Quantum Physics Paper Analysis

The stabiliser fragment of quantum theory is a foundational building block for quantum error correction and the fault-tolerant compilation of quantum programs. In this article, we develop a sound, universal and complete denotational semantics for stabiliser operations which include measurement, classically-controlled Pauli operators, and affine classical operations, in which quantum error-correcting codes are first-class objects. The operations are interpreted as certain affine relations over finite fields. This offers a conceptually motivated and computationally-tractable alternative to the standard operator-algebraic semantics of quantum programs (whose time complexity grows exponentially as the state space increases in size). We demonstrate the power of the resulting semantics by describing a small, proof-of-concept assembly language for stabiliser programs with fully-abstract denotational semantics.

Qubit reuse offers a promising way to reduce the hardware demands of quantum circuits, but current approaches are largely restricted to reordering measurements and applying qubit resets. In this work, we present an approach to further optimize quantum circuits by fully utilizing the potential of dynamic quantum circuits-more precisely by moving measurements and introducing dynamic circuit primitives such as classically controlled gates in a way that forges entirely new pathways for qubit reuse. This significantly reduces the number of required qubits for a variety of circuits, creating new opportunities for running complex circuits on near-term devices with limited qubit counts. We show that the proposed approach drastically outperforms existing methods, reducing qubit requirements where previous approaches are unable to do so for popular quantum circuits such as Quantum Phase Estimation (QPE), Quantum Fourier Transform~(QFT), and Variational Quantum Eigensolver (VQE) ansätze, as well as leading to improvements of up to 95% for sparse random circuits.

In recent years, a particularly interesting line of research has focused on designing quantum algorithms for code and lattice problems inspired by Regev's reduction. The core idea is to use a decoder for a given code to find short codewords in its dual. For example, Jordan et al. demonstrated how structured codes can be used in this framework to exhibit some quantum advantage. In particular, they showed how the classical decodability of Reed-Solomon codes can be leveraged to solve the Optimal Polynomial Intersection (OPI) problem quantumly. This approach was further improved by Chailloux and Tillich using stronger soft decoders, though their analysis was restricted to a specific setting of OPI. In this work, we reconcile these two approaches. We build on a recent formulation of the reduction by Chailloux and Hermouet in the lattice-based setting, which we rewrite in the language of codes. With this reduction, we show that the results of Jordan et al. can be recovered under Bernoulli noise models, simplifying the analysis. This characterization then allows us to integrate the stronger soft decoders of Chailloux and Tillich into the OPI framework, yielding improved algorithms.

Clifford noise reduction (CliNR) is a partial error correction scheme that reduces the logical error rate of Clifford circuits at the cost of a modest qubit and gate overhead. The CliNR implementation of an $n$-qubit Clifford circuit of size $s$ achieves a vanishing logical error rate if $snp^2\rightarrow 0$ where $p$ is the physical error rate. Here, we propose a recursive version of CliNR that can reduce errors on larger circuits with a relatively small gate overhead. When $np \rightarrow 0$, the logical error rate can be vanishingly small. This implementation requires $\left(2\left\lceil \log(sp)\right\rceil+3\right)n+1$ qubits and at most $24 s \left\lceil(sp)^4\right\rceil $ gates. Using numerical simulations, we show that the recursive method can offer an advantage in a realistic near-term parameter regime. When circuit sizes are large enough, recursive CliNR can reach a lower logical error rate than the original CliNR with the same gate overhead. The results offer promise for reducing logical errors in large Clifford circuits with relatively small overheads.

State-of-the-art single-qubit gates on superconducting transmon qubits can achieve the fidelities required for error-corrected computations. However, parameter fluctuations due to qubit instabilities, environmental changes, and control inaccuracies make it difficult to maintain this performance. To mitigate the effects of these parameter variations, we numerically derive gates robust to amplitude and frequency errors using gradient ascent pulse engineering (GRAPE). We analyze how fluctuations in qubit frequency, drive amplitude, and coherence affect gate performance over time. The robust pulses suppress coherent errors from drive amplitude drifts over 15 times more than a Gaussian pulse with derivative removal by adiabatic gate (DRAG) corrections. Furthermore, the robust gates, originally designed to compensate for quasi-static errors, also demonstrate resilience to stochastic, time-dependent noise, which is reflected in the dephasing time. They suppress added errors during increases in dephasing by up to 1.7 times more than DRAG.

Equivalence checking of hybrid quantum circuits is of primary importance, given that quantum circuit transformations are omnipresent along the quantum compiler chain. While some approaches exist for automating this task, most focus on the simple case of unitary circuits. At the same time, real quantum computing requires hybrid circuits equipped with measurement operators. Moreover, the few approaches targeting the hybrid case are limited to a restricted class of problems. We propose tackling the Quantum Hybrid Circuit Equivalence Checking problem through lifting unitary circuit verification using a transformation known as deferred measurement. We show that this approach alone significantly outperforms prior work, and that, with the addition of specific unitary-level techniques we call separation and projection, it can handle much larger classes of hybrid circuit equivalence problems. We have implemented and evaluated our method over standard circuit transformations such as teleportation, one-way measurement, or the IBM Qiskit compiler, demonstrating its promises. As a side finding, we have identified and reported several unexpected behaviours with the Qiskit compiler.

One of the main enablers in quantum computing is having qubit control that is precise and fast. However, qubits typically have multilevel structures making them prone to unwanted transitions from fast gates. This leakage out of the computational subspace is especially detrimental to algorithms as it has been observed to cause long-lived errors, such as in quantum error correction. This forces a choice between either achieving fast gates or having low leakage. Previous works focus on suppressing leakage by mitigating the first to second excited state transition, overlooking multi-photon transitions, and achieving faster gates with further reductions in leakage has remained elusive. Here, we demonstrate single qubit gates with a total leakage error consistently below $2.0\times10^{-5}$, and obtain fidelities above $99.98\%$ for pulse durations down to 6.8 ns for both $X$ and $X/2$ gates. This is achieved by removing direct transitions beyond nearest-neighbor levels using a double recursive implementation of the Derivative Removal by Adiabatic Gate (DRAG) method, which we name the R2D method. Moreover, we find that at such short gate durations and strong driving strengths the main error source is from these higher order transitions. This is all shown in the widely-used superconducting transmon qubit, which has a weakly anharmonic level structure and suffers from higher order transitions significantly. We also introduce an approach for amplifying leakage error that can precisely quantify leakage rates below $10^{-6}$. The presented approach can be readily applied to other qubit types as well.

We present a systematic method for translating fault-tolerant quantum circuits between their braiding and lattice surgery (LS) representations within the surface code. Our approach employs the ZX calculus to establish an equivalence between these two paradigms, enabling verified, bidirectional conversion of arbitrary surface-code-level circuits. We show that both braiding and LS operations can be uniformly expressed as compositions of multibody measurements and demonstrate that the Raussendorf compression rule encompasses all known braid and bridge optimizations. We also introduce a novel CNOT circuit with LS. Our framework provides a foundation for the automated verification, compilation, and benchmarking of large-scale surface code computations, advancing toward a unified formal language for topological quantum computation.

Neutral-atom quantum processors employ Rydberg blockade for multiqubit phase operations but lack similar native exchange and conditional exchange gates, which are essential primitives for state verification, fermionic and XY-model simulation, and efficient routing in large qubit arrays. We demonstrate that by lifting the degeneracy between interfering transition pathways, a single Rydberg-excited atom can control state exchange between pairs of atoms. Using this mechanism, we realize a direct controlled-SWAP (Fredkin) operation with more than 99\% fidelity and an order-of-magnitude reduction in circuit depth and reduced exposure to decay and decoherence of Rydberg state components compared with decomposed implementations. The mechanism operates robustly under Doppler broadening at ~150 $μ$K and realistic laser-intensity noise and extends naturally to an entire family of useful gates, including multi-control conditional exchanges (C$_k$-SWAP) and conditional multiplexed SWAP gates. By incorporating controlled exchange operations as native physical operations on neutral atoms, our work provides multiqubit gates that enable higher-order state-verification protocols, occupation-dependent simulations, and conditional routing across optical lattices.

Quantum computing algorithms can be decomposed into a universal set of elementary one- and two-qubit gates. Different physical implementations of quantum computing, however, employ interactions that permit direct conditional dynamics on multiple qubits in a single step. In this work, we leverage quantum optimal control techniques to design single continuous laser pulses that implement multi-qubit controlled-phase, -NOT and -swap (Fredkin) gates on Rydberg atom quantum processors. The identification of robust multi-qubit operations leads to reduced operation time and less decoherence, and the control field provides continuous protection of the atoms from environmental noise. Notably, we find that the controlled-swap (Fredkin) gate, implemented using this approach achieves 99.74\% fidelity while accounting for imperfections such as spontaneous emission, laser fluctuations, and Doppler dephasing.

Quantum error correction (QEC) requires ancilla qubits to extract error syndromes from data qubits which store quantum information. However, ancilla errors can propagate back to the data qubits, introducing additional errors and limiting fault-tolerance. In superconducting quantum circuits, Kerr-cat qubits (KCQs), which exhibit strongly biased noise, have been proposed as ancillas to suppress this back-action and enhance QEC performance. Here, we experimentally demonstrate a beamsplitter interaction between a KCQ and a transmon, realizing an effective $σ_zσ_x$ coupling that can be employed for parity measurements in QEC protocols. We characterize the interaction across a range of cat sizes and drive amplitudes, confirming the expected scaling of the interaction rate. These results establish a step towards hybrid architectures that combine transmons as data qubits with noise-biased bosonic ancillas, enabling hardware-efficient syndrome extraction and advancing the development of fault-tolerant quantum processors.

Quantum computing platforms are evolving to a point where placing high numbers of qubits into a single core comes with certain difficulties such as fidelity, crosstalk, and high power consumption of dense classical electronics. Utilizing distributed cores, each hosting logical data qubits and logical ancillas connected via classical and quantum communication channels, offers a promising alternative. However, building such a system for logical qubits requires additional optimizations, such as minimizing the amount of state transfer between cores for inter-core two-qubit gates and optimizing the routing of magic states distilled in a magic state factory. In this work, we investigate such a system and its statistics in terms of classical and quantum resources. First, we restrict our quantum gate set to a universal gate set consisting of CNOT, H, T, S, and Pauli gates. We then developed a framework that can take any quantum circuit, transpile it to our gate set using Qiskit, and then partition the qubits using the KaHIP graph partitioner to balanced partitions. Afterwards, we built an algorithm to map these graphs onto the 2D mesh of quantum cores by converting the problem into a Quadratic Assignment Problem with Fixed Assignment (QAPFA) to minimize the routing of leftover two-qubit gates between cores and the total travel of magic states from the magic state factory. Following this stage, the gates are scheduled using an algorithm that takes care of the timing of the gate set. As a final stage, our framework reports detailed statistics such as the number of classical communications, the number of EPR pairs and magic states consumed, and timing overheads for pre- and post- processing for inter-core state transfers. These results help to quantify both classical and quantum resources that are used in distributed logical quantum computing architectures.

"Forgetful" measurements-physically similar to dephasing-are of interest both for applications to fault-tolerant quantum computing and fundamentally, in studying how entanglement and entropy spread. This paper investigates measurement-induced phase transitions (MIPT) in random Clifford circuits when measurement outcomes are partially forgotten. Our findings reveal a local thermalization rate that remains constant regardless of system size. We also numerically calculate the decay behavior at the turning points in the entropy diagram. We observe a counterintuitive phenomenon where the entropy reaches a threshold and stops evolving, even as the system size increases. This challenges an intuition, drawn from previous studies of noisy random circuits, that noise will cause the thermalization of the whole system. Additionally, we identify the disappearance of the purification transition and discuss the implications of these entanglement dynamics for quantum error-correction codes.

We propose and validate on real quantum computing hardware a new method for extended two-qubit gate set design, replacing iterative, fine calibration with fast characterization of a small number of gate parameters which are then tracked and corrected in circuit compilation. Coherent contributions to the pulse unitary that would traditionally be considered sources of error are treated as part of the gate definition, and compensated in software via single-qubit rotations. This approach enables rapid device-wide generation of high-fidelity two-qubit entangling gates, which are combined with standard calibrated gates to produce an expanded gate set. We show how these gates are directly usable as part of a quantum compiler, synthesizing generic two-qubit circuit blocks into minimal-duration sequences of the characterized gates interleaved with compensating single-qubit rotations. Benchmarking against circuits compiled using the default $CX$ gate alone on 127-qubit IBM hardware shows up to 7X improvement in success probability for Quantum Fourier Transform circuits up to 26 qubits, and up to 9X lower mean-square error in Trotter simulations of the one-dimensional transverse-field Ising model. Our hardware-agnostic characterization and compilation methodology makes it practical to scale up expressive gate sets on quantum computing architectures while minimizing the need for onerous fine-tuning of low-level control waveforms.

Real-time decoding is crucial for fault-tolerant quantum computing but likely requires specialized hardware such as field-programmable gate arrays (FPGAs), whose parallelism can alter relative algorithmic performance. We analyze FPGA-tailored versions of three decoder classes for quantum low-density parity-check (qLDPC) codes: message passing, ordered statistics, and clustering. For message passing, we analyze the recently introduced Relay decoder and its FPGA implementation; for ordered statistics decoding (OSD), we introduce a filtered variant that concentrates computation on high-likelihood fault locations; and for clustering, we design an FPGA-adapted generalized union-find decoder. We design a systolic algorithm for Gaussian elimination on rank-deficient systems that runs in linear parallel time, enabling fast validity checks and local corrections in clustering and eliminating costly full-rank inversion in filtered-OSD. Despite these improvements, both remain far slower and less accurate than Relay, suggesting message passing is the most viable route to real-time qLDPC decoding.

Nonstabilizerness, or quantum magic, presents a valuable resource in quantum error correction and computation. We study the dynamics of locally injected magic in unitary Clifford circuits, where the total magic is conserved. However, the absence of physical observables quantifying magic precludes a direct microscopic or hydrodynamic description of its local distribution and dynamics. Using insights from stabilizer quantum error correcting codes, we rigorously show that the spatial distribution of magic can be inferred from a canonical representation of low-magic states, dubbed the bipartite magic gauge. Moreover, we propose two operationally relevant magic length scales. We numerically establish that, at early times, both length scales grow ballistically at distinct velocities set by the entanglement velocity, after which magic delocalizes. Our work sheds light on the spatiotemporal structure of quantum resources and complexity in many-body dynamics, opening up avenues for investigating their transport properties and further connections with quantum error correction.

Recent experimental progress in realizing surface code on hardware, including demonstrations of break-even logical memory on devices with up to hundreds of physical qubits, has materially advanced the prospects for fault-tolerant quantum computation. This progress creates urgency for the development of compilation workflows that directly target the forthcoming generation of devices with thousands of physical qubits, for which algorithm execution becomes practical. We develop a pipeline for compiling logical algorithms to physical circuits implementing lattice surgery on the surface code, and use this pipeline to identify the requirements for achieving algorithmic break-even -- where quantum error correction improves the performance of a quantum algorithm -- for two prominent quantum algorithms: the quantum approximate optimization algorithm (QAOA) and quantum phase estimation (QPE). Our pipeline integrates several open-source software tools, and leverages recent advances in error-aware unitary gate synthesis, high-fidelity magic state production, and the calculation of correlation surfaces in the surface code. We perform classical simulations of physical Clifford proxy circuits produced by our pipeline, and find that both 5-qubit QAOA and QPE can reach algorithmic break-even with 2517 physical qubits (surface code distance $d=11$) at physical error rates of $p=10^{-3}$, or 1737 physical qubits ($d=9$) at $p=5\times 10^{-4}$. Our work thereby identifies conditions for achieving algorithmic break-even with near-term quantum hardware and paves the way towards an end-to-end compiler for early-fault-tolerant surface code architectures.

Neutral atom arrays provide a versatile platform for quantum information processing. However, in large-scale arrays, efficient photon collection remains a bottleneck for key tasks such as fast, non-destructive qubit readout and remote entanglement distribution. We propose a cavity-based approach that enables fast, parallel operations over many atoms using multiple modes of a single optical cavity. By selectively shifting the relevant atomic transitions, each atom can be coupled to a distinct cavity mode, allowing independent simultaneous processing. We present practical system designs that support cavity-mode multiplexing with up to 50 modes, enabling rapid mid-circuit syndrome extraction and significantly enhancing entanglement distribution rates between remote atom arrays. This approach offers a scalable solution to core challenges in neutral atom arrays, advancing the development of practical quantum technologies.

High-fidelity numerical methods that model the physical layout of a device are essential for the design of many technologies. For methods that characterize electromagnetic effects, these numerical methods are referred to as computational electromagnetics (CEM) methods. Although the CEM research field is mature, emerging applications can still stress the capabilities of the techniques in use today. The design of superconducting circuit quantum devices falls in this category due to the unconventional material properties and important features of the devices covering nanometer to centimeter scales. Such multiscale devices can stress the fundamental properties of CEM tools which can lead to an increase in simulation times, a loss in accuracy, or even cause no solution to be reliably found. While these challenges are being investigated by CEM researchers, knowledge about them is limited in the broader community of users of these CEM tools. This review is meant to serve as a practical introduction to the fundamental aspects of the major CEM techniques that a researcher may need to choose between to model a device, as well as provide insight into what steps they may take to alleviate some of their challenges. Our focus is on highlighting the main concepts without rigorously deriving all the details, which can be found in many textbooks and articles. After covering the fundamentals, we discuss more advanced topics related to the challenges of modeling multiscale devices with specific examples from superconducting circuit quantum devices. We conclude with a discussion on future research directions that will be valuable for improving the ability to successfully design increasingly more sophisticated superconducting circuit quantum devices. Although our focus and examples are taken from this area, researchers from other fields will still benefit from the details discussed here.

We present optimized quantum circuits for GF$(2^m)$ multiplication and division operations, which are essential computing primitives in various quantum algorithms. Our ancilla-free GF multiplication circuit has the gate count complexity of $O(m^{\log_2{3}})$, an improvement over the previous best bound of $O(m^2)$. This was achieved by developing an efficient $O(m)$ circuit for multiplication by the constant polynomial $1+x^{\lceil{m/2}\rceil}$, a key component of Van Hoof's construction. This asymptotic reduction translates to a factor of 100+ improvement of the CNOT gate counts in the implementation of the multiplication by the constant for parameters $m$ of practical importance. For the GF division, we reduce gate count complexity from $O(m^2 \log(m))$ to $O(m^2 \log \log(m)/\log(m))$ by selecting irreducible polynomials that enable efficient implementation of both the constant polynomial multiplication and field squaring operations. We demonstrate practical advantages for cryptographically relevant values of $m$, including reductions in both CNOT and Toffoli gate counts. Additionally, we explore the complexity of implementing square roots of linear reversible unitaries and demonstrate that a root, although itself still a linear reversible transformation, can require asymptotically deeper circuit implementations than the original unitary.

