaming algorithm requires polynomial space. In sharp contrast, existing results for Shannon entropy estimation in the quantum query model achieve only a quadratic speedup. Our work establishes a natural problem with practical applications in computer networking that admits an exponential quantum space advantage, revealing a fundamental gap between quantum query complexity and streaming space complexity.

Non-Hermitian dynamics in open systems can give rise to a variety of fascinating non-equilibrium phenomena, ranging from symmetry-breaking transitions to directional energy flow. Parity-time (PT) symmetry breaking determines the occurrence of dynamical instabilities, while non-reciprocal interactions enable asymmetric energy transfer between modes. Here, we present a versatile optomechanical platform based on a vacuum-levitated nanoparticle that allows full control over the coupling of its mechanical modes, including non-reciprocal and non-conservative interactions. By engineering the spatial ellipticity and polarization of the trapping beam, we continuously tune the system from a reciprocal to a strongly non-reciprocal regime. This allows us to observe PT-symmetry phase transitions and to isolate a unidirectional regime in which one mode remains effectively decoupled while driving the other. We demonstrate that elliptical polarisation of the trapping beam spanning unidirectional and reciprocal regimes induces asymmetric intermodal energy transfer. This results in the spontaneous cooling of one mechanical mode without external feedback. Both modes share identical mass, size, charge, and optical environment, providing a clean and robust setting for exploring non-Hermitian dynamics, exceptional-point physics, and energy redistribution in minimal systems. Combined with recent advances in ground-state cooling, our results provide a direct route to realising non-Hermitian phenomena in the quantum regime.

We show numerically that a repulsive Bose-Einstein condensate can be driven into implosive dynamics by a direct topological quench. We first realize giant vortices by quasi-adiabatic phase imprinting, and then perform a sudden anti-imprint that cancels the accumulated winding in a single step, abruptly switching the condensate from a highly charged vortex state to the trivial sector. The resulting phase-density mismatch launches a rapid inward radial flow and produces a strong central density buildup, despite the repulsive interactions. We find a clear threshold in the initial winding for the onset of this focusing. After the first implosion, the dynamics evolves into circular nonlinear wave fronts that subsequently undergo breaking of azimuthal symmetry (axisymmetry) down to a polygonal one, whose shape is determined by the way the giant vortex is built. These results establish topological engineering as a new tool for studying implosive dynamics and symmetry-breaking instabilities in quantum fluids.

Accurate modeling of surface catalytic processes often requires methods capable of describing strong correlation, charge transfer, and multiple closely lying electronic states. While density functional theory remains widely used, its limitations for localized electronic states motivate the use of wavefunction-based approaches and, more recently, quantum computing algorithms. However, the performance of quantum ansätze in chemically motivated, multistate settings remains largely unexplored. Here, we benchmark state-averaged factorized unitary coupled cluster with singles and doubles (SA-fUCCSD) and the adaptive, problem-tailored ansatz (SA-ADAPT) using an embedded cluster model of NO adsorption on Rh-doped TiO2(110). The system exhibits pronounced multiconfigurational character and multiple state crossings, providing a stringent test. State-averaged CASSCF serves as a reference, and the quantum ansätze are evaluated as solvers for the corresponding CASCI problem within a fixed orbital basis. We find that SA-fUCCSD improves with increasing circuit depth but requires many parameters and shows sensitivity to initialization. In contrast, SA-ADAPT achieves near-CASSCF accuracy with significantly fewer operators. A modified operator selection scheme, incorporating multiple operators per iteration, substantially accelerates convergence. Our results demonstrate the efficiency of adaptive ansätze for multistate problems and establish a controlled benchmark for quantum algorithms in chemically motivated systems beyond minimal models.

We introduce a traceable operator-algebraic framework for incompressible transport on M= T3 (and, more generally, compact Riemannian manifolds endowed with a smooth invariant probability measure). Given an autonomous divergence-free velocity field u, the time-1 map $Φ$ induces the Koopman unitary U on L2(M) and the crossed-product finite von Neumann algebra Mu\,:= L$\infty$(M) ___$α$ Z= W$\star$(L$\infty$(M),U), equipped with its canonical faithful normal trace $τ$u. Within Mu we define tracial complexity functionals from commutators [U,Mf] (with Mf the multiplication operators) and associated positive elements, and we connect these quantities to Fuglede--Kadison determinants and entropy-like tracial functionals. In parallel, we introduce bounded regularized advection operators T(s) u\,:= KsTuKs as differential-level probes of transport oncommutativity, and we recall the Lie-bracket commutator identity at the formal generator level. This provides a natural algebraic setting in which tracial invariants are well posed and, in principle, computable on discretizations (e.g. cavity flow and vortex benchmarks).