Quantum Key Distribution (QKD) is revolutionizing cryptography by promising information-theoretic security through the immutable laws of quantum mechanics. Yet, the challenge of transforming these idealized security models into practical, resilient systems remains a pressing issue, especially as quantum computing evolves. In this review, we critically dissect and synthesize the latest advancements in QKD protocols and their security vulnerabilities, with a strong emphasis on rigorous security proofs. We actively categorize contemporary QKD schemes into three key classes: uncertainty principle-based protocols (e.g., BB84), hybrid architectures that enable secure direct communication (eg, three-stage protocol), and continuous-variable frameworks. We further include two modern classes of QKD protocols, namely Twin-field QKD and Device-Independent QKD, both of which were developed to have practical implementations over the last decade. Moreover, we highlight important experimental breakthroughs and innovative mitigation strategies, including the deployment of advanced Quantum Error Correction Codes (QECCs), that significantly enhance channel fidelity and system robustness. By mapping the current landscape, from sophisticated quantum attacks to state-of-the-art error correction methods, this review fills an important gap in the literature. To bring everything together, the relevance of this review concerning quantum augmented networks (QuANets) is also presented. This allows the readers to gain a comprehensive understanding of the security promises of quantum key distribution from theoretical proofs to experimental validations.

Quantum error correction typically requires repeated syndrome extraction due to measurement noise, which results in substantial time overhead in fault-tolerant computation. Single-shot error correction aims to suppress errors using only one round of syndrome extraction. However, for most codes, it requires high-weight checks, which significantly degrade, and often eliminate, single-shot performance at the circuit level. In this work, we introduce local single-shot checks, where we impose constraints on check weights. Using a dynamic measurement scheme, we show that the number of required measurement rounds can be reduced by a factor determined by this constraint. As an example, we show through numerical simulation that our scheme can improve decoding performance compared to conventional checks when using sliding-window decoding with a reduced window size under circuit-level noise models for toric codes. Our work provides a new direction for constructing checks that can reduce time overhead in large-scale fault-tolerant quantum computation.

We present a theoretical scheme for a family of fast and high-fidelity two-qubit iSWAP gates between neutral atoms separated by more than 20 um, enabled by resonant dipole-dipole spin-exchange interactions between Rydberg states. The protocol harnesses coherent excitation-exchange-deexcitation dynamics between the qubit and the Rydberg states within a single and smooth laser pulse, in the presence of strong dipole-dipole interactions. We utilize optimal control methods to achieve theoretical gate fidelities and durations comparable to blockade-based gates in the presence of relevant noise, while extending the effective interaction range by an order of magnitude. This enables entanglement well beyond the blockade radius, offering a route toward fast, high-connectivity quantum processors.

The Gottesman-Kitaev-Preskill (GKP) error correcting code uses a bosonic mode to encode a logical qubit, and has the attractive property that its logical Clifford gates can be implemented using Gaussian unitary gates. In contrast, a direct unitary implementation of the ${T}$ gate using the cubic phase gate has been shown to have logical error floor unless the GKP codestate has a biased noise profile [1]. In this work, we propose a method for on-demand noise biasing based on a standard GKP error correction circuit. This on-demand biasing circuit can be used to bias the GKP codestate before a $T$ gate and return it to a non-biased state afterwards. With the on-demand biasing circuit, we prove that the logical error rate of the $T$ gate can be made arbitrarily small as the quality of the GKP codestates increases. We complement our proof with a numerical investigation of the cubic phase gate subject to a phenomenological noise model, showing that the ${T}$ gate can achieve average gate fidelities above $99\%$ with 12 dB of GKP squeezing without the use of postselection. Moreover, we develop a formalism for finding optimal unitary representations of logical diagonal gates in higher levels of the Clifford hierarchy that is based on a framework of ``polynomial phase stabilizers'' whose exponents are polynomial functions of one of the quadrature operators. This formalism naturally extends to multi-qubit logical gates and even to number-phase bosonic codes, providing a powerful algebraic tool for analyzing non-Clifford gates in bosonic quantum codes. [1] J. Hastrup, M. V. Larsen, J. S. Neergaard-Nielsen, N. C. Menicucci, and U. L. Andersen, Phys. Rev. A 103, 032409 (2021)

Non-Markovian noise, arising from environmental memory effects, is the most general and challenging form of noise in quantum computing, and is typically difficult to characterize and suppress. Here, we analyze and experimentally demonstrate a non-Markovian noise suppression scheme inspired by quantum purification protocols. We theoretically prove that, even without noise calibration and assumptions on specific noise models, the scheme can exponentially reduce non-Markovian error rates with respect to the ancillary system size. We implement the protocol using nuclear spins, demonstrating that non-Markovian noise can be suppressed for both unitary operations and non-unitary channels. The observed fidelities and process tomography show close agreement with theoretical predictions, confirming the practicality and effectiveness of the scheme.

The configuration space, i.e. the Hilbert space, of compound quantum systems grows exponentially with the number of its subsystems: its dimensionality is given by the product of the dimensions of its constituents. Therefore a full quantum treatment is rarely possible analytically and can be carried out numerically for fairly small systems only. Fortunately, in order to obtain interesting physics, approximations often very well suffice. One of these approximations is given by the cumulants expansion, where expectation values of products of operators are approximated by products of expectation values of said operators, neglecting higher-order correlations. The lowest order of this approximation is widely known as the mean field approximation and used routinely throughout quantum physics. Despite its ubiquitous presence, a general criterion for applicability and convergence properties of higher order cumulants expansions remains to be found. In this paper, we discuss two problems in quantum electrodynamics and quantum information, namely the collective radiative dissipation of a dipole-dipole interacting chain of atoms and the factorization of a bi-prime by annealing in an adiabatic quantum simulator. In the first case we find smooth, convergence behavior, where the approximation performs increasingly better with higher orders, while in the latter going beyond mean field turns out useless and, even for small system sizes, we are puzzled by numerically challenging and partly non-physical solutions.

Superconducting parametric amplifiers (SPAs) are critical components for ultralow-noise qubit readout in quantum computing, addressing the critical challenge of amplifying weak quantum signals without introducing noise that degrades coherence and computational fidelity. Unlike classical amplifiers, SPAs can achieve or closely approach quantum-limited performance, specifically the Standard Quantum Limit (SQL) of half a photon of added noise for phase-preserving amplification. The core principle of SPAs relies on parametric amplification, where energy is transferred from a strong pump tone to a weak input signal through non-dissipative nonlinear mixing processes. This is enabled by intrinsic nonlinearities in superconducting materials, primarily kinetic inductance in thin films (e.g., NbTiN, Al) and, more significantly, the Josephson effect in Josephson junctions. These nonlinear elements facilitate frequency mixing (three-wave or four-wave mixing) and can operate in phase-preserving or phase-sensitive amplification modes, with the latter allowing for noise squeezing below the SQL. This chapter emphasizes the significant role of resonator design in determining critical SPA performance metrics such as gain, bandwidth, and noise characteristics. It details both lumped-element (LC) and distributed-element (coplanar waveguide, CPW) resonators, discussing their unique properties, suitability for different frequency ranges, and the importance of achieving high-quality factors (Q) for efficient energy storage and minimal loss. A practical design and simulation of a meandered quarterwavelength CPW resonator coupled to a feed line is presented, illustrating how precise control over geometric parameters optimizes resonant frequency, coupling strength, and quality factor for high-fidelity qubit state discrimination.

Fault tolerance is widely regarded as indispensable for achieving scalable and reliable quantum computing. However, the spacetime overhead required for fault-tolerant quantum computating remains prohibitively large. A critical challenge arises in many quantum algorithms with Clifford + $\varphi$ compiling, where logical rotation gates $R_{Z_L}(\varphi)$ serve as essential components. The Eastin-Knill theorem prevents their transversal implementation in quantum error correction codes and necessitating resource-intensive workarounds through T-gate compilation combined with magic state distillation and injection. In this work, we consider error-structure-tailored fault tolerance, where fault-tolerance conditions are analyzed by combining perturbative analysis of realistic dissipative noise processes with the structural properties of stabilizer codes. Based on this framework, we design 1-fault-tolerant continuous-angle rotation gates in stabilizer codes, implemented via dispersive-coupling Hamiltonians. Our approach could circumvent the need for T-gate compilation and distillation, offering a hardware-efficient solution that maintains simplicity, minimizes physical footprint, and requires only nearest-neighbor interactions. Integrating with recent small-angle-state preparation techniques, we can suppress the gate error to $91|\varphi| p^2$ for small rotation angle (where p denotes the physical error rate). For current achievable hardware parameters ($p=10^{-3}$), this enables reliable execution of over $10^7$ small-angle rotations when $|\varphi|\approx 10^{-3}$, meeting the requirements of many near-term quantum applications. Compared to the 15-to-1 magic state distillation and magic state cultivation approaches, our method reduces spacetime resource costs by factors of 1337.5 and 43.6, respectively, for a Heisenberg Hamiltonian simulation task under realistic hardware assumptions.

In this letter, we introduce a method to synthesize an $n$-qubit Clifford unitary $C$ from the stabilizer tableau of its inverse $C†$, using ancilla qubits and measurements. The procedure uses ancillary $|+\rangle$ states, controlled-Paulis, $X$-basis measurements and single-qubit Pauli corrections on the data qubits (based on the measurement results). This introduces a new normal form for Clifford synthesis, with the number of two-qubit gates required exactly equal to the weight of the stabilizer tableau, and a depth linear in $n$.

TorchQuantumDistributed (tqd) is a PyTorch-based [Paszke et al., 2019] library for accelerator-agnostic differentiable quantum state vector simulation at scale. This enables studying the behavior of learnable parameterized near-term and fault- tolerant quantum circuits with high qubit counts.

Variational quantum algorithms face a fundamental trainability crisis: barren plateaus render optimization exponentially difficult as system size grows. While recent Lie algebraic theory precisely characterizes when and why these plateaus occur, no practical optimization method exists with finite-sample guarantees for navigating them. We present the sequential plateau-adaptive regime-testing algorithm (SPARTA), the first measurement-frugal scheduler that provides explicit, anytime-valid risk control for quantum optimization. Our approach integrates three components with rigorous statistical foundations: (i) a $χ^2$-calibrated sequential test that distinguishes barren plateaus from informative regions using likelihood-ratio supermartingales; (ii) a probabilistic trust-region exploration strategy with one-sided acceptance to prevent false improvements under shot noise; and (iii) a theoretically-optimal exploitation phase that achieves the best attainable convergence rate. We prove geometric bounds on plateau exit times, linear convergence in informative basins, and show how Lie-algebraic variance proxies enhance test power without compromising statistical calibration.

Blocks composed of {CNOT, Rz} are ubiquitous in modern quantum applications, notably in circuits such as QAOA ansatzes and quantum adders. After compilation, many of them exhibit large CNOT counts or depths, which lowers fidelity. Therefore, we introduce HOPPS: a SAT-based hardware-aware optimal phase polynomial synthesis algorithm that could generate {CNOT, Rz} blocks with CNOT count or depth optimality. Sometime {CNOT, Rz} blocks are large, such as in QAOA ansatzes, HOPPS's pursuit of optimality limits its scalability. To address this issue, we introduce an iterative blockwise optimization strategy: large circuits are partitioned into smaller blocks, each block is optimally refined, and the process is repeated for several iterations. Empirical results show that HOPPS is more efficient comparing with existing near optimal synthesis tools. Used as a peephole optimizer, HOPPS reduces the CNOT count by up to 50.0% and the CNOT depth by up to 57.1% under OLSQ. For large QAOA circuit, after mapping by Qiskit, circuit can be reduced CNOT count and depth by up to 44.4% and 42.4% by our iterative blockwise optimization. Index Terms-Phase Polynomial, Quantum Circuit Synthesis, Quantum Circuit Optimization.

This work establishes a new probabilistic bound on the number of elements to generate finite nilpotent groups. Let $\varphi_k(G)$ denote the probability that $k$ random elements generate a finite nilpotent group $G$. For any $0 < ε< 1$, we prove that $\varphi_k(G) \ge 1 - ε$ if $k \ge \operatorname{rank}(G) + \lceil \log_2(2/ε) \rceil$ (a bound based on the group rank) or if $k \ge \operatorname{len}(G) + \lceil \log_2(1/ε) \rceil$ (a bound based on the group chain length). Moreover, these bounds are shown to be nearly tight. Both bounds sharpen the previously known requirement of $k \ge \lceil \log_2 |G| + \log_2(1/ε) \rceil + 2$. Our results provide a foundational tool for analyzing probabilistic algorithms, enabling a better estimation of the iteration count for the finite Abelian hidden subgroup problem (AHSP) standard quantum algorithm and a reduction in the circuit repetitions required by Regev's factoring algorithm.

In this paper, we propose a novel approach for optimizing the linear layer used in symmetric cryptography. It is observed that these matrices often have circulant structure. The basic idea of this work is to utilize the property to construct a sequence of transformation matrices, which allows subsequent heuristic algorithms to find more efficient implementations. Our results outperform previous works for various linear layers of block ciphers. For Whirlwind M0 , we obtain two implementations with 159 XOR counts (8% better than Yuan et al. at FSE 2025) and depth 17 (39% better than Shi et al. at AsiaCrypt 2024) respectively. For AES MixColumn, our automated method produces a quantum circuit with depth 10, which nearly matches the manually optimized state-of-the-art result by Zhang et al. at IEEE TC 2024, only with 2 extra CNOTs.

Quantum technologies offer significant advancements in information processing and communication, notably in the domain of random number generation (RNG). The use of Bell inequalities enables users to certify the randomness of outputs produced by untrusted quantum RNG devices. We present a method for quantitatively analyzing Bell expressions used to certify randomness in quantum systems. Using this method, we conducted a comprehensive analysis on more than half a million Bell expressions involving configurations with four measurement settings for one party and three for the other. We identified five notable examples based on entropy scores under varying levels of white noise. As an extension of these results, we further incorporate the concept of self-testing for boxes (Banacki et al 2022, New J. Phys. 24 083003), enabling a more comprehensive characterization of quantum correlations through the evaluation of $Boxes(α, B)$ and the corresponding measure $Flex(α, B)$.

The basic element of circuit quantum electrodynamics (cQED) is a cavity resonator strongly coupled to a superconducting qubit. Since the inception of the field, the choice of the cavity frequency was, with a few exceptions, been limited to a narrow range around 7 GHz due to a variety of fundamental and practical considerations. Here we report the first cQED implementation, where the qubit remains a regular transmon at about 5 GHz frequency, but the cavity's fundamental mode raises to 21 GHz. We demonstrate that (i) the dispersive shift remains in the conventional MHz range despite the large qubit-cavity detuning, (ii) the quantum efficiency of the qubit readout reaches 8%, (iii) the qubit's energy relaxation quality factor exceeds $10^7$, (iv) the qubit coherence time reproducibly exceeds $100~μ\rm{s}$ and can reach above $300~μ\rm{s}$ with a single echoing $π$-pulse correction. The readout error is currently limited by an accidental resonant excitation of a non-computational state, the elimination of which requires minor adjustments to the device parameters. Nevertheless, we were able to initialize the qubit in a repeated measurement by post-selection with $2\times 10^{-3}$ error and achieve $4\times 10^{-3}$ state assignment error. These results encourage in-depth explorations of potentially transformative advantages of high-frequency cavities without compromising existing qubit functionality.

Large atomic-orbital (AO) basis sets of at least triple and preferably quadruple-zeta (QZ) size are required to adequately converge Kohn-Sham density functional theory (DFT) calculations towards the complete basis set limit. However, incrementing the cardinal number by one nearly doubles the AO basis dimension, and the computational cost scales as the cube of the AO dimension, so this is very computationally demanding. In this work, we develop and test a natural atomic orbital (NAO) scheme in which the NAOs are obtained as eigenfunctions of atomic blocks of the density matrix in a one-center orthogonalized representation. The NAO representation enables one-center compression of the AO basis in a manner that is optimal for a given threshold, by discarding NAOs with occupation numbers below that threshold. Extensive tests using the Hartree-Fock functional suggest that a threshold of $10^{-5}$ can yield a compression factor (ratio of AO to compressed NAO dimension) between 2.5 and 4.5 for the QZ pc-3 basis. The errors in relative energies are typically less than 0.1 kcal/mol when the compressed basis is used instead of the uncompressed basis. Between 10 and 100 times smaller errors (i.e., usually less than 0.01 kcal/mol) can be obtained with a threshold $10^{-7}$, while the compression factor is typically between 2 and 2.5.

Quantum architecture search (QAS) automates the design of parameterized quantum circuits for variational quantum algorithms. The framework finds a well-suited problem-specific structure of a variational ansatz. Among possible implementations of QAS the reinforcement learning (RL) stands out as one of the most promising. Current RL approaches are single-agent-based and show poor scalability with a number of qubits due to the increase of the action space dimension and the computational cost. We propose a novel multi-agent RL algorithm for QAS with each agent acting separately on its own block of a quantum circuit. This procedure allows to significantly accelerate the convergence of the RL-based QAS and reduce its computational cost. We benchmark the proposed algorithm on MaxCut problem on 3-regular graphs and on ground energy estimation for the Schwinger Hamiltonian. In addition, the proposed multi-agent approach naturally fits into the set-up of distributed quantum computing, favoring its implementation on modern intermediate scale quantum devices.

We uncover a class of nonlinear odd viscoelastic effects in three spatial dimensions. We show that these dissipationless effects arise upon combining strains in two orthogonal directions, yielding momentum flow in the third direction. We demonstrate that the effect arises from nontrivial geometric tensors in quantum states, and can be scaled up with integer topological invariants. We further demonstrate that the effect fingerprints the multiband Hilbert-space geometry of underlying quantum states, as encoded in three-state geometric tensors. Our findings unravel the role of multistate geometry in viscoelastic phenomena, paving a path for experimental observation of uncharted nonlinear odd viscoelastic responses in quantum systems.

Entangled photons are fundamental resources for quantum communication, computing, and networking. Among them, polarization-entangled photon pairs play an important role due to their straightforward state manipulation and direct use in quantum key distribution, teleportation, and network protocols. However, realizing compact, efficient, and scalable polarization-entangled sources that meet the requirements of practical deployment remains a major challenge. Here, we present a simple yet high-performance on-chip polarization-entangled photon-pair source on thin-film lithium niobate (TFLN). Our device employs dual quasi-phase matching (D-QPM) that sequentially supports type-0 and type-I spontaneous parametric down-conversion in a single nanophotonic waveguide, eliminating the need for interferometers, polarization rotators, or other complex circuits. The source directly produces high-fidelity Bell states with broad bandwidth, high brightness, and low noise. Using this integrated platform, we realize wavelength-multiplexed entanglement distribution in a four-user quantum network deployed over metropolitan fiber links up to 50 km. These results establish a robust and scalable pathway toward practical quantum communication systems and multi-user quantum mesh networks based on integrated photonics.

This paper develops the foundations of Quantum Granular Computing (QGC), extending classical granular computing including fuzzy, rough, and shadowed granules to the quantum regime. Quantum granules are modeled as effects on a finite dimensional Hilbert space, so granular memberships are given by Born probabilities. This operator theoretic viewpoint provides a common language for sharp (projective) and soft (nonprojective) granules and embeds granulation directly into the standard formalism of quantum information theory. We establish foundational results for effect based quantum granules, including normalization and monotonicity properties, the emergence of Boolean islands from commuting families, granular refinement under Luders updates, and the evolution of granules under quantum channels via the adjoint channel in the Heisenberg picture. We connect QGC with quantum detection and estimation theory by interpreting the effect operators realizing Helstrom minimum error measurement for binary state discrimination as Helstrom type decision granules, i.e., soft quantum counterparts of Bayes optimal decision regions. Building on these results, we introduce Quantum Granular Decision Systems (QGDS) with three reference architectures that specify how quantum granules can be defined, learned, and integrated with classical components while remaining compatible with near term quantum hardware. Case studies on qubit granulation, two qubit parity effects, and Helstrom style soft decisions illustrate how QGC reproduces fuzzy like graded memberships and smooth decision boundaries while exploiting noncommutativity, contextuality, and entanglement. The framework thus provides a unified and mathematically grounded basis for operator valued granules in quantum information processing, granular reasoning, and intelligent systems.

Infinite projected entangled-pair states (iPEPS) provide a powerful tensor network ansatz for two-dimensional quantum many-body systems in the thermodynamic limit. In this paper we introduce an approach to accurately compute the energy variance of an iPEPS, enabling systematic extrapolations of the ground-state energy to the exact zero-variance limit. It is based on the contraction of a large cell of tensors using the corner transfer matrix renormalization group (CTRMG) method, to evaluate the correlator between pairs of local Hamiltonian terms. We show that the accuracy of this approach is substantially higher than that of previous methods, and we demonstrate the usefulness of variance extrapolation for the Heisenberg model, for a free fermionic model, and for the Shastry-Sutherland model. Finally, we apply the approach to compute $\langle \langle \mathcal{L}^\dagger \mathcal{L} \rangle \rangle$ for an open quantum system described by the Liouvillian $\mathcal{L}$, in order to assess the quality of the steady-state solution and to locate first-order phase transitions, using the dissipative quantum Ising model as an example.

Out-of-time-order correlators (OTOCs) are central probes of quantum scrambling, and their generalizations have recently become key primitives for both benchmarking quantum advantage and learning the structure of Hamiltonians. Yet their behavior has lacked a unified algorithmic interpretation. We show that higher-order OTOCs naturally fit within the framework of quantum signal processing (QSP): each $\mathrm{OTOC}^{(k)}$ measures the $2k$-th Fourier component of the phase distribution associated with the singular values of a spatially resolved truncated propagator. This explains the contrasting sensitivities of time-ordered correlators (TOCs) and higher-order OTOCs to causal-cone structure and to chaotic, integrable, or localized dynamics. Based on this understanding, we further generalize higher-order OTOCs by polynomial transformation of the singular values of the spatially resolved truncated propagator. The resultant signal allows us to construct frequency-selective filters, which we call \emph{OTOC spectroscopy}. This extends conventional OTOCs into a mode-resolved tool for probing scrambling and spectral structure of quantum many-body dynamics.

Two photons from the ground state para-positronium annihilation are emitted in a maximally entangled singlet state of orthogonal polarizations. In case of the Compton scattering of both photons the phenomenon of quantum entanglement leads to a measurable increase in the azimuthal correlations of scattered photons, as opposed to a classical description treating the two scattering events as independent. The probability of the scattering of the system of the entangled photons is described by the Pryce-Ward cross section dependent on a difference of the azimuthal scattering angles in the fixed coordinate frame, while the independent scattering of single photons is described by the Klein-Nishina cross section dependent on the azimuthal angle relative to each photon's initial polarization. Since the singlet state of orthogonal polarizations is rotationally invariant, it does not carry any physical information on the initial polarizations of the single annihilation photons. In such bipartite state the angular origin for the Klein-Nishina cross section is undefined, making the Pryce-Ward and Klein-Nishina descriptions mutually exclusive. However, semi-classical simulations of the joint Compton scattering of entangled photons - implementing the Pryce-Ward cross section, but still treating the two photons as separate entities - can reconcile the Pryce-Ward correlations with the Klein-Nishina statistics for single photons by implementing a modified version of a scattering cross section presented in this work.

Modified divacancies in the 4H polytype of silicon carbide (SiC) exhibit enhanced charge stability and spin addressability at room temperature, making them highly attractive for quantum applications. However, their low formation yield, both at the single-defect and ensemble levels, has limited further progress. Here, we demonstrate a controllable and efficient method for generating modified divacancy color centers in 4H-SiC via oxygen-ion implantation. Based on their distinct optical signatures and spin-resonance characteristics, we experimentally resolve four types of modified divacancies. Remarkably, single modified divacancies constitute above 90% of the total defect population and exhibit superior optical properties and spin coherence compared with defects created through conventional carbon- or nitrogen-ion implantation. We characterize the zero-phonon lines of these modified divacancies and reveal a distinct temperature-dependent behavior in the spin-readout contrast. By systematically optimizing the implantation dose and annealing temperature, we further achieve high-density ensembles and observe clear Rabi-oscillation beating patterns associated with different orientations of basal-type defects. These results establish oxygen-ion implantation as a powerful and versatile approach to engineering high-quality spin-active defects in SiC, representing a significant advance toward scalable solid-state quantum technologies. Furthermore, our findings provide key insights into the atomic configurations of modified divacancies in 4H-SiC.

Lie Algebras are powerful mathematical structures used in physics to describe sets of operators and associated combinations. A central task is to identify a minimal set of generators from which the algebra can be constructed. The classical search for such generators has so far relied on greedy construction steps applied to an exponentially growing number of candidate operators, making it rapidly computationally intractable. We propose a general, polynomial-scaling and optimal strategy, based on Lie-Algebraic basic properties, to overcome this bottleneck. It allows for the efficient construction of these generators, also known as Minimal Complete Pools (MCPs), for a target Lie Algebra. As an immediate application, efficiently constructing user-defined MCPs that respect fermionic algebra is crucial in the context of adaptive Variational Quantum Eigensolver for quantum chemistry. Thus, we introduce MB-ADAPT-VQE, which incorporates optimally constructed MCPs into batched ADAPT-VQE to reduce quantum resources and improve convergence under strong correlation. These MCPs also unlock fixed-ansatz methods based on a Lie-algebraic structure such as the gradient-free NI-DUCC-VQE, enabling simulations surpassing prior MCP limits. The presented mathematical framework is general and applicable well beyond chemistry in fields including quantum error correction, quantum control, quantum machine learning, and more universally wherever compact Pauli basis are required.

The Kibble-Zurek mechanism (KZM) successfully predicts the density of topological defects deposited by the phase transitions, but it is not clear why. Its key conjecture is that, near the critical point of the second-order phase transition, critical slowing down will result in a period when the system is too sluggish to follow the potential that is changing faster than its reaction time. The correlation length at the freeze-out instant $\hat t$ when the order parameter catches up with the post-transition broken symmetry configuration is then decisive, determining when the mosaic of broken symmetry domains locks in topological defects. To understand why the KZM works so well we analyze Landau-Ginzburg model and show why temporal evolution of the order parameter plays such a key role. The analytical solutions we obtain suggest novel, hitherto unexplored, experimentally accessible observables that can shed light on symmetry breaking dynamics while testing the conjecture on which the KZM is based.

Photon-pressure circuits are the circuit implementation of the cavity optomechanical Hamiltonian and discussed for qubit readout, low-frequency quantum photonics and dark matter axion detection. Due to the enormous design flexibility of superconducting circuits, photon-pressure systems provide fascinating possibilities to explore unusual parameter regimes of the optomechanical Hamiltonian. Here, we report the realization of a photon-pressure platform, in which a GHz circuit interacts with a MHz circuit via a magnetic-flux-tunable combination of dispersive and dissipative photon-pressure. In addition, both coupling rates are considerably enhanced by nonlinearities of the GHz-mode, which leads to the multi-photon coupling rates scaling stronger with the pump photon number $n_\mathrm{c}$ than the usual $\sqrt{n_\mathrm{c}}$ dependence. We demonstrate that interference of the two interaction paths leads to a Fano-like response in photon-pressure induced transparency, and that the dynamical backaction is considerably modified compared to the dispersive case, including a parametric instability caused by a red-detuned pump tone.

Bell inequalities limit the possible observations of non-communicating parties. Here, we present analogous inequalities for any number of communicating parties under the causal constraints of static causal order, definite causal order, and bi-causal order. All derived inequalities are remarkably simple. They correspond to upper bounds on the winning chance in graphical games: Given a specific directed graph over the parties, the parties are challenged to communicate along a randomly chosen arc. In the case of definite causal order, every game that we find is specified by a kefalopoda digraph. Based on this we define weakly causal correlations as those that satisfy all kefalopoda inequalities. We show that the problem of deciding whether some correlations are weakly causal is solvable in polynomial time in the number of parties.

The two main notions of control in quantum programming languages are often referred to as "quantum" control and "classical" control. With the latter, the control flow is based on classical information, potentially resulting from a quantum measurement, and this paradigm is well-suited to mixed state quantum computation. Whereas with quantum control, we are primarily focused on pure quantum computation and there the "control" is based on superposition. The two paradigms have not mixed well traditionally and they are almost always treated separately. In this work, we show that the paradigms may be combined within the same system. The key ingredients for achieving this are: (1) syntactically: a modality for incorporating pure quantum types into a mixed state quantum type system; (2) operationally: an adaptation of the notion of "quantum configuration" from quantum lambda-calculi, where the quantum data is replaced with pure quantum primitives; (3) denotationally: suitable (sub)categories of Hilbert spaces, for pure computation and von Neumann algebras, for mixed state computation in the Heisenberg picture of quantum mechanics.

Pure states are usually used to observe quantum phenomena. In this study, we show that a quantum superposition of spatially displaced mixed cat states can be generated within an optical waveguide via nonparaxial unitary evolution of the initial low coherence (low purity) light beam. It is shown that highly mixed Schrodinger cat states can be observed at a well-defined propagation distance. The importance of the long-term decoherence and recoherence of the original wave packet in observing the mixed cat states is demonstrated. The Heisenberg and Schrodinger-Robertson uncertainty relations for mixed cat states are evaluated. We have demonstrated the feasibility of our method using accurate numerical simulations for the parameters of the source and optical waveguide available in practice.

Efficient fidelity estimation of multiqubit quantum states is crucial to many applications in quantum information processing. However, to estimate the infidelity $ε$ with multiplicative precision, conventional estimation protocols require (order) $1/ε^2$ different circuits in addition to $1/ε^2$ samples, which is quite resource-intensive for high-precision fidelity estimation. Here we introduce an efficient estimation protocol by virtue of common randomized measurements (CRM) integrated with shadow estimation based on the Clifford group, which only requires $1/ε$ circuits. Moreover, in many scenarios of practical interest, in the presence of depolarizing or Pauli noise for example, our protocol only requires a constant number of circuits, irrespective of the infidelity $ε$ and the qubit number. For large and intermediate quantum systems, quite often one circuit is already sufficient. In the course of study, we clarify the performance of CRM shadow estimation based on the Clifford group and 4-designs and highlight its advantages over standard and thrifty shadow estimation.

In this work we derive the replica field theory for monitored quantum many-body systems evolving under the quantum jumps protocol, corresponding to a non-Hermitian evolution interspersed with random quantum jumps whose distribution is state-dependent. We show that the density matrix of $R$ replicas evolves according to a master equation where the non-Hermitian term is replica-diagonal while coupling among replicas are due to quantum jumps. We write down the associated Keldysh action and study its behavior for the specific case of the Ising Chain with monitoring of particle density and tunable anisotropy, interpolating between free fermions with strong U(1) symmetry and the Ising chain with Z$_2$ symmetry. We derive the effective field theory in terms of slowly varying fields and obtain the replica-diagonal saddle point, which we show to describe the average state. We then go beyond saddle point and derive the effective field theory describing the replica off-diagonal sector, which takes the form of a Non-Linear Sigma Model. The symmetry class is either DIII or D, depending on the parameters of the Ising chain, except at a special symmetric point, where we recover the results for free fermions. We discuss the implications of these findings for the entangling phase observed numerically for the monitored Ising chain.

Fidelity is the standard measure for quantifying the similarity between two quantum states. It is equal to the square of the minimum Bhattacharyya coefficient between the probability distributions induced by quantum measurements on the two states. Though established for over thirty years, the structure of fidelity-optimal quantum measurements remains unclear when the two density operators are singular (not invertible). Here we address this gap, with a focus on minimal optimal measurements, which admit no nontrivial coarse graining that is still optimal. We show that there exists either a unique minimal optimal measurement or infinitely many inequivalent choices. Moreover, the first case holds if and only if the two density operators satisfy a weak commutativity condition. In addition, we provide a complete characterization of all minimal optimal measurements when one state is pure, leveraging geometric insights from the Bloch-sphere representation. The connections with quantum incompatibility, operator pencils, and geometric means are highlighted.

We report electrical spin state readout and coherent control of a small ensemble (<450) of silicon vacancies in a silicon carbide-on-insulator (SiCOI) platform, with excitation wavelengths from 780 to 990 nm. Demonstrating for the first time spin state readout well beyond the zero phonon line of the V2 silicon vacancies. By implementing photoelectrical detection of magnetic resonance (PDMR) in thin-film SiCOI, we merge a scalable and optics-free spin readout technique together with a promising platform for scalable and CMOS-compatible integrated photonics. Furthermore, we provide a comparison of optical and electrical readout between bulk SiC and thin-film SiCOI, revealing that our thin-film processing has no significant effect on the bulk T2 time of ~ 7 microseconds. These results establish SiCOI as a versatile platform for not only integrated photonics but also electronic and spin-based devices for scalable quantum technologies over a wide range of excitation wavelengths.

We report an experimental demonstration of room-temperature Hong-Ou-Mandel (HOM) interference at a radio-wave frequency of 120 MHz using conditional build-up of quantum states from classical phase-averaged coherent states. This approach enables observation of quantum effects in spectral regimes where conventional single-photon sources and detectors are unavailable or require cryogenic conditions. By constructing a high-fidelity approximation of a single-photon state with phase-averaged coherent states, we observe the normalized second-order intensity correlation dips significantly below the classical limit of 0.5. The method allows for tunable noise suppression via optimization of the state representation. Our results establish the feasibility of using conditionally prepared classical states to simulate quantum interference phenomena in the radio-frequency domain. This technique opens the door to realizing other quantum protocols, such as Bell inequality tests, in frequency ranges where standard quantum technologies are currently infeasible.

The unitary cluster Jastrow (UCJ) ansatz and its variant known as local UCJ (LUCJ) are promising choices for variational quantum algorithms for chemistry due to their combination of physical motivation and hardware efficiency. The parameters of these ansatzes can be initialized from the output of a coupled cluster, singles and doubles (CCSD) calculation performed on a classical computer. However, truncating the number of repetitions of the ansatz, as well as discarding interactions to accommodate the connectivity constraints of near-term quantum processors, degrade the approximation to CCSD and the resulting energy accuracy. In this work, we propose two methods to improve the parameter initialization. The first method, which is applicable to both expectation value- and sample-based algorithms, uses compressed double factorization of the CCSD amplitudes to improve or recover the CCSD approximation. The second method, which is applicable to sample-based algorithms, uses approximate tensor network simulation to improve the quality of samples produced by the ansatz circuit. We validate our methods using exact state vector simulation on systems of up to 52 qubits, as well as experiments on superconducting quantum processors using up to 65 qubits. Our results indicate that our methods can significantly improve the output of both expectation value- and sample-based quantum algorithms.

We establish a connection between quantum mechanics and computation, revealing fundamental limitations for algorithms computing spectra, especially in non-Hermitian settings. Introducing the concept of locally trivial pseudospectra (LTP), we show such assumptions are necessary for spectral computation. LTP adapts dynamically to system energies, enabling spectral analysis across a broad class of challenging non-Hermitian problems. Exploiting this framework, we overcome a longstanding obstacle by computing the eigenvalues and eigenfunctions of the imaginary cubic oscillator $H_{\mathrm{B}} = p^2 + i x^3$ with error bounds and no spurious modes -- yielding, to our knowledge, the first such error-controlled result. We confirm, for instance, the 100th eigenvalue as $627.6947122484365113526737029011536\ldots$. Here, truncation-induced $\mathcal{PT}$-symmetry breaking causes spurious eigenvalues -- a pitfall our method avoids, highlighting the link between truncation and physics. Finally, we illustrate the approach's generality via spectral computations for a range of physically relevant operators. This letter provides a rigorous framework linking computational theory to quantum mechanics and offers a precise tool for spectral calculations with error bounds.

In a recent work [B. J. P. Jones and J. A. Formaggio, Phys. Rev. Lett. 135, 111801 (2025)], the possibility of superradiant neutrino emission from atomic condensates has been theoretically proposed. Subsequent analysis by Y. K. Lu, H. Lin, and W. Ketterle [arXiv:2510.21705] questioned this scenario, emphasizing the limiting role of the fermionic nature of the decayed atoms. In this study, we revisit the problem and discuss under which conditions collective emission phenomena might still emerge in cold-atom systems.

Studying the performance of a quantum interferometer coupled to an external environment is a problem of conceptual and practical importance. If we consider a quantum interferometer featuring Heisenberg-limited sensitivity, then a typical result is that introducing coupling with the environment degrades the sensitivity to the shot-noise limit. Here we argue that this result crucially depends on whether the interferometer-environment coupling term is subject (or not) to the so-called Kac rescaling that restores extensivity, i.e., whether the coupling Hamiltonian is extensive or not. We present results of the Lindblad equation in the presence and absence of Kac rescaling of the coupling constant. Our results show that for a linear coupling and a harmonic model of the environment, often used in modeling of a quantum interferometer coupled with an environment, the Heisenberg-limited sensitivity may be restored after the Kac rescaling. This result points out the need and the importance to characterize the (model of the) environment of the interferometer at hand.

Berry monopoles always cancel when summing over a complete set of energy eigenstates. We demonstrate that analogous sum rules exist for geometric phases and their underlying 2-forms in non-adiabatic evolution. Our result has implications for qudit computation as it limits the types of gates that can be implemented by purely geometric means.