We construct a family of positive but not completely positive linear maps acting on four dimensional space. We employ these maps to detect bound entanglement in high dimensional quantum systems.

Microwave photon detection is a key technology for low-temperature superconducting electronics and quantum information processing. A promising possibility is to use switching processes in parametric superconducting devices at criticality, which can be triggered by small perturbations. Here we demonstrate the unique sensing properties of the superconducting Kerr parametric resonator when operated in the proximity of the phase transition boundary. We utilize a semiclassical approximation to provide numerical and analytical results for the Heisenberg-Langevin and Fokker-Planck equations that describe the switching mechanism. We show that the probability of switching events is enhanced by probe input states with energies down to single quanta levels.

Molecular optomechanical cavities have recently emerged as a promising platform for frequency upconversion, enabling the quantum coherent conversion of infrared signal into the visible range. In a recent work [F. Zou et al., Phys. Rev. Lett. 132, 153602 (2024)], we proposed an amplification mechanism that can enhance the intensity of the upconverted infrared signals by a factor of 1000 or more within such a cavity under the ideal case without any noise. In this work, we employ the power spectrum method to investigate the noise added to the upconverted signal in a molecular optomechanical cavity along with the conversion efficiency from infrared signal into visible range. In the red-detuned regime, the anti-Stokes sideband achieves superior conversion efficiency relative to the Stokes sideband. Conversely, the Stokes sideband dominates under the blue-detuned condition, which amplifies the infrared signal. We further demonstrate the dependence of the added noise on the coupling strength and decay rates of the system. In particular, we find that when the infrared signal is amplified, the added noise approaches the quantum limit of one quantum.

In this paper, we apply the deterministic quantum imaginary time evolution (QITE) algorithm to obtain the ground state of a two-dimensional pure $\mathbb{Z}_2$ lattice gauge theory. We first construct the set of Pauli operators commuting with Gauss's law constraints, generalizing a previous result. This makes the deterministic QITE gauge-invariant and reduces both the measurement and gate costs significantly without adding extra algorithm errors in the QITE. Then, the classical numerical simulation of the deterministic QITE using tensor networks is performed, and the results are compared with the density matrix renormalization group (DMRG) to evaluate the accuracy of the algorithm. Specifically, we investigate the coupling and system size dependence, and find that the deterministic QITE can achieve a relative error of less than $0.1\%$ up to a twelve-plaquette system and coupling values in a regime that we study. Furthermore, the error dependence on the number of time steps is studied and discussed.

We derive a tight and saturable monogamy relation for three-qubit pure states that bounds the sum of concurrence and concurrence of assistance by the entanglement with an external qubit. The bound decreases strictly with increasing external entanglement, establishing a precise trade-off between internal and environment-induced entanglement. Equivalent formulations in terms of negativity and its convex-roof extensions follow. Our result provides a unified and quantitative constraint on entanglement distribution in open multipartite quantum systems.

We study resonances for the semiclassical magnetic Laplacian in the full plane with a compactly supported magnetic field in the framework of semiclassical complex scaling and black box scattering theory. Assuming that the magnetic field is locally constant, we prove the existence of semiclassical resonances near the Landau levels with exponentially small imaginary parts. We also prove that resonances emerge from a magnetic step discontinuity along a curved interface or a non-degenerate magnetic well, and in the vicinity of anharmonic Landau levels if the field has an isolated zero.

Recently, Hausmann and Renner have pointed out that several famous paradoxes relating to black holes have a similar character to various Extended Wigner's Friend paradoxes. In this paper I consider what the connection between these things could teach us about the Wigner's Friend scenarios. I argue that if we take the analogy between these cases seriously, the black hole paradoxes appear to favour a certain class of response to the Wigner's Friend scenario - specifically, those which posit intrinsic relationality, rather than effective and emergent relationality, and also those which posit some kind of retrocausality.