Catalysis refers to the possibility of performing an otherwise impossible local state transformation by sharing an additional state, i.e. a catalyst, which is returned at the end of the protocol. There is a stronger version, known as supercatalysis, in which the borrowed catalyst is returned in an enhanced form, i.e. more entangled. However, this phenomenon has remained little explored. In this work we introduce the supercatalytic entanglement gain as a figure of merit taking values in [0,1] that quantifies the performance of the protocol (with 0 corresponding to the standard case of catalysis and 1 representing the maximal possible gain) and we study in which cases it can be greater than zero and which strategies can maximize it. While it turns out that every catalytic transformation can be implemented in a supercatalytic fashion with entanglement gain equal to 1 if the state that is borrowed is chosen appropriately, other choices can make the gain strictly less than 1 and even 0. In fact, we prove that a large class of catalytic transformations are not fully supercatalyzable, i.e. there is at least one choice of catalyst for which the entanglement gain vanishes. On the other hand, the construction that shows that supercatalysis is always possible with maximal gain uses artificially highly entangled catalysts. For this reason, we also study minimal supercatalysis, where the entanglement content of the borrowed state is constrained in a precise and natural way. While we consider a scenario where we prove it is impossible to have entanglement gain equal to 1 in this case, we show that there exist minimal supercatalytic transformations with gain as close to 1 as desired. We also explore several examples and observe that, although choosing a catalyst with the least possible entanglement is often an optimal strategy for minimal supercatalysis, this is not necessarily always the case.

We propose a quantum-enhanced picostrain sensor that achieves Heisenberg-limited strain sensing using superconducting qubits. A strain-sensitive qubit s Hamiltonian is coupled to the momentum quadrature of a microwave resonator, transducing mechanical strain $ε$ into amplified spatial displacements of the resonator s phase space. Using homodyne detection of the resonator field and multipartite entanglement of N qubits, the protocol achieves a strain sensitivity $Δε\sim pε$ (picostrain), two orders of magnitude better than classical sensors. The scheme integrates natively with superconducting processors, enabling in-situ diagnostic and nanoscale material characterization.

We introduce a theory of quantum resource degradation grounded in a decomposition of observational entropy, which partitions the total resource into inter-block coherence ($\mathcal{C}_{\text{rel}}$) and intra-block noise ($\mathcal{D}_{\text{rel}}$). Under free operations, the total quantum resource is transformed into classical noise while its overall quantity remains conserved. We demonstrate that the metric $η$ functions as a diagnostic indicator, providing a new lens on optimization stagnation, particularly the barren plateau phenomenon (BPP) in variational quantum algorithms (VQAs). We substantiate this framework through rigorous mathematical analysis and numerical simulations, and we explore how these channels can be physically implemented in real quantum systems. Our approach offers a unified viewpoint on quantum thermalization, measurement-induced disturbance, and the degradation of quantum advantage in practical devices, while also improving optimization strategies for current and near-term noisy quantum hardware.

Most quantum batteries studied so far with notable exception of Sachdev-Ye-Kitaev (SYK) batteries are based on integrable models, where superlinear scaling of charging power and hence a quantum advantage can be achieved, but at the cost of unstable stored energy due to integrability. Here, by considering the sunburst quantum Ising battery driven by periodic delta-kicks, we show that in the quantum chaotic regime a quantum advantage is achieved for number of batteries $n_b\leq 4$, together with excellent stability of energy storage. In the integrable regime optimal energy storage and extraction are possible irrespective of the initial state of the charger. Finally, we show that the observed advantage does not originate from multipartite entanglement within the battery subsystem and is therefore classical in nature.

Collective effects, such as superradiance and subradiance are central to emerging quantum technologies -- from sensing to energy storage -- and play an important role in light-harvesting. These effects enhance or suppress rates of dynamic processes (absorption, emission, and transfer) due to the formation of symmetric or antisymmetric collective states. However, collective effects in different contexts -- absorption, emission, and transfer -- have often been defined disparately, especially across different communities, leading to results that are not immediately transferable between different contexts. Here, we describe all three types of collective effects using a common Dicke framework that resolves the apparent discrepancies between different approaches. It allows us to generalise previously known collective effects involving spins into new ones involving aggregates of harmonic oscillators or other degrees of freedom. It also explains how collective effects can be engineered to be robust against both disorder and noise, paving the way for more resilient quantum devices.

An array of initially excited emitters coupled to a one-dimensional waveguide exhibits superradiant decay under the Born-Markov approximation, manifested as a coherent burst of photons in the output field. In this work, we employ tensor-network methods to investigate its non-Markovian dynamics induced by finite time delays in photon exchange among the emitters. We find that the superradiant burst breaks into a structured train of correlated photons, each intensity peak corresponding to a specific photon number. We quantify the emitter-photon and emitter-emitter entanglement generated during this process and show that the latter emerges in the long-time limit, as part of the excitation becomes trapped within the emitters' singlet subspace. We finally consider the decay of the system's most radiant state, the symmetric Dicke state, and show that time delay can lead to decay rates exceeding those predicted by the Markovian approximation.

Quantum computing has the potential to transform simulations of quantum many-body problems at the heart of electronic structure theory. Efficient quantum algorithms to compute the eigenstates of fermionic Hamiltonians, such as quantum phase estimation, rely critically on high-accuracy initial state preparation. While several state preparation algorithms have been proposed for fermionic ground states, the preparation of excited states remains a major challenge, limiting the applicability of quantum algorithms to photochemistry and photophysics. In this contribution, we describe a physically motivated adiabatic state preparation technique for low-lying excited states using the explicit coupling between electrons and photons. Our approach systematically converges to the first optically accessible excited state and can target different symmetry sectors by changing the photon polarization. We demonstrate the preparation of high-fidelity excited states for the Hubbard model and methylene molecule across a range of correlation regimes, and perform a successful hardware implementation for a model Hamiltonian.

Quantum networks are becoming increasingly important because of advancements in quantum computing and quantum sensing, such as recent developments in distributed quantum computing and federated quantum machine learning. Routing entanglement in quantum networks poses several fundamental as well as technical challenges, including the high dynamicity of quantum network links and the probabilistic nature of quantum operations. Consequently, designing hand-crafted heuristics is difficult and often leads to suboptimal performance, especially if global network topology information is unavailable. In this paper, we propose RELiQ, a reinforcement learning-based approach to entanglement routing that only relies on local information and iterative message exchange. Utilizing a graph neural network, RELiQ learns graph representations and avoids overfitting to specific network topologies - a prevalent issue for learning-based approaches. Our approach, trained on random graphs, consistently outperforms existing local information heuristics and learning-based approaches when applied to random and real-world topologies. When compared to global information heuristics, our method achieves similar or superior performance because of its rapid response to topology changes.

The quasi-particle excitations in Weyl semimetals, known as Weyl fermions, are usually forced to emerge in charge-conjugate pairs by the Nielsen--Ninomiya theorem. When the Brillouin zone is non-orientable, this constraint is replaced by a $\mathbb{Z}_2$ charge cancellation, as a result of the chirality becoming ill-defined on such manifolds; this results in configurations with seemingly non-zero total chirality. Here, we set out to explain this behaviour from a purely topological perspective, and provide a classification of non-orientable Weyl semimetal topology in terms of exact sequences of twisted (co)homology groups. This leads to several discoveries of direct physical importance: in particular, we recover the $\mathbb{Z}_2$ charge cancellation in a coordinate-independent way, allowing meaningful limits to be set on its physical interpretation. A detailed discussion is provided on a specific Klein bottle-like topology induced by a momentum-space glide symmetry, including a full review of the insulating and semimetallic invariants of the system and a classification of the surface states on the non-orientable boundary. Beyond this, we provide a complete survey of all possible non-orientable Brillouin zones and their associated invariants, and extend our formalism into the realm of non-Hermitian topological physics and inversion-symmetric Weyl semimetals. Our work exemplifies the vast potential of fundamental mathematical descriptions to not only aid the corresponding physical intuition, but also predict novel and hitherto overlooked phenomena of great relevance throughout the physics research forefront.

Harmonic oscillators are promising continuous-variable (CV) quantum resources because their infinite-dimensional Hilbert spaces allow for resource-efficient quantum computing and simulation. To reach their full potential, CV platforms need to be able to efficiently implement non-Gaussian operations. However, schemes for generating arbitrary non-Gaussian operations are restricted to single modes, i.e., the implementation of anharmonic potentials. Here, we introduce a method for implementing arbitrary non-Gaussian operations applicable to both single- and multi-mode systems, allowing the generation of both anharmonicities and nonlinear multi-mode couplings. Our method synthesizes a target Hamiltonian by decomposing it into a Fourier series whose terms are implemented via bosonic quantum signal processing, which uses a discrete-variable (DV) system to induce a nonlinearity in the CV system. Our hybrid CV-DV protocol allows for the direct simulation of a broad range of CV phenomena (such as those in lattice gauge theory, chemical dynamics, and quantum chaos) and provides a richer toolbox for CV circuit compilation.

A central challenge in quantum metrology is to effectively harness quantum resources to surpass classical precision bounds. Although recent studies suggest that the indefinite causal order may enable sensitivities to attain the super-Heisenberg scaling, the physical origins of such enhancements remain elusive. Here, we introduce the nilpotency index $\mathcal{K}$, which quantifies the depth of non-commutativity between operators during the encoding process, can act as a fundamental parameter governing quantum-enhanced sensing. We show that a finite $\mathcal{K}$ yields an enhanced scaling of root-mean-square error as $N^{-(1+\mathcal{K})}$. Meanwhile, the requirement for indefinite causal order arises only when the nested commutators become constant. Remarkably, in the limit $\mathcal{K} \to \infty$, exponential precision scaling $N^{-1}e^{-N}$ is achievable. We propose experimentally feasible protocols implementing these mechanisms, providing a systematic pathway towards practical quantum-enhanced metrology.

Graph states form a large family of quantum states that are in one-to-one correspondence with mathematical graphs. Graph states are used in many applications, such as measurement-based quantum computation, as multipartite entangled resources. It is thus crucial to understand when two such states have the same entanglement, i.e. when they can be transformed into each other using only local operations. In this case, we say that the graph states are LU-equivalent (local unitary). If the local operations are restricted to the so-called Clifford group, we say that the graph states are LC-equivalent (local Clifford). Interestingly, a simple graph rule called local complementation fully captures LC-equivalence, in the sense that two graph states are LC-equivalent if and only if the underlying graphs are related by a sequence of local complementations. While it was once conjectured that two LU-equivalent graph states are always LC-equivalent, counterexamples do exist and local complementation fails to fully capture the entanglement of graph states. We introduce in this thesis a generalization of local complementation that does fully capture LU-equivalence. Using this characterization, we prove the existence of an infinite strict hierarchy of local equivalences between LC- and LU-equivalence. This also leads to the design of a quasi-polynomial algorithm for deciding whether two graph states are LU-equivalent, and to a proof that two LU-equivalent graph states are LC-equivalent if they are defined on at most 19 qubits. Furthermore, we study graph states that are universal in the sense that any smaller graph state, defined on any small enough set of qubits, can be induced using only local operations. We provide bounds and an optimal, probabilistic construction.

Continuous monitoring of open quantum-optical systems offers a promising route towards quantum-enhanced estimation precision. In such continuous-measurement-based sensing protocols, the ultimate precision limit is dictated, through the quantum Cramér-Rao bound, by the global quantum Fisher information associated with the joint system-environment state. Reaching this limit with established continuous measurement techniques in quantum optics remains an outstanding challenge. Here we present a sensing protocol tailored for open quantum-optical sensors that exhibit dissipative criticality, enabling them to significantly narrow the gap to the ultimate precision limit. Our protocol leverages a previously unexplored interplay between the quantum criticality and the quantum measurement backaction inherent in continuous general-dyne detection. We identify a performance sweet spot, near which the ultimate precision limit can be efficiently approached. Our protocol establishes a new pathway towards quantum-enhanced precision in open quantum-optical setups and can be extended to other sensor designs featuring similar dissipative criticality.

We study the properties of a generalized Dicke-Ising model realized with an array of Rydberg atoms, driven by microwave electric fields and coupled to an optical cavity. As this platform allows for a precisely tunable anisotropy parameter, the model exhibits a rich landscape of phase transitions and critical phenomena, induced by the interplay of rotating-wave, counter-rotating-wave, and Ising interactions. We develop an improved quantum Monte Carlo algorithm based on the stochastic series expansion that explicitly tracks the Fock state of the quantum cavity. In the superradiant (SR) phase, this allows us to determine, through data collapse, the scaling laws of the photon number. We also demonstrate the vanishing of parity symmetry in finite-size simulations and show that the Rydberg blockade leads to a significant suppression of cavity occupation. Notably, stronger quantum fluctuations induced by the counter-rotating wave terms slightly favor the superradiant solid (SRS) phase over the Solid-1/2 state. Finally, we confirm that the SR phase transition and the transition from the Solid-1/2 to the SRS are second-order. In contrast, the transitions from the Solid-1/2 or SRS to the SR phase are both first-order for any value of the normalized anisotropy parameter.

This study proposes a time-symmetric framework for quantum measurement that restores microscopic reversibility at the level of the dynamical description while remaining compatible with causality and thermodynamic consistency. Instead of invoking a stochastic wavefunction collapse, the measurement process is modeled as a bidirectional informational update between a forward-evolving state and a backward-propagating effect, governed by a completely positive generator and its adjoint. Within this operator-based formalism, pre- and post-selected statistics are treated on an equal footing, yielding a unified description of both. The proposed scheme rigorously preserves complete positivity, normalization, and the no-signalling principle, and it is shown to satisfy Spohn's inequality for the associated quantum Markov semigroup, thereby ensuring non-negative entropy production within this setting. The framework admits a direct experimental interpretation across a range of scenarios, including weak measurements, EPR-Bell tests, homodyne detection, and photon counting. Furthermore, in the classical limit, the bidirectional update is demonstrated to reduce to the well-established Kalman filter and Rauch-Tung-Striebel (RTS) smoother used in classical estimation theory. These results support the view that the apparent temporal asymmetry of quantum measurement arises not from fundamental dynamical irreversibility, but from informational conditioning, specifically, the one-sided way in which measurement outcomes are incorporated into our description. In this sense, the arrow of time in measurement theory may be understood as an arrow of information.

We study how to recover timelike worldlines in AdS from CFT data as a toy model for holographically reconstructing realistic observers. We give a bulk extremization procedure that determines composite timelike-spacelike geodesics that connect timelike-separated boundary points. The total geodesic length matches the length extracted from CFT correlators at the timelike-separated points. We show agreement in Poincaré AdS, for generic boundary points in global AdS, and also for the BTZ solution, in which the timelike segment probes behind the horizon. We refine related methods to compute timelike entanglement entropy in AdS$_3$/CFT$_2$ and recover known results.

The accurate treatment of electron correlation in extended molecular systems remains computationally challenging using classical electronic structure methods. Hybrid quantum-classical algorithms offer a potential route to overcome these limitations; however, their practical deployment on existing quantum computers requires strategies that both reduce problem size and mitigate hardware noise. In this work, we combine Density Matrix Embedding Theory (DMET) with Sample-based Quantum Diagonalization (SQD) to compute ground-state energies of a set of natural ligand-like molecules in the minimal Slater Type Orbital (STO-3G) basis set. DMET provides a systematic fragmentation of a molecule into embedded impurity subproblems, while SQD enables construction and classical diagonalization of reduced configuration spaces through quantum sampling enhanced by iterative configuration recovery. The resulting embedded Hamiltonians are solved on IBM's Eagle R3 superconducting quantum hardware (IBM Sherbrooke). The DMET-SQD energies obtained for all systems considered exhibit strong agreement with DMET-FCI benchmark values within chemical accuracy (1 kcal/mol). These results demonstrate that sample-based quantum methods, when integrated with a robust embedding framework, can reliably extend quantum computation towards simulation of chemically relevant molecular systems, showcasing potential applications in the field of drug discovery.

Quantum federated learning (QFL) combines quantum computing and federated learning to enable decentralized model training while maintaining data privacy. QFL can improve computational efficiency and scalability by taking advantage of quantum properties such as superposition and entanglement. However, existing QFL frameworks largely focus on homogeneity among quantum \textcolor{black}{clients, and they do not account} for real-world variances in quantum data distributions, encoding techniques, hardware noise levels, and computational capacity. These differences can create instability during training, slow convergence, and reduce overall model performance. In this paper, we conduct an in-depth examination of heterogeneity in QFL, classifying it into two categories: data or system heterogeneity. Then we investigate the influence of heterogeneity on training convergence and model aggregation. We critically evaluate existing mitigation solutions, highlight their limitations, and give a case study that demonstrates the viability of tackling quantum heterogeneity. Finally, we discuss potential future research areas for constructing robust and scalable heterogeneous QFL frameworks.

We derive closed-form analog quantum-speed-limit (QSL) bounds for highly nonlocal optical beams whose paraxial propagation is mapped to a reversed (inverted) harmonic-oscillator generator. Treating the longitudinal coordinate $z$ as an evolution parameter (propagation distance), we construct the propagator, evaluate the Bures distance, and obtain analytic Mandelstam--Tamm and Margolus--Levitin bounds that fix a propagation-distance limit $z_{\mathrm{PDL}}$ to reach a prescribed mode distinguishability. This distance-domain constraint is the classical optical analogue of the minimal orthogonality time in quantum mechanics. We then propose a compact self-defocusing PDL beam shaper that achieves strong transverse-mode conversion within millimeter scales. We further show that small variations in refractive index, beam power, or temperature shift $z_{\mathrm{SL}}$ with high leverage, enabling speed-limit-based metrology with index sensitivities down to $10^{-7}$ RIU and temperature resolutions of order $1$ mK. The results bridge distance-domain QSL geometry and practical photonic applications.

The active manipulation of topologically protected states represents a pivotal frontier for quantum technologies, offering a unique confluence of topological robustness and precise quantum control. We propose an adiabatic pumping scheme for the long-range transfer of topological corner states in a two-dimensional Su-Schrieffer-Heeger model. The protocol utilizes a modular lattice architecture composed of four topologically distinct subblocks, enabling the modulation of a topological dark state by precise tuning of lattice couplings. This approach is based on coherent tunneling by adiabatic passage among topological corner and interface states. We establish a multi-level model for the adiabatic pumping that provides an accurate description of the underlying mechanism. In comparison with a sequential two-stage Thouless pumping, our protocol offers superior performance in both transfer fidelity and efficiency.

Magnonic systems present a compelling platform for quantum technology, owing to their strong capacity to form hybrid quantum systems via diverse couplings. To unlock the full potential of these systems, the engineering of flexible coupling between multiple magnon modes is essential. Here, we propose a method to realize switchable dissipative Ising coupling in magnon systems, leveraging the three-body coupling among photon, phonon, and magnon. This type of dissipative coupling is a critical component for constructing Ising machines designed to solve complex combinatorial optimization problems. By dynamically tuning the phase of a nonlinear mechanical pump, we demonstrate the realization of both ferromagnetic and antiferromagnetic dissipative interactions. The validity of the scheme is confirmed by numerical simulations, which also demonstrate its robustness against a strong uncontrollable part of dissipation. Our work provides a versatile tool that can facilitate the implementation of magnon-based quantum computing and the exploration of many-body magnon physics.

Two-dimensional organic-inorganic hybrid perovskite (2D-OIHP) quantum wells are emerging as promising light sources for quantum communication technologies, owing to their ability to generate polarization-encoded optical signals. In this work, we explore how nonlinear optical phenomena can be exploited for quantum information applications, demonstrating the versatility that arises from resonant coupling among excited states. By tracking changes in the ellipticities of signal photons on femtosecond timescales in four-wave-mixing experiments, we first establish a method for information encoding based on exciton spin dynamics and biexciton correlations. Using single-photon detection, we then implement the BB84 quantum key distribution protocol by mapping these polarization states onto binary sequences. While the polarizations of weak coherent pulses are typically manipulated with optical elements in traditional quantum key distribution approaches, the intrinsic electronic structure and spin relaxation processes within the 2D-OIHP system determine the characteristics of the signal photons in our method. As a demonstration, an ASCII message consisting of 56 bits is transmitted through the polarization states of photons emitted by 2D-OIHP quantum wells. These results show that the information transmission efficiency depends strongly on contributions from biexciton states, highlighting the potential of spin-dependent nonlinear optical processes for quantum communication.

While for non-relativistic short-range interactions, the spread of information is local, remaining confined in an effective light cone, long-range interactions can generate either nonlocal (faster-than-ballistic) or local (ballistic) spread of correlations depending on the initial conditions. This makes long-range interactions a rich platform for controlling the spread of information. Here, we derive an effective Hamiltonian analytically and identify the specific interaction term that drives nonlocality in a wide class of long-range spin chains. This allows us to understand the conditions for the emergence of local behavior in the presence of nonlocal interactions and to identify a regime where the causal space-time landscape can be precisely designed. Indeed, we show that for large long-range interaction strength or large system size, initial conditions can be chosen in a way that allows a local perturbation to generate nonlocal signals at programmable distant positions, which then propagate within effective light cones. The possibility of engineering the emergence of nonlocal Lieb-Robinson-like light cones allows one to shape the causal landscape of long-range interacting systems, with direct applications to quantum information processing devices, quantum memories, error correction, and information transport in programmable quantum simulators.

We present a quantum sensing protocol for coupled qubit-oscillator systems that surpasses the standard quantum limit (SQL) by exploiting a geometrical phase. The signal is encoded in the geometrical phase that is proportional to the area enclosed in oscillator phase space. This area is amplified through squeezing, enabling sensitivities beyond the SQL. Our method is independent of oscillator's initial state, amenable to sensing with high-temperature or logical error-corrected states. The protocol shows robustness to qubit Markovian noise and preserves its state-independence, underscoring its practicality for next-generation quantum metrology. We demonstrate application to force sensing beyond the SQL in longitudinally coupled systems, and to high-precision measurements of couplings and pulse calibration surpassing SQL in dispersively coupled circuit quantum electrodynamics (cQED) architectures.

This report introduces a novel class of reasoning architectures, termed Quantum Circuit Reasoning Models (QCRM), which extend the concept of Variational Quantum Circuits (VQC) from energy minimization and classification tasks to structured logical inference and reasoning. We posit that fundamental quantum mechanical operations, superposition, entanglement, interference, and measurement, naturally map to essential reasoning primitives such as hypothesis branching, constraint propagation, consistency enforcement, and decision making. The resulting framework combines quantum-inspired computation with differentiable optimization, enabling reasoning to emerge as a process of amplitude evolution and interference-driven selection of self-consistent states. We develop the mathematical foundation of QCRM, define its parameterized circuit architecture, and show how logical rules can be encoded as unitary transformations over proposition-qubit states. We further formalize a training objective grounded in classical gradient descent over circuit parameters and discuss simulation-based implementations on classical hardware. Finally, we propose the Quantum Reasoning Layer (QRL) as a differentiable hybrid component for composable reasoning models applicable to scientific, biomedical, and chemical inference domains.

Photons are promising candidates for quantum information technology due to their high robustness and long coherence time at room temperature. Inspired by the prosperous development of photonic computing techniques, recent research has turned attention to performing quantum machine learning on photonic platforms. Although photons possess a high-dimensional quantum feature space suitable for computation, a general understanding of how to harness it for learning tasks remains blank. Here, we establish both theoretically and experimentally a scalable advantage in quantum machine learning with multi-photon states. Firstly, we prove that the learning capacity of linear optical circuits scales polynomially with the photon number, enabling generalization from smaller training datasets and yielding lower test loss values. Moreover, we experimentally corroborate these findings through unitary learning and metric learning tasks, by performing online training on a fully programmable photonic integrated platform. Our work highlights the potential of photonic quantum machine learning and paves the way for achieving quantum enhancement in practical machine learning applications.

Escalating cyber threats and the high-dimensional complexity of IoT traffic have outpaced classical anomaly detection methods. While deep learning offers improvements, computational bottlenecks limit real-time deployment at scale. We present a quantum autoencoder (QAE) framework that compresses network traffic into discriminative latent representations and employs quantum support vector classification (QSVC) for intrusion detection. Evaluated on three datasets, our approach achieves improved accuracy on ideal simulators and on the IBM Quantum hardware demonstrating practical quantum advantage on current NISQ devices. Crucially, moderate depolarizing noise acts as implicit regularization, stabilizing training and enhancing generalization. This work establishes quantum machine learning as a viable, hardware-ready solution for real-world cybersecurity challenges.

We study information-theoretic inequalities for holographic correlation measures $J_W$ and $D_W$, establishing rigorous topological frameworks that prove monotonicity, monogamy, and strong superadditivity. While earlier work proposed bulk duals of classical correlation and quantum discord, their information-theoretic properties were unclear. We derive multiple inequalities involving entanglement wedge cross sections (EWCS) and show that monotonicity holds for both measured and unmeasured parties in $J_W$ and for the unmeasured party in $D_W$. Unlike their original counterparts, we find that $J_W$ is monogamous for both parties and obeys one-way strong superadditivity, whereas $D_W$ is polygamous for the unmeasured party in pure tripartite states. These results highlight distinctive features of holographic states and support a conjectured duality between $J_W$ and distillable entanglement. Motivated by the relation between EWCS and reflected entropy, we introduce boundary analogues $J_R$ and $D_R$, which serve as computable proxies for classical and quantum correlations without optimization. We analyze their inequalities, proving several and presenting counterexamples. Overall, we provide a systematic "zoo" of correlation inequalities in and beyond holography, clarifying connections among bulk geometry, discord-type correlations, and distillable entanglement.

In electronic structure calculations, the transcorrelated method enables a reduction of the basis set size by incorporating the electron-electron correlations directly into the Hamiltonian. However, the transcorrelated Hamiltonian is non-Hermitian, which makes many common quantum algorithms inapplicable. Recently, a quantum eigenvalue estimation algorithm was proposed for non-Hermitian Hamiltonians with real spectra [FOCS 65, 1051 (2024)]. Here we investigate the cost of this algorithm applied to transcorrelated electronic Hamiltonians of second-row atoms and compare it to the cost of applying standard qubitization to non-transcorrelated Hamiltonians. We find that the ground state energy of the transcorrelated Hamiltonian in the STO-6G basis is more accurate than that of a standard Hamiltonian in the cc-pVQZ basis. The T gate counts of the two methods are comparable, while the qubit count of the transcorrelated method is 2.5 times smaller.

We report two types of singularities that arise from fluctuations during the formation of charge- or spin-density waves. The first is the exceptional point (EP), corresponding to a higher-order pole of the retarded Green's function. Such EPs lead to algebraic corrections in the decay of quasiparticle occupations and are observable through time-resolved angle-resolved photoemission spectroscopy (Tr-ARPES). The second is a spectral cusp, defined by the coalescence of three extrema in the real-frequency spectral function $A(\mathbf{k}, ω)$. This cusp enforces the formation of Fermi arcs and induces a "threading" structure in the nearby band structure, both of which are directly observable in ARPES.

Entanglement does not always require one particle per party. It was predicted some thirty years ago that a single photon traversing a beam splitter could violate a Bell inequality. Although initially debated, single-photon nonlocality was eventually demonstrated via homodyne measurements. Here, we present an alternate realisation that avoids the complexity of homodyne measurements and potential loopholes in their implementation. We violate a Bell inequality by performing joint measurements on two copies of the same single-photon entangled state, where one photon acts as a phase reference for the other, making it self-referential. We observe CHSH parameters of $2.71\pm 0.09$ and $2.23\pm 0.07$, depending on the joint measurements implemented. This offers a new perspective on single-photon nonlocality and a more accessible experimental route, potentially applicable to general mode-entangled states in diverse platforms.

We argue that the presence of \emph{any} exact $U(1)$ higher-form symmetry, under mild assumptions, presents a fundamental obstruction to ergodicity under unitary dynamics in lattice systems with local interactions and finite on-site Hilbert space dimension. Focusing on the two-dimensional case, we show that such systems necessarily exhibit Hilbert space fragmentation and explicitly construct Krylov sectors whose number scales exponentially with system size. While these sectors cannot be distinguished by symmetry quantum numbers, we identify the emergent integrals of motion which characterize them. Our symmetry-based approach is insensitive to details of the Hamiltonian and the lattice, providing a systematic explanation for ergodicity-breaking in a range of systems, including quantum link models.

We develop a novel holographic framework for mixed-state phases in random quantum circuits, both unitary and non-unitary, with a global symmetry $G$. Viewing the circuit as a tensor network, we decompose it into two parts: a symmetric layer, which defines an emergent gauge wavefunction in one higher dimension, and a random non-symmetric layer, which consists of random multiplicity tensors. For unitarity circuits, the bulk gauge state is deconfined, but under a generic non-unitary circuit (e.g. channels), the bulk gauge theory can undergo a decoherence-induced phase transition: for $G\,{=}\,\mathbb{Z}_N$ with local symmetric noise, the circuit can act as a quantum error-correcting code with a distinguished logical subspace inheriting the $\mathbb{Z}_N$-surface code's topological protection. We then identify that the charge sharpening transition from the measurement side is complementary to a decodability transition in the bulk: noise of the bulk can be interpreted as measurement from the environment. For $N\,{\leq}\,4$, weak measurements drive a single transition from a charge-fuzzy phase with sharpening time $t_{\#}\sim e^{L}$ to a charge-sharp phase with $t_{\#}\sim \mathcal{O}(1)$, corresponding to confinement that destroys logical information. For $N>4$, measurements generically generate an intermediate quasi-long-range ordered Coulomb phase with gapless photons and purification time $t_{\#}\sim \mathcal{O}(L)$.

Advantage Distillation (AD) is a classical post-processing technique that enhances Quantum Key Distribution (QKD) protocols by increasing the maximum acceptable Quantum Bit Error Rate (QBER) and thus extending the distance at which QKD links can be securely established. AD operates by post-selecting blocks of bits and extracting fewer high-fidelity bits, exhibiting a reduced QBER and thus lowering the amount of information that has to be disclosed during the information reconciliation step. In this work we present the first comprehensive finite key-size analysis of decoy-state BB84 enhanced via AD post-processing. We demonstrate that through the use of AD the maximum acceptable QBER increases from around $9.5\%$ to around $17.3\%$ for realistic key sizes. This result shows that substantial performance enhancements can be achieved in scenarios which are constrained by the maximum tolerable QBER via improvements of the post-processing method alone.

Ground state energy estimation for strongly correlated quantum systems remains a central challenge in computational physics and chemistry. While tensor network methods like DMRG provide efficient solutions for one-dimensional systems, higher-dimensional problems remain difficult. Here we present a variational double bracket flow (vDBF) algorithm that leverages Sparse Pauli Dynamics, a technique originally developed for classical simulation of quantum circuits, to efficiently approximate ground state energies. By combining greedy operator selection with coefficient truncation and energy-variance extrapolation, the method achieves less than 1% error relative to DMRG benchmarks for both Heisenberg and Hubbard models in one and two dimensions. For a 10x10 Heisenberg lattice (100 qubits), vDBF obtains accurate results in approximately 10 minutes on a single CPU thread, compared to over 50 hours on 64 threads for DMRG. For an 8x8 Hubbard model (128 qubits), the speedup is even more pronounced. These results demonstrate that classical simulation techniques developed in the context of quantum advantage benchmarking can provide practical tools for many-body physics.

We show that any nonclassicality criterion based on factorial moments, including several higher-order parameters such as the Mandel $Q^{(\ell)}$ parameter, the Lee antibunching function $d^{(\ell-1)}_h$, and the Agarwal--Tara parameter $A_3$, can be computed straightforwardly for photon-subtracted and photon-added states by performing operator reordering of the factorial moments. Within this approach, all relevant quantities depend solely on the normalization constant of the given state.

Quantum operations that are perfectly admissible in non-relativistic quantum theory can enable signalling between spacelike separated regions when naively imported into quantum field theory (QFT). Prominent examples of such "impossible measurements", in the sense of Sorkin, include certain unitary kicks and projective measurements. It is generally accepted that only those quantum operations whose physical implementation arises from a fully relativistically covariant interaction, between the quantum field and a suitable probe, should be regarded as admissible. While this idea has been realised at the level of abstract algebraic QFT, or via particular measurement models, there is still no general set of operational criteria characterising which measurements are physically implementable. In this work we adopt the local S-matrix formalism, and make use of a hierarchy of factorisation conditions that exclude both superluminal signalling and retrocausality, thereby providing such a criterion. Realising the local S-matrices through explicit interactions between smeared field operators and a pointer degree of freedom, we further derive local causality conditions for the induced Kraus operators, which guarantee the absence of signalling in "impossible measurement" scenarios. Finally, we show that the accuracy with which local field observables can be measured is fundamentally limited by the retarded propagator of the field, which also plays an essential role in a factorisation identity we prove for the field Kraus operators.

Versatile, tunable, and potentially scalable single-photon sources are a key asset in emergent photonic quantum technologies. In this work, a single-photon source based on WS$_2$ micro-domes, created via hydrogen ion irradiation, is realized and integrated into an open, tunable optical microcavity. Single-photon emission from the coupled emitter-cavity system is verified via the second-order correlation measurement, revealing a $g^{(2)}(τ=0)$ value of 0.3. A detailed analysis of the spectrally selective, cavity enhanced emission features shows the impact of a pronounced acoustic phonon emission sideband, which contributes specifically to the non-resonant emitter-cavity coupling in this system. The achieved level of cavity-emitter control highlights the potential of open-cavity systems to tailor the emission properties of atomically thin quantum emitters, advancing their suitability for real-world quantum technology applications.

Quantum walks, the quantum analogue to the classical random walk, have been shown to model fluid dynamics. Neutral atom hardware is a promising choice of platform for implementing quantum walks due to its ability to implement native multiqubit ($\geq\!3$-qubit) gates and to dynamically re-arrange qubits. Using error modelling for multiqubit Rydberg gates via two-photon adiabatic rapid passage, we present the gate sequences and predicted final state fidelities for some toy quantum walks, including `lazy' quantum walks. These `lazy' quantum walks include a rest state and therefore provide an integral step towards quantum walks for fluid simulation.

We present a new way of deriving classical mechanics from quantum mechanics. A key feature of the method is its compatibility with the standard approach used to derive transition rates between quantum states due to interactions. We apply the developed method to derive the main formulas of physical kinetics. We observe that, through the Liouville equation, we can deduce the non-collision part of the Boltzmann equation, and that, through the matrix of transition rates, we can deduce the collision integral. As a final result of the manuscript, we derive the Boltzmann equation from the Schrödinger equation as a single piece of formal mathematical manipulation, without any non-rigorous plausible reasoning used to glue together its different parts.

We introduce a unified framework that relates orbital and heat magnetizations to experimentally accessible excitation spectra, through thermoelectric probes and generalized sum rules. By analyzing zero-temperature transport coefficients and applying Kramers-Kronig relations, we derive spectral representations of magnetization densities from thermoelectric correlation functions. Excitation rates under chiral thermoelectric drives then naturally emerge as direct probes of these Kubo-type correlators, placing orbital and heat magnetizations on equal footing with the topological Chern number. As a direct consequence of our formalism, we introduce a hierarchical construction that organizes orbital and heat magnetizations into distinct physical contributions accessible through sum rules, and also derive real-space markers of these magnetizations. From an experimental standpoint, we propose concrete implementations of thermoelectric dichroic measurements in quantum-engineered platforms based on modulated strain fields. These results establish thermoelectric dichroic measurements as a versatile route to access and disentangle fundamental ground-state properties.

Motivated by the search for unconventional orders in frustrated quantum magnets, we present a multi-method investigation into the nature of the quantum phase diagram of the spin-$1/2$ Heisenberg model on the maple-leaf lattice with three symmetry-inequivalent nearest-neighbor interactions. It has been argued that the parameter regime with antiferromagnetic couplings on hexagons $J_h$ and ferromagnetic couplings on triangles $J_t$ and dimer $J_d$ bonds, is potentially host to a cornucopia of emergent phases with unconventional orders. Our analysis indeed identifies an extended region where any conventional dipolar magnetic order is absent. A hexagonal singlet state is found in the region around $J_{d}=J_{t}=0$, while a dimerized hexagonal singlet order of a lattice nematic character appears proximate to the phase boundary with the c$120^\circ$ antiferromagnetic order. Interestingly, upon traversing the bulk of the paramagnetic (PM) region, we find a variety of distinct correlation profiles, which are qualitatively different from those of the hexagonal singlet and dimerized hexagonal singlet orders but feature no appreciable spin-nematic response, while the boundary with the ferromagnetic phase shows evidence of spin-nematic order. This PM region is thus likely host to an ensemble of nonmagnetic phases which could putatively include quantum spin liquids. Our phase diagram is built from a complementary application of state-of-the-art implementations of the cluster mean-field and pseudo-fermion functional renormalization group approaches, together with an unconstrained Luttinger-Tisza treatment of the model providing insights from the semi-classical limit.

We propose a hidden U(1) gauge interaction that couples exclusively to quantum coherence in massive systems. The central innovation is a conserved coherence current operator constructed from the Noether mass current via operator-level coarse-graining. This current vanishes for classical matter distributions but is nonzero for spatial superpositions and entangled states, yielding a gauge interaction that is dormant in classical regimes but activated by quantum coherence. The framework predicts three distinctive signatures: (i) interferometric phase shifts scaling linearly with fringe visibility, (ii) decoherence rates with characteristic m^2 scaling and spatial dependence distinct from collapse models, and (iii) entanglement-selective forces between distant massive qubits. The theory maintains full gauge invariance, causality, and positive time evolution. We show that state-of-the-art atom interferometers and levitated nanoparticles can place first constraints on this interaction class, complementary to classical fifth-force searches. This approach provides a novel theoretical framework for probing coherence-selective fundamental interactions and their potential role in the quantum-classical transition. To make this more concrete, we also spell out a simple benchmark latent-field model and work out, in detail, how a representative large-momentum-transfer atom interferometer constrains the corresponding coupling strength.

The dissipative quantum Rabi model exhibits rich non-equilibrium physics, including a dissipative phase transition from the normal phase to the superradiant phase. In this work, we investigate the stability of the superradiant phase in the presence of a weak spin relaxation. We find that even a weak spin relaxation can render the superradiant phase to a superradiant metastable phase, in which symmetry-breaking states are stable only for a finite time. This arises because each spin-jump induced by relaxation applies as a strong perturbation to the system, potentially driving the system from a symmetry-breaking state to the symmetry-preserving saddle point with finite probability, before it eventually relaxes back to a symmetry-breaking state. Such dynamical processes lead to a finite lifetime of the symmetry-breaking states and restore the symmetry in the steady state. To substantiate these results, we combine mean-field and cumulant expansion analyses with exact numerical simulations. The lifetime of the symmetry-breaking states are analyzed in finite-size systems, and the conclusions are extrapolated to the thermodynamic limit via finite-size scaling. Our findings establish the metastable nature of the symmetry-breaking states in the dissipative quantum Rabi model and reveal the complexity of the dissipative phase transition beyond their equilibrium counterpart. The mechanisms uncovered here can be generalized to a broad class of open quantum systems, highlighting fundamental distinctions between equilibrium phase transitions and steady-state phase transitions.

Active matter denotes a system of particles immersed in an external environment, from which the particles extract energy continuously in order to perform motion. Extending the paradigm of active matter to a quantum framework requires an open quantum system description. In this work, we consider a driven quantum particle whose external driving exhibits characteristics of classical activity. We model the dynamics with time-local master equations and analyze the particle motion at different time scales for different forms of the master equations. By systematically comparing several types of master equations, we uncover how the particle motion evolves under the interplay of quantum effects and active-like dynamics. These results are essential for guiding possible experiments aimed at realizing quantum analogues of classical active systems.

We develop the theory describing the quantum coupled dynamics of the center-of-mass motion of a nanoparticle and an ensemble of ions co-trapped in a dual-frequency linear Paul trap. We first derive analytical expressions for the motional frequencies and classical trajectories of both nanoparticle and ions. We then derive a quantum master equation for the ion-nanoparticle system and quantify the sympathetic cooling of the nanoparticle motion enabled by its Coulomb coupling to a continuously Doppler-cooled ion. We predict that motional cooling down to sub-kelvin temperatures is achievable in state-of-the-art experiments even in the absence of motional feedback and in the presence of micromotion. We then extend our analysis to an ensemble of $N$ ions, predicting a linear increase of the cooling rate as a function of $N$ and motional cooling of the nanoparticle down to tenths of millikelvin in current experimental platforms. Our work establishes the theoretical toolbox needed to explore the ion-assisted preparation of non-Gaussian motional states of levitated nanoparticles.

The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of standard quantum mechanics based on the concept of stochastic trajectories in the configuration space of a quantum system. For particle systems, configuration space is made up out of their coordinates and, if relevant, their orientation. Quantum analytical mechanics derives equations of motion for these variables which allow a description of the measurement process as a dynamical physical process. After all, it is exactly these variables experiments are designed to interact with. The theory is not a replacement of Hilbert space quantum mechanics but a mathematical completion enriching our toolset for the description of quantum phenomena.

The ionization dynamics of a hydrogen molecule, serving as a fundamental benchmark in quantum chemistry, is investigated within a comprehensive framework combining quantum electrodynamics and the Lindblad master equation. This approach enables a first-principles description of light--matter interactions while accounting for dissipative processes and external particle influx. We systematically explore the system's evolution across three distinct regimes: closed, dissipative open, and influx-driven open quantum systems. Our results reveal a universal tendency towards the formation of the neutral hydrogen molecule ($|\rm{H}_2\rangle$) across all configurations. The dissipation strengths for photons ($γ_Ω$), electrons ($γ_e$), and phonons ($γ_ω$) are identified as critical control parameters, with $γ_Ω$ significantly accelerating system stabilization. Furthermore, the introduction of particle influx ($μ_k$) leads to a complex redistribution of energy, notably populating the atomic state ($|\rm{H},\rm{H}\rangle$). The ionization pathway is exquisitely sensitive to the initial quantum state, dictated by the composition and number of photons, which governs the accessible spin-selective excitation channels. This is conclusively demonstrated in a model with an embedded anode, where the maximum ionization probability is fundamentally constrained to $\frac{3}{4}$ by orbital hybridization. This study provides a unified theoretical foundation for quantum-controlled chemistry, with direct implications for future experiments in cavity QED and quantum information processing.

We give a systematic construction of new quasi-exactly solvable systems via Bethe ansatz and supersymmetric quantum mechanics (SUSYQM). Methods based on the intertwining of supercharges have been extensively used in the literature for exactly solvable systems. We generalize the state-deleting (Krein-Adler) supersymmetric transformations to quasi-exactly exactly solvable (QES) systems building on the Bethe ansatz method and related Bethe roots. This enables us to construct superpartners for a wide class of known QES systems classified previously through a hidden $sl(2)$ algebra. We present our constructions of factorizations and intertwining relations related to 1st-order SUSYQM and the $n=1$ state for 10 nonequivalent types, denoted I,...,X. In order to have a unified treatment we rely on their ODE standard form as this is also the appropriate setting to obtain the Bethe ansatz equations which constrain the polynomial solutions. This setting also allows one to deal with systems with $n$ states in a unified manner, using analysis based on the Bethe ansatz equations to build the supersymmetric transformations in terms of the Bethe ansatz roots. We derive the Schrödinger potentials for the $n=1$ superpartners of the 10 QES cases and give closed-form solutions for the spectra and wavefunctions of the corresponding QES SUSYQM systems. Furthermore, we present numerical results for higher excited states up to the $n=10$ level. The results obtained may have wider applicability as our framework is built on ODEs with polynomial coefficients.

Quantum entanglement, as one of the fundamental concepts in quantum mechanics, has garnered significant attention over the past few decades for its extraordinary nonlocality. With the advancement of quantum technology, quantum entanglement holds promising application for exploring fundamental physical theories. The experimental scheme of Quantum Gravity Induced Entanglement of Masses (QGEM) was proposed to investigate the quantum effects of gravity based on the Local Operations and Classical Communication (LOCC) theory. In this study, we analyze the quantum properties of the entangled final states generated in the QGEM scheme. Our findings reveal that the photon emission rates (transition rates) are closely related to the degree of entanglement. Specifically, the transition rate decreases as the degree of entanglement increases when the distance between particle pairs is small, then it gradually approaches an asymptotic value that is independent of entanglement as the distance increases. We then discuss the possibility of using photon emission rates to detect quantum entanglement with these results.

The Kibble-Zurek effect is studied around a tricritical point, where the adiabatic-impulse scenario breaks down. Several new scaling forms are also proposed.

We theoretically investigated how the quantum entanglement between the spin of the photoelectron and the polarization of the emitted X-ray photon depends on the excited core-level, using the 3$d\rightarrow\ $2$p$ and 3$d\rightarrow\ $3$p$ SPR-XEPECS (spin- and polarization-resolved XEPECS) processes for $\rm Ti_{2}O_{3}$-type system, and the 4$f\rightarrow\ $4$d$ SPR-XEPECS process for $\rm CeF_{3}$-type system. In the calculation for $\rm Ti_{2}O_{3}$-type system, we used $\rm TiO_{6}$ cluster model with the full-multiplet structure of the Ti ion and the charge-transfer effect between Ti 3$d$ and ligand O 2$p$ orbitals. For $\rm CeF_{3}$-type system, we used ionic model with the full-multiplet structure of the Ce ion. We found two distinct mechanisms for entanglement generation in the 3$d\rightarrow\ $2$p$ and 4$f\rightarrow\ $4$d$ cases. The first is generated by the spin-orbit interaction of the 2$p$ core electron, whereas the second is generated by the spin-orbit interaction of the 4$f$ valence electron and strong exchange interaction between the 4$f$ and 4$d$ electrons. However, in the 3$d\rightarrow\ $3$p$ case with the strong 3$d-$3$p$ exchange interaction, we found that the entanglement is not generated due to the crystal field effect. These results reveal the existence of two distinct mechanisms for entanglement generation in X-ray inner-shell excitation processes.

A basic postulate of modern compositional approaches to generalised physical theories is the generalised Born rule, in which probabilities are postulated to be computable from the composition of states and effects. In this paper we consider whether this postulate, and the strength of the identification between scalars and probabilities, can be argued from basic principles. To this end, we first consider the most naive possible process-theoretic interpretation of textbook quantum theory, in which physical processes (unitaries) along with states and effects (kets and bras) and a probability function from states and effects satisfying just some basic compatibility axioms are identified. We then show that any process theory equipped with such structure is equivalent to an alternative process theory in which the generalised Born rule holds. We proceed to consider introduction of noise into any such theory, and observe that the result of doing so is a strengthening of the identification between scalars and probabilities; from bare monoid homomorphisms to semiring isomorphisms.

Portfolio optimization is a cornerstone of financial decision-making, traditionally relying on classical algorithms to balance risk and return. Recent advances in quantum computing offer a promising alternative, leveraging quantum algorithms to efficiently explore complex solution spaces and potentially outperform classical methods in high-dimensional settings. However, conventional quantum approaches typically assume a one-to-one correspondence between qubits and variables (e.g. financial assets), which severely limits the applicability of gate-based quantum systems due to current hardware constraints. As a result, only quantum annealing-like methods have been used in realistic scenarios. In this work, we show how a gate-based variational quantum algorithm can be applied to a real-world portfolio optimization problem by assigning multiple variables per qubit. Specifically, we address a problem involving over 250 variables, where the market graph representing a real stock market is iteratively partitioned into sub-portfolios of highly correlated assets. This approach enables improved scalability compared to traditional variational methods and opens new possibilities for quantum-enhanced financial applications.

Permutation symmetry plays a central role in the understanding of collective quantum dynamics. On the other hand, interactions are rarely uniform in real systems. By introducing power law couplings that algebraically decay with the distance between the spins $r$ as $1/r^α$, we break this symmetry with a non-zero $α$, and probe the emergence of new dynamical behaviors, including thermalization. As we increase $α$, the system interpolates from an infinite range spin system at $α=0$ exhibiting permutation symmetry, to a short range integrable model as $α\rightarrow \infty$ where this permutation symmetry is absent. We focus on the change in the behavior of the system as $α$ is tuned, using dynamical quantities like total angular momentum operator $J^2$ and the von Neumann entropy $S_{N/2}$. Starting from the chaotic limit of the permutation symmetric Hamiltonian at $α=0$, we find that for small $α$, the steady state values of these quantities remain close to the permutation symmetric subspace values corresponding to $α=0$. At intermediate $α$ values, these show signatures of thermalization exhibiting values corresponding to that of random states in full Hilbert space. On the other hand, the large $α$ limit approaches the values corresponding to integrable kicked Ising model. In addition, we also study the dependence of thermalization on the driving period $τ$, with results indicating the onset of thermalization for smaller values of $α$ when $τ$ is large, thereby extending the intermediate range of $α$. We further confirm these results using effective dimension and spectral statistics.

We formulate and prove an Agreement Theorem for quantum mechanics (QM), describing when two agents, represented by separate laboratories, can or cannot maintain differing probability estimates of a shared quantum property of interest. Building on the classical framework (Aumann, 1976), we define the modality of "common certainty" through a hierarchy of certainty operators acting on each agent's Hilbert space. In the commuting case -- when all measurements and event projectors commute -- common certainty leads to equality of the agents' conditional probabilities, recovering a QM analog of the classical theorem. By contrast, when non-commuting operators are allowed, the certainty recursion can stabilize with different probabilities. This yields common certainty of disagreement (CCD) as a distinctive QM phenomenon. Agreement is restored once measurement outcomes are recorded in a classical register. The classical Agreement Theorem can therefore be seen as emergent from the quantum world via recording. We establish an impossibility result stating that QM forbids a scenario where one agent is certain that a property of interest occurs, and is also certain that the other agent is certain that the property does not occur. In this sense, QM admits non-classical disagreement, but disagreement is still bounded in a disciplined way. We argue that our analysis offers a rigorous approach to the longstanding issue of how to understand intersubjectivity across agents in QM.

The decoy-state Bennett-Brassard 1984 (BB84) quantum key distribution (QKD) protocol is widely regarded as the de facto standard for practical implementations. On the receiver side, passive basis choice is attractive because it significantly reduces the need for random number generators and eliminates the need for optical modulators. Despite these advantages, a finite-key analytical security proof for the decoy-state BB84 protocol, where the basis is chosen passively with a biased probability, has been lacking. In this work, we present a simple analytical finite-key security proof for this setting, yielding a closed-form secret-key rate formula that can be directly evaluated using experimentally accessible parameters. Numerical simulations show that the key rates of passiveand active-measurement implementations are nearly identical, indicating that passive measurement does not compromise key-generation efficiency in practical QKD systems.

Fermi's golden rule which describes the transition rates between two electronic levels under external stimulations is used ubiquitously in different fields of physics. The original Fermi's golden rule was derived from perturbative time-dependent Schrödinger's equation without the direct contribution by decoherence effect. However, as a result of recent developments of quantum computing and ultra fast carrier dynamics, the decoherence becomes a prominent topic in fundamental research.Here, by using the non-adiabatic molecular dynamics which goes beyond the time-dependent Schrödinger's equation by introducing decoherence, we study the effect of decoherence on Fermi's golden rule for the fixed basis and the adiabatic basis, respectively. We find that when the decoherence time becomes short, there is a significant deviation from the Fermi's golden rule for both bases. By using monolayer $\mathrm{WS_2}$ as an example, we investigate the decoherence effect in the carrier transitions induced by the electron-phonon coupling with first-principle method.

We introduce a cost-effective quantum error mitigation technique that builds on the recent Ansatz-based gate and readout error mitigation method (M0). The technique, tiled M0, leverages the unique structure of tiled Ansätze (e.g., tUPS, QNP, hardware-efficient circuits) to apply a locality approximation to M0 that results in an exponential reduction in the QPU cost of the noise characterization. We validate the technique for molecular ground state energy calculations with the tUPS Ansatz on LiH, molecular hydrogen, water, butadiene, and benzene ($4-12$ qubits), demonstrating little to no loss in accuracy compared to M0 in noisy simulations. We also show the performance of the technique in quantum experiments, highlighting its potential use in near-term applications.

Many optimally scaling quantum simulation algorithms employ controlled time evolution of the Hamiltonian, which is typically the major bottleneck for their efficient implementation. This work establishes a compression protocol for encoding the controlled time evolution operator of translationally invariant, local Hamiltonians into a quantum circuit. It achieves a near-optimal scaling in circuit depth $\mathcal{O}(t \text{ polylog}(t N/ε))$, while reducing the control overhead from a multiplicative to an additive factor. We report that this compression protocol enables the implementation of Iterative Quantum Phase Estimation with as few as 414 CNOT gates for a frustrated quantum spin system on a 6x6 triangular lattice and delivers ground state energy errors below 1% (with $\pm$ 1.5% variation, calculated with a hardware noise aware pipeline) on a 4x4 triangular lattice using the noisy emulator of the Quantinuum H2 trapped ion device.

Nucleation and wetting transitions are studied in a three-component Bose-Einstein condensate mixture within Gross-Pitaevskii theory. For special cases of intermediate segregation between components 1 and 2, the nucleation phase transition of a surfactant film of component 3 is obtained by exact solution. Additional exact results for the nucleation transition are derived in the limit of strong segregation between components 1 and 2. In this limit the exact first-order wetting phase boundary is obtained using analytical and numerical methods, and is contrasted with the exact nucleation and wetting phase boundary derived previously for a two-component Bose-Einstein condensate mixture at a hard optical wall. Exact results for the three-component mixture are compared with results from the double-parabola approximation used in an earlier work.

Entanglement for pure bipartite states is most commonly quantified in a state-by-state manner to each pure state of a bipartite system a scalar quantity, such as the von Neumann entropy of a reduced density matrix. This provides a precise local characterization of how entangled a given state is. At the same time, this local description naturally invites a set of complementary, more global questions about the structure of the space of pure states: How abundant are the states with a given amount of entanglement within the full state space? Do the manifolds of constant entanglement exhibit distinct geometric regimes? These questions shift the focus from assigning an entanglement value to a single state to understanding the global organization and geometry of entanglement across the entire manifold of pure states. In this work, we develop a geometric framework in which these questions become natural. We regard the projective Hilbert space of pure states, endowed with the Fubini-Study metric, as a Riemannian manifold and promote bipartite entanglement to a macroscopic functional on this manifold. Its level sets stratify the space of pure states into hypersurfaces of constant entanglement, and we define a geometric entanglement entropy as the log-volume of these hypersurfaces, weighted by the Fubini-Study gradient of entanglement. This quantity plays the role of a microcanonical entropy in entanglement space: it measures the degeneracy of a given entanglement value in the natural quantum geometry. The framework is illustrated first in the simplest case of a single spin-1/2 and then for bipartite entanglement of spin systems, including a two-qubit example where explicit calculations can be carried out, along with a sketch of the extension to spin chains.

Zitterbewegung (ZBW), the trembling motion predicted by the Dirac equation, has long remained unobservable in free electrons due to its sub-Compton scale. We elaborately construct a relativistic vortex electron wave packet as a coherent superposition of both positive- and negative-energy Dirac states and derive their space-time dynamics. Our analysis demonstrates that introducing orbital angular momentum provides a mechanism for amplifying the ZBW amplitude far beyond that of conventional Gaussian packets, while maintaining coherence. The resulting relativistic vortex states unify Gaussian and Bessel-Gaussian models within a single framework and opens new possibilities for observing relativistic quantum dynamics in structured electron wave packets.

Atom-like defects in hexagonal boron nitride (hBN) provide room-temperature single-photon emission and coherent spin states, making them attractive for quantum-computing and -sensing applications. However, their random spatial and spectral characteristics hamper deterministic coupling with nano-optical cavities, limiting their use as bright single-photon sources and sensitive quantum sensors. Here, we present tip-enhanced quantum-sensing spectroscopy of single-photon emitters in hBN. Through precise spatial positioning of individual emitters within tip-cavities with different plasmon resonances, we adaptively control the enhancement rates of both excitation and emission, as well as the single-photon purity. In this way, optimal selection of their relative contributions can effectively reconfigure solid-state single-photon sources, with simultaneous nano-spectroscopic space- and time-resolved analyses. Furthermore, we demonstrate tip-enhanced quantum-sensing with single spin defects through optically detected magnetic resonance (ODMR) experiments in tip-coupled hBN nanoflakes. Our approach provides a unique pathway toward highly-sensitive and deterministic quantum-sensing with room-temperature single-photon emitters.

We study a fluid of quantum hard-spheres treated with affine-quantization. Assuming that the fluid obeys to Bose-Einstein statistics we solve for its thermodynamic properties using the path integral Monte Carlo method.

We develop a unified framework to analyze $d$-dimensional quantum teleportation through the joint geometry of two complementary figures of merit: average fidelity $F$ (how well a protocol works on average) and fidelity deviation $D$ (how uniformly it works across the inputs). Technically, we formulate a representation-theoretical framework based on Schur-Weyl duality and permutation symmetry calculus that reduce the higher-moment Haar averages to a finite set of trace invariants of the composed correction unitaries. This yields closed-form expressions for $F$ and $D$ in arbitrary Hilbert-space dimension and delivers tight bounds that link the admissible deviation directly to the gap from the optimal average performance. In particular, any measured pair $(F, D)$ can be ported into a visibility estimate for isotropic channel resources, turning the $(F, D)$-plane into a calibrated diagnostic map. We further cast the teleportation advantage and CGLMP-inequality violation as two witnesses lines in the $(F,D)$ plane: one line certifies that $F$ beats the classical benchmark $2/(d{+}1)$, while the other line certifies the Bell nonlocality. Their identical slope but distinct intercepts expose a quantitative gap between "entangled yet local" and "genuinely nonlocal" resources.

We characterize optimality of Quantum strategies for the Odd-Cycle game. Separate from other game-theoretic settings, parallel repetition for the Odd-Cycle game is related to the foam problem, which can be formulated through a minimization of the surface area. In comparison to previous works on minimizing the surface area, we quantify how properties of the marked giant connected component can be related to the maximum winning probability using Quantum strategies. Objects that we introduce to formulate such connections include the topological odd-blocker, previous examples of error bounds for other Quantum games that have been formulated by the author, pearls, consistent regions, and the cycle elimination problem.

We propose a scheme to generate multi-paths entanglement in an optomechanical system by exploiting polarized electromagnetic fields and dark mode control. Our system consists of two mechanically coupled mechanical resonators, which are driven by a common electromagnetic field. An inclusion of a polarizer induces linear polarizations of the electromgnetic field corresponding to the vertical (transverse electric ($\rm{TE}$) and horizontal (transverse magnetic [($\rm{TM}$]) modes, which drive the mechanical resonators. Without the mechanical coupling $J_m=0$, the polarization angle ($φ$) controls dark mode in the system. The breaking of this dark mode leads to multi-paths engineering of bipartite optomechanical entanglements. By switching on the phonon hopping rate ($J_m\neq0$), both the polarization angle and the modulation phase of the mechanical coupling allow a further control of the dark mode. The simultaneous Dark Mode Breaking (\rm{DMB}) conditions under these two parameters leads to multi-paths bipartite and tripartite entanglements. For a fine tuning of the polarization angle ($φ=π/4$) this scheme enables a generation of twin entangled states, where the bipartite/tripartite generated entangled states are degenerated and might be of great interest for quantum information processing, quantum communication and diverse quantum computational tasks. The generated entanglements are more resilient against thermal fluctuations in the \rm{DMB} regime, i.e., up to two order of magnitude robust than in the Unbreaking regime. Our work sheets light on new possibilities to generate noise-tolerant quantum resources that are useful for plethora of modern quantum technologies.

Quantum Krylov algorithms have emerged as a promising approach for ground-state energy estimation in the near-term quantum computing era. A major challenge, however, lies in their inherently substantial sampling cost, primarily due to the individual measurement of each term in the Hamiltonian. While various techniques have been proposed to mitigate this issue, the sampling overhead remains a significant bottleneck, especially for practical large-scale electronic structure problems. In this work, we introduce an alternative method, dubbed mirror subspace diagonalization (MSD), which approaches the theoretical lower bound of the sampling cost for quantum Krylov algorithms. MSD leverages a finite-difference formula to express the Hamiltonian operator as a linear combination of time-evolution unitaries with symmetrically shifted timesteps, enabling efficient estimation of the Hamiltonian matrix within the Krylov subspace. In this scheme, the finite difference and statistical errors are simultaneously minimized by optimizing the timestep parameter and shifting the energy spectrum. Consequently, MSD attains the lower bound of the sampling cost of the quantum Krylov algorithms up to a logarithmic factor. Furthermore, we employ classical post-processing to infer Hamiltonian moments, which are used to mitigate the ground state energy error based on the Lanczos scheme. Through theoretical analysis of the sampling cost, we demonstrate that MSD is particularly effective when the spectral norm of the Hamiltonian is significantly smaller than its 1-norm. Such a situation arises, for example, in high-accuracy simulations of molecules using large basis sets that incorporate strong electronic correlations. Numerical results for various molecular models reveal that MSD can achieve sampling cost reductions ranging from approximately 10 to 10,000 times compared to the conventional quantum Krylov algorithm.

The heralded optical parametric amplifier (OPA) has emerged as a promising tool for quantum state engineering. However, its potential has been limited to coherent state inputs. Here, we introduce a generalized heralded OPA protocol that unlocks a vastly expanded class of quantum phenomena by accepting arbitrary non-classical inputs. With a squeezed vacuum input, the setup functions as an integrated two-photon subtractor, deterministically generating high-fidelity, larger-amplitude squeezed Schrödinger cat states -- an operation previously requiring complex, discrete setups. Furthermore, when fed a small-amplitude SC state, the protocol acts as a non-Gaussianity amplifier, distilling it into high-purity approximations of key quantum resources like specific photon-number superpositions. This work transforms the OPA from a specialized source into a versatile and practical platform for advanced quantum state engineering, enabling the generation of a wide array of non-Gaussian states from a single, integrated setup.

Two-sample tests have been extensively employed in various scientific fields and machine learning such as evaluation on the effectiveness of drugs and A/B testing on different marketing strategies to discriminate whether two sets of samples come from the same distribution or not. Kernel-based procedures for hypothetical testing have been proposed to efficiently disentangle high-dimensional complex structures in data to obtain accurate results in a model-free way by embedding the data into the reproducing kernel Hilbert space (RKHS). While the choice of kernels plays a crucial role for their performance, little is understood about how to choose kernel especially for small datasets. Here we aim to construct a hypothetical test which is effective even for small datasets, based on the theoretical foundation of kernel-based tests using maximum mean discrepancy, which is called MMD-FUSE. To address this, we enhance the MMD-FUSE framework by incorporating quantum kernels and propose a novel hybrid testing strategy that fuses classical and quantum kernels. This approach creates a powerful and adaptive test by combining the domain-specific inductive biases of classical kernels with the unique expressive power of quantum kernels. We evaluate our method on various synthetic and real-world clinical datasets, and our experiments reveal two key findings: 1) With appropriate hyperparameter tuning, MMD-FUSE with quantum kernels consistently improves test power over classical counterparts, especially for small and high-dimensional data. 2) The proposed hybrid framework demonstrates remarkable robustness, adapting to different data characteristics and achieving high test power across diverse scenarios. These results highlight the potential of quantum-inspired and hybrid kernel strategies to build more effective statistical tests, offering a versatile tool for data analysis where sample sizes are limited.

In conventional quantum mechanics, all unitary evolution takes place within the space-time Hilbert space $\mathcal H_{xt}=L^2(\mathcal M_{xt})$, with time as the sole evolution parameter. The momentum-energy representation $φ(k,E)$ is treated merely as a Fourier re-expression of the same state-kinematically equivalent but dynamically inert. Here we restore the fundamental symmetry between the conjugate pairs $(x,t)$ and $(k,E)$ by extending the quantum theory to an enlarged Hilbert space $\mathcal H_{\text{total}} = \mathcal H_{xt} \oplus \mathcal H_{kE}$, within which the momentum-energy sector $\mathcal H_{kE}=L^2(\mathcal M_{kE})$ carries its own autonomous unitary evolution generated by a self-adjoint operator $\hat{\mathcal T}$. The resulting structure establishes a meta-symmetry: a symmetry between two conjugate dynamical projections of a single global quantum state. It produces a dual-manifold geometry in which each domain is locally complete yet globally open, with divergent limits in one mapping onto extended regions in the other. Remarkably, the dual-manifold symmetry alone reproduces both the uniform dark-energy background and the exponential boundary mapping near black-hole horizons that underlies Hawking radiation. This framework thus opens a quantum-theoretic route to cosmological phenomena that are ordinarily treated within general relativity.

Superconducting nanowire single-photon detectors (SNSPDs) are among the most sensitive single-photon detectors available and have the potential to transform fields ranging from infrared astrophysics to molecular spectroscopy. However, extending their performance into the mid-infrared spectral region - crucial for applications such as exoplanet transit spectroscopy and vibrational fingerprinting of molecules - has remained a major challenge, primarily due to material limitations and scalability constraints. Here, we report on the development of SNSPDs based on tungsten germanide, a novel material system that combines high infrared sensitivity with compatibility for large-scale fabrication. Our detectors exhibit saturated internal detection efficiency at wavelengths up to 29 $\mathrm{μm}$. This advance enables scalable, high-performance single-photon detection in a spectral region that was previously inaccessible, opening new frontiers in remote sensing, thermal imaging, environmental monitoring, molecular physics, and astronomy.

The recent development of bootstrap methods based on semidefinite relaxations of positivity constraints has enabled rigorous two-sided bounds on local observables directly in the thermodynamic limit. However, these bounds inevitably become loose in symmetry broken phases, where local constraints are insufficient to capture long-range order. In this work, we identify the origin of this looseness as order parameter defects which are difficult to remove using local operators. We introduce a $\textit{defect bootstrap}$ framework that resolves this limitation by embedding the system into an auxiliary $\textit{defect model}$ equipped with ancilla degrees of freedom. This construction effectively enables local operators to remove order parameter defects, yielding tighter bounds in phases with spontaneous symmetry breaking. This approach can be applied broadly to pairwise-interacting local lattice models with discrete or continuous internal symmetries that satisfy a property we call $\textit{defect diamagnetism}$, which requires that the ground state energy does not decrease upon adding any finite number of symmetry defects. Applying the method to the transverse field Ising models in 1D and 2D, we obtain significantly improved bounds on energy densities and spin correlation functions throughout the symmetry broken phase in 1D and deep within the phase in 2D. Our results demonstrate that physically motivated constraint sets can dramatically enhance the power of bootstrap methods for quantum many-body systems.

This work investigates a quantum system described by a Hamiltonian operator in a two dimensional noncommutative space. The system consists of an electron subjected to a perpendicular magnetic field $\mathbf{B}$, coupled to a harmonic potential and an external electric field $\mathbf{E}$, within the context of non-extensive statistical thermodynamics. The noncommutative geometry introduces a fundamental minimal length that modifies the phase space structure. The thermodynamics of this quantum system is developed within the framework of Tsallis statistics through the derivation of $q$-generalized versions of the partition function, magnetization, and magnetic susceptibility, following the application of a generalized Hilhorst transformation adapted to non-commutative geometry. The combined effects of the non-extensivity parameter $q$ and the noncommutativity parameter $θ$ are analyzed by considering the limit $q \rightarrow 1$, revealing new thermodynamic regimes and anomalous electromagnetic properties specific to quantum systems in non-commutative geometry.

The preparation and control of quantum states lie at the heart of quantum information science (QIS). Recent advances in solid-state quantum emitters (QEs) and nanophotonics have transformed the landscape of quantum photonic technologies, enabling scalable generation of quantum states of light and matter. A new frontier in solid-state quantum photonics is the engineering of many-body interactions between QEs and photons to achieve robust coherence and controllable many-body entanglement. These entangled states, including photonic graph and cluster states, superradiant emission, and emergent quantum phases, are promising for quantum computation, sensing, and simulation. However, intrinsic inhomogeneities and decoherence in solid-state platforms pose significant challenges to realize such complex entangled states. This review provides an overview of the fundamental many-body interactions and dynamics at the light-matter interfaces of solid-state QEs, and discusses recent advances in mitigating decoherence and harnessing robust many-body coherence.

The quantum Zeno effect typically refers to freezing the dynamics of a quantum system through frequent observations. In general, quantum Zeno dynamics is obtained with an error of order $\mathcal{O}(1/N)$, where $N$ is the number of projective measurements performed within a fixed evolution time. In this work, we develop higher-order Zeno sequences that achieve faster convergence to Zeno dynamics, yielding an improved error scaling of $\mathcal{O}(1/N^{2k})$, where $k$ describes the order of the Zeno sequence. This is achieved by relating higher-order Zeno sequences to higher-order Trotter formulas that achieve similar convergence behavior. We leverage this relation to develop higher-order Zeno sequences for different manifestations of the quantum Zeno effect, including frequent projective measurements and unitary kicks. We go on to discuss achieving quantum Zeno dynamics through periodic control fields of high frequency. We explicitly develop control fields that yield a second-order type improvement in the Zeno error scaling and present shorter Zeno sequences. Finally, we discuss the connection to randomized and Uhrig dynamical decoupling to develop more efficient implementations in the weak coupling regime.

We introduce a superresolution technique that combines spatial mode demultiplexing (SPADE) with emitter blinking. We show that temporal fluctuations not only enhance the precision of SPADE imaging, but also drastically simplify the measurement required to recover full object information -- in the presence of fluctuations, SPADE can be replaced by the much simpler image inversion interferometry. Both gains are enabled by exploiting temporal cumulants of the detected signal.

We discuss the exact quantization of general one-dimensional potentials in view of the exact-WKB formalism. Building on our previous work, we perform analytic continuations across different sectors via the complexification to the spectral (energy) parameter $u$ and identify continuous and discontinuous transitions of the exact spectrum for generic potentials. When the transition is discontinuous, it is characterized by the Stokes phenomena, inducing different exact (median) quantization conditions, thereby distinct trans-series structures valid in different sectors. We analyze two illustrative examples, namely asymmetric triple-well (ATW) and tilted double-well (TDW), and verify the general qualitative analysis by deriving exact (median) quantization conditions in each sector. Moreover, by obtaining the trans-series solutions for each system, we identify bion/bounce configurations and show that the trans-series of ATW is organized in accordance with the cluster expansion of the bion gas and there should exist a previously neglected complex saddle in the TDW system. These identifications further strengthen the link between path integral and exact-WKB formalisms, while also demonstrating the predictive power of the latter. In parallel, for the P-NP relations of genus-1 systems, we derive transformation rules between any perturbative and non-perturbative pair of WKB-cycles. Our results show that the entire resurgence data of a genus-1 system transforms only by the change of classical parameters, i.e. frequencies and bion/bounce actions, and the perturbative energy series. This also reveals the underlying reasons of the previously found $S$-duality transformations.

Electron-on-neon (eNe) charge states coupled to superconducting circuits are a promising platform for quantum computing. Control over the formation of these charge states requires techniques to track and control the growth of solid Ne films on the circuit surface. We demonstrate a real-time Ne film-growth monitor using high-transition-temperature (high-$T_c$) YBCO microwave resonators. The high $T_c$ enables tracking of the film thickness near Ne's triple temperature and below. Across more than 300 solidification experiments, we find that the final Ne thickness varies stochastically from a few nm to a few $μ$m for films solidified from the liquid phase. By increasing the driving power in the resonator, we consistently reduce the final thickness to below 100 nm. These results represent an important step toward controlled formation of Ne films for eNe qubits and highlight the broader utility of high-$T_c$ resonators for hybrid quantum systems.

Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for models with multiple fields, unless a regularity condition is satisfied. This has so far restricted the use of RCMPS to toy models with a single self-interacting field. We address this long standing problem by introducing a Riemannian optimization framework, that allows to minimize the energy density over the regular submanifold of multi-field RCMPS, and thus to retain purely variational results. We demonstrate its power on a model of two interacting scalar fields in $1+1$ dimensions. The method captures distinct symmetry-breaking phases, and the signature of a Berezinskii-Kosterlitz-Thouless (BKT) transition along an $O(2)$-symmetric parameter line. This makes RCMPS usable for a far larger class of problems than before.

In a wide range of quantum gravity theories, quasiclassical geometries, which are solutions to the Einstein field equations approximately, are described by "coherent states." Here we propose a Hamiltonian formalism for gravitational dynamics with respect to this coherent state basis, which generates time evolution of the spacetime with respect to a clock at infinity. Since the coherent states are not orthogonal, an initial quasiclassical geometry is dynamically driven into a superposition of different amplitudes. Our framework provides a dynamical mechanism for tunneling between geometries that is ubiquitous in a number of approaches to quantum gravity, from loop quantum gravity to the Euclidean path integral. We apply our framework to the problem of black hole evaporation, providing a hint at how unitarity may be preserved with the inclusion of quantum corrections to the semiclassical evolution of the black hole.

Introducing new components and functionalities into quantum devices is critical in advancing state-of-the-art hardware. Here, we propose superconducting diodes (SDs) as a coherent nonreciprocal element in circuit quantum electrodynamics (cQED) architectures. In particular, we use an asymmetric SQUID as an SD controlled with a flux bias. We spectroscopically characterize SD and show that flux bias acts cooperatively with the nonlinear diode response to induce direction-dependent resonance shifts in the transmission spectrum. We use the SD as an elementary component to realize coherent nonreciprocal qubit-qubit coupling. With a minimal two qubit system, we demonstrate a nonreciprocal half-iSWAP gate with tunable Bell-state generation, thereby showcasing the potential of intrinsic nonreciprocity as a tool in coherent control in quantum technologies. Our work enables high-fidelity signal routing and entanglement generation in all-to-all connected microwave quantum networks, where nonreciprocity is embedded at the device level.

The integration of Nitrogen-Vacancy color centers into diamond anvil cells has opened the door to quantum sensing at megabar pressures. Despite a multitude of experimental demonstrations and applications ranging from quantum materials to geophysics, a detailed microscopic understanding of how stress affects the NV center remains lacking. In this work, using a combination of first principles calculations as well as high-pressure NV experiments, we develop a complete description of the NV's optical properties under general stress conditions. In particular, our ab initio calculations reveal the complex behavior of the NV's inter-system crossing rates under stresses that both preserve and break the defect's symmetry. Crucially, our proposed framework immediately resolves a number of open questions in the field, including: (i) the microscopic origin of the observed contrast-enhancement in (111)-oriented anvils, and (ii) the surprising observation of NV contrast-inversion in certain high-pressure regimes. Our work lays the foundation for optimizing the performance of NV high-pressure sensors by controlling the local stress environment, and more generally, suggests that symmetry-breaking stresses can be utilized as a novel tuning knob for generic solid-state spin defects.

We revisit whether a semiclassical baby universe in AdS/CFT necessarily possess a trivial one-dimensional Hilbert space or may instead carry a large entropy. Recent results on Haar random encoding suggest a breakdown of complementary recovery, in which no logical operators can be reconstructed from individual bipartite subsystems. Motivated by this, we propose an interpretation where a baby universe emerges as logical degrees of freedom that cannot be accessed from either boundary alone, assuming pseudorandom dynamics in holographic CFTs. We then analyze two conceptual puzzles: an apparent cloning of baby-universe microstates and its eventual fate at the singularity. Both puzzles are avoided because no single boundary observer can access the baby-universe degrees of freedom, be it classical or quantum, reflecting an emergent form of complementarity due to the structure of random encoding. In this interpretation, observers arise naturally: the same heavy operator that prepares the baby-universe geometry also serves as observer-like degrees of freedom that define an observer-dependent baby-universe microstate.

Optimal routing in quantum-repeater networks requires finding the best path that connects a pair of end nodes. Most previous work on routing in quantum networks assumes utility functions that are isotonic, meaning that the ordering of two paths does not change when extending both with the same edge. However, we show that utility functions that take into account both the rate and quality of the entanglement generation (e.g., the secret-key rate) are often non-isotonic. This makes pathfinding difficult as classical algorithms such as Dijkstra's become unsuitable, with the state of the art for quantum networks being an exhaustive search over all possible paths. In this work we present improved algorithms. First, we present two best-first-search algorithms that use destination-aware merit functions for faster convergence. One of these provably finds the best path, while the other uses heuristics to achieve an effectively sublinear scaling of the query count in the network size while in practice always finding a close-to-optimal path. Second, we present metaheuristic algorithms (simulated annealing and a genetic algorithm) that enable tuning a tradeoff between path quality and computational overhead. While we focus on swap-ASAP quantum repeaters for concreteness, our algorithms are readily generalized to different repeater schemes and models.

Given a tensor network state, how can we determine conserved operators (including Hamiltonians) for which the state is an eigenstate? We answer this question by presenting a method to extract geometrically $k$-local conserved operators that have the given infinite projected entangled pair state (iPEPS) in 2D as an (approximate) eigenstate. The key ingredient is the evaluation of the static structure factors of multi-site operators through differentiating the generating function. Despite the approximation errors, we show that our method is still able to extract from exact or variational iPEPS to good precision both frustration-free and non-frustration-free parent Hamiltonians that are beyond the standard construction and obtain better locality. In particular, we find a 4-site-plaquette local Hamiltonian that approximately has the short-range RVB state as the ground state. Moreover, we find a Hamiltonian that has the deformed toric code state at any string tension as excited eigenstates at the same energy, which might be potential candidates for quantum many-body scars.

Exceptional points are spectral singularities where both eigenvalues and eigenvectors collapse onto a single mode, causing the system behavior to shift abruptly and making it highly responsive to even small perturbations. Although widely studied in optical and quantum systems, using them for energy storage in quantum systems has been difficult because existing approaches rely on gain, precise balanced loss, or explicitly non-Hermitian Hamiltonians. Here we introduce a quantum energy-storage mechanism that realizes exceptional-point physics in a fully passive, physically consistent open quantum system. Instead of amplification, we use trace-preserving reservoir engineering to create an effective complex interaction between a charging mode and a storage mode through a dissipative mediator, generating an exceptional point directly in the drift matrix of the Heisenberg-Langevin equations while preserving complete positivity. The resulting dynamics exhibit two regimes: a stable phase where the stored energy saturates, and a broken phase where energy grows exponentially under a bounded coherent drive. This rapid charging arises from dissipative interference that greatly boosts energy flow between the modes without gain media or nonlinear amplification. The mechanism is compatible with optomechanical devices, superconducting circuits, and magnonic systems, offering a practical route to fast, robust, and scalable quantum energy-storage technologies and new directions in quantum thermodynamics.

The non-Hermitian skin effect (NHSE) -- the anomalous boundary accumulation of an extensive number of bulk modes -- has emerged as a hallmark of non-Hermitian physics, with broad implications for transport, sensing, and topological classification. A central open question is how magnetic or synthetic gauge fields influence this boundary phenomenon. Here, we develop a theoretical framework for magnetic control of the NHSE along line boundaries in two-dimensional single-band lattices. Using a non-Hermitian extension of the anisotropic Harper--Hofstadter model as a representative example, we show that magnetic fields suppress the geometric skin effect in reciprocal models, whereas skin localization can persist in nonreciprocal systems. The analysis disentangles the interplay of flux, nonreciprocity, and boundary geometry, revealing that magnetic fields mitigate or suppress the NHSE through distinct physical mechanisms -- such as bulk localization via Landau or Anderson physics, or the restoration of effective reciprocity. In particular, the geometry-dependent skin effect in reciprocal systems is found to be fragile against even weak magnetic fields.

We present an emulator-based and hardware feasibility study of Aurora-DD, a phase-coherence compensation method that integrates a sign-based feedback update of a global phase offset (Delta phi) with a fixed-depth XY8 dynamical decoupling (DD) scaffold. The feedback optimization is performed offline on a calibrated emulator and the resulting Delta phi* is deployed as pre-calibrated phase compensation on hardware. This represents an "offline closed-loop, online open-loop" feasibility demonstration. Using an Aer-based emulator calibrated with ibm_fez device parameters, Aurora-DD achieves substantial reductions in mean-squared error of the measured expectation value <Z>, yielding 68-97% improvement across phase settings phi = 0.05, 0.10, 0.15, 0.20 over n=30 randomized trials. These large-n emulator results provide statistically stable evidence that the combined effect of XY8 and Delta phi* suppresses both dephasing and systematic phase bias. On real superconducting hardware (ibm_fez), we perform a small-sample (n=3) multi-phase validation campaign. Aurora-DD yields point estimates corresponding to approximately 99.2-99.6% reduction in absolute error relative to a no-DD baseline across all tested phase points. These hardware numbers are reported transparently as feasibility evidence under tight queue and credit constraints. In contrast, the auxiliary Aurora+ZNE branch exhibits instability: shallow two-point ZNE occasionally amplifies calibration inconsistencies and produces large error outliers. We therefore relegate ZNE analysis to the Appendix and position Aurora-DD (without ZNE) as the primary contribution. Overall, the combined results support pre-calibrated Aurora-DD as a practical, stable, and hardware-compatible phase-coherence compensator for NISQ devices in single-qubit settings.

The rapid deployment of AI models necessitates robust, quantum-resistant security, particularly against adversarial threats. Here, we present a novel integration of post-quantum cryptography (PQC) and zero trust architecture (ZTA), formally grounded in category theory, to secure AI model access. Our framework uniquely models cryptographic workflows as morphisms and trust policies as functors, enabling fine-grained, adaptive trust and micro-segmentation for lattice-based PQC primitives. This approach offers enhanced protection against adversarial AI threats. We demonstrate its efficacy through a concrete ESP32-based implementation, validating a crypto-agile transition with quantifiable performance and security improvements, underpinned by categorical proofs for AI security. The implementation achieves significant memory efficiency on ESP32, with the agent utilizing 91.86% and the broker 97.88% of free heap after cryptographic operations, and successfully rejects 100% of unauthorized access attempts with sub-millisecond average latency.

We resolve a conjecture of De Palma and Trevisan by proving the triangle inequality for a quantum 2-Wasserstein distance. The proof relies on complex analysis methods to establish a new integral representation of the cost in the optimal transport problem.

We present a quantum thermometric protocol for the estimation of multiple temperatures within the collisional model framework. Employing the formalism of multiparameter quantum metrology, we develop a systematic strategy to estimate the temperatures of several thermal reservoirs with minimal estimation error. We prove a necessary and sufficient condition for the singularity of the Fisher information matrix for a bi-parametrized qubit state. By using controlled rotations of ancillary systems between successive interaction stages, we eliminate parameter interdependencies, thereby rendering the quantum Fisher information matrix non-singular. Remarkably, we demonstrate that precision enhancement in the joint estimation of multiple temperatures can be achieved even in the absence of correlations among the ancillas, surpassing the corresponding thermal Fisher information limits. Exploiting correlations within the ancillary system yields additional enhancement of Fisher information. Finally, we identify the dimensionality of the ancillary systems as a key factor governing the efficiency of multiparameter temperature estimation.

The complex valence band structure of bulk cuprous oxide necessitates going beyond the parabolic approximation to precisely estimate exciton binding energies. The same is true for excitons in cuprous oxide quantum wells, for which many effects have been obtained so far only qualitatively within a hydrogenlike two-band model. Here, we derive the complete Hamiltonian for excitons in cuprous oxide quantum wells based on the Luttinger-Kohn model, taking into account the full complex valence band structure. Symmetry properties of the system are discussed. Numerical results based on the diagonalization of the Hamiltonian using B-spline functions reveal the energy shifts and the lifting of degeneracies due to the nondiagonal coupling terms of the complex valence band. The relative oscillator strengths of the excitonic transitions induced by circularly polarized light are also calculated.

In quasi-Hermitian quantum mechanics (QHQM) of unitary systems, an optimal, calculation-friendly form of Hamiltonian is generally non-Hermitian, $H \neq H^\dagger$. This makes its physical interpretation ambiguous. Without altering $H$, this ambiguity is resolved by specifying a nontrivial inner-product metric $Θ$ in Hilbert space. Here, we focus on an alternative strategy: transforming $H$ into a Hermitian form via the Dyson map $Ω: H \to \mathfrak{h}$. This construction of the Hermitian isospectral twin $\mathfrak{h}$ of $H$ does not only restore the conventional correspondence principle between quantum and classical physics, but it also provides a framework for the exhaustive classification of all admissible probabilistic interpretations of quantum systems in QHQM framework.

We estimate the run-time and energy consumption of simulating non-equilibrium dynamics on neutral atom quantum computers in analog mode, directly comparing their performance to state-of-the-art classical methods, namely Matrix Product States and Neural Quantum States. By collecting both experimental data from a quantum processing unit (QPU) in analog mode and numerical benchmarks, we enable accurate predictions of run-time and energy consumption for large-scale simulations on both QPUs and classical systems through fitting of theoretical scaling laws. Our analysis shows that neutral atom devices are already operating in a competitive regime, achieving comparable or superior performance to classical approaches while consuming significantly less energy. These results demonstrate the potential of analog neutral atom quantum computing for energy-efficient simulation and highlight a viable path toward sustainable computational strategies.

In this study, we investigate the effect of the Lorentz transformation on the measures of quantum coherence in an entangled atomic system. Here, we consider the effect of this relativistic boosts on two-particle entangled generalized Gaussian wave packets in two scenarios. In the first scenario, we consider that the relativistic boost affects the one particle and other remains unaffected while in the second scenario, we consider that both the particles are affected by the effect of the relativistic boost. The coherence of the wave function as measured by the boosted observer is studied as a function of the boost parameter and the width of the Gaussian wave packets. Using various formulations of coherence, it is shown that in general the coherence decays with increase in the width of the Gaussian wave packet, higher values of boost parameter, and the number of particles on which boost is applied.

We investigate photon tunneling in a pair of coupled inverted circular split-ring microwave resonators with four discrete chiral orientations. By varying the spacing between the resonators, we observe strong modulation of the transmission spectra, including mode splitting, interference effects, and the formation of dark states. Measurements on fabricated devices show clear signatures of hybridization that depend on both chirality and proximity, and these results are consistent with full-wave electromagnetic simulations. To describe the observed behavior, we develop a circuit quantum electrodynamics model that captures the dependence of the coupling strength on geometry and the reversal of its sign. Although the experimental excitation is classical, the system reproduces features expected from two quantized harmonic oscillators, providing a classical analogue of a chiral quantum hybrid platform. The ability to control photon tunneling through structural design and excitation parameters suggests potential applications in reconfigurable photonic devices, quantum communication, chiral sensing, and polarization-selective signal processing.

We study quantum measurement retrodiction using the principle of minimum change. For quantum-to-classical measurement channels, we show that all standard quantum divergences select the same retrodictive update, yielding a unique and divergence-independent quantum Bayesian inverse for any POVM and prior state. Using this update, we construct a symmetric joint distribution for pairs of POVMs and introduce the mutual retrodictability, for which we also derive a general upper bound that depends only on the prior state and holds for all measurements. This structure leads to two retrodictive entropic uncertainty relations, expressed directly in terms of the prior state and the POVMs, but valid independently of the retrodictive framework and fully compatible with the conventional operational interpretation of entropic uncertainty relations. Finally, we benchmark these relations numerically and find that they provide consistently tighter bounds than existing entropic uncertainty relations over broad classes of measurements and states.

We propose a scheme to manipulate the Goos-Hänchen shift (GHS) of a reflected probe field in a non-Hermitian cavity magnomechanical system. The platform consists of a yttrium-iron-garnet sphere coupled to a microwave cavity, where a strong microwave drive pumps the magnon mode and a weak field probes the cavity. The traveling field's interaction with the magnon induces gain, yielding non-Hermitian dynamics. When the traveling field is oriented at $π/2$ relative to the cavity's $x$-axis, the system realizes $\mathcal{PT}$ symmetry; eigenvalue analysis reveals a third-order exceptional point ($\mathrm{EP}_3$) at a tunable effective magnon-photon coupling. Under balanced gain-loss and finite effective magnomechanical coupling, we demonstrate coherent control of the GHS by steering the system across the $\mathcal{PT}$-symmetric transition and through $\mathrm{EP}_3$ via the effective magnon-photon coupling, enabling pronounced enhancement or suppression of the lateral shift. Furthermore, we show that without effective magnomechanical coupling, the system exhibits a second-order exceptional point ($\mathrm{EP}_2$) with a distinct GHS phase transition. This phase transition vanishes when the effective magnomechanical coupling exceeds a parametric threshold, where strong absorption at resonance suppresses the GHS. We also identify the intracavity length as an additional control parameter for precise shift tuning. Notably, the $\mathcal{PT}$-symmetric configuration yields substantially larger GHS than its Hermitian counterpart. These results advance non-Hermitian magnomechanics and open a route to GHS-based microwave components for quantum switching and precision sensing.

In this work, we investigate the Kitaev honeycomb model employing the recently developed Clifford Circuits Augmented Matrix Product States (CAMPS) method. While the model in the gapped phase is known to reduce to the toric code model - whose ground state is entirely constructible from Clifford circuits - we demonstrate that the very different gapless quantum spin liquid (QSL) phase can also be significantly disentangled with Clifford circuits. Specifically, CAMPS simulations reveal that approximately two-thirds of the entanglement entropy in the isotropic point arises from Clifford-circuit contributions, enabling dramatically more efficient computations compared to conventional matrix product state (MPS) methods. Crucially, this finding implies that the Kitaev QSL state retains significant Clifford-simulatable structure, even in the gapless phase with non-abelian anyon excitations when time reversal symmetry is broken. This property not only enhances classical simulation efficiency significantly but also suggests substantial resource reduction for preparing such states on quantum devices. As an application, we leverage CAMPS to study the Kitaev-Heisenberg model and determine the most accurate phase boundary between the anti-ferromagnetic phase and the Kitaev QSL phase in the model. Our results highlight how Clifford circuits can effectively disentangle the intricate entanglement of Kitaev QSLs, opening avenues for efficiently simulating related and similar strongly correlated models.

Flat-band lattices hosting compact localized states are highly sensitive to external modulation, and the tailored design of a perturbation to imprint specific features becomes relevant. Here we show that periodic driving in the high-frequency regime transforms the all-flat-band diamond chain into one featuring two tunable quasi-flat bands and a residual flat band pinned at $E=0$. The interplay between lattice geometry and the symmetries of the driven system gives rise to drive-induced tunneling processes that redefine the interference conditions and open a controllable route to escaping Aharonov-Bohm caging. Under driving, the diamond chain effectively acquires the geometry of a dimerized lattice, exhibiting charge oscillations between opposite boundaries. This feature can be exploited to generate two-particle entanglement that is directly accessible experimentally. The resulting drive-engineered quasi-flat bands thus provide a versatile platform for manipulating quantum correlations, revealing a direct link between spectral fine structure and dynamical entanglement.

The Quantum Approximate Optimization Algorithm (QAOA) is widely studied for combinatorial optimization and has achieved significant advances both in theoretical guarantees and practical performance, yet for general combinatorial optimization problems the expected performance and classical simulability of fixed-round QAOA remain unclear. Focusing on Max-Cut, we first show that for general graphs and any fixed round $p\ge2$, exactly evaluating the expectation of fixed-round QAOA at prescribed angles is $\mathrm{NP}$-hard, and that approximating this expectation within additive error $2^{-O(n)}$ in the number $n$ of vertices is already $\mathrm{NP}$-hard. To evaluate the expected performance of QAOA, we propose a dynamic programming algorithm leveraging tree decomposition. As a byproduct, when the $p$-local treewidth grows at most logarithmically with the number of vertices, this yields a polynomial-time \emph{exact} evaluation algorithm in the graph size $n$. Beyond Max-Cut, we extend the framework to general Binary Unconstrained Combinatorial Optimization (BUCO). Finally, we provide reproducible evaluations for rounds up to $p=3$ on representative structured families, including the generalized Petersen graph $GP(15,2)$, double-layer triangular 2-lifts, and the truncated icosahedron graph $C_{60}$, and report cut ratios while benchmarking against locality-matched classical baselines.

The radical pair mechanism (RPM) in the chemical magnetic compass model is considered to be one of the most promising candidates for the avian magnetic navigation, and quantum needle phenomenon further boosts the navigation precision to a new high level. It is well known that there are also a variety of methods in the field of magnetic field sensing in laboratory, e.g. Ramsey protocol of NV centers in diamond. Here, we compare the RPM model and Ramsey-like model under laboratory conditions and under in vivo conditions respectively. The results are both surprising and reasonable. Under laboratory conditions, if we have precise control over time and a reasonably accurate prior knowledge of the magnetic field direction, the Ramsey-like model will outperform the RPM model. However, when such information is unavailable, as under in vivo conditions, the RPM model stands out. The RPM model achieves greater practicality at the cost of reduced accuracy.

Bilayer graphene is a maturing material platform for gate-defined quantum dots that hosts long-lived spin and valley states. Implementing solid-state qubits in bilayer graphene requires a fundamental understanding of such confined electronic systems. In particular, states of two and three carriers, for which the exchange interaction between particles plays a crucial role, are a cornerstone for qubit readout and manipulation. Here we report on the spectroscopy of few-carrier states in bilayer graphene quantum dots, using circuit quantum electrodynamics (cQED) techniques that offer substantially improved energy resolution compared to standard transport techniques. Measurements using a superconducting high-impedance resonator capacitively coupled to the double quantum dot reveal dispersive features of two and three electron states, enabling the detection of Pauli spin and valley blockade and the characterization of the spin-orbit gap at zero magnetic field. The results deepen our understanding of few-carrier spin and valley states in bilayer graphene quantum dots and demonstrate that cQED techniques are a powerful state-selective probe for semiconductor nanostructures.

Improving our understanding of electron dynamics is essential for advancing energy transfer, optoelectronics, light harvesting systems and quantum computing. Recent developments in attosecond x-ray sources provide the fundamental possibility of observing these dynamics with atomic-scale resolution. However, connecting a time-resolved signal to dynamics is challenging due to the broad bandwidth of an attosecond probe pulse. This makes exploring the capabilities of different attosecond imaging techniques crucial. Here, we propose attosecond momentum-resolved resonant inelastic x-ray scattering as a prominent technique for tracking ultrafast dynamics. We demonstrate that the scattering signal contains an information about the instantaneous distribution of charge density across the scattering atoms. To illustrate this, we consider scattering from an $α$-sexithiophene molecule, in which coupled electron-hole dynamics are excited.

The precise measurement of the leptonic CP-violating phase $δ_{CP}$ remains one of the major open challenges in neutrino physics, as current experiments achieve only very limited accuracy. We address this issue through the lens of quantum estimation theory. A distinctive feature of neutrino oscillation experiments is that they cannot freely optimize the probe or measurement, since both are constrained by the production and detection of flavor eigenstates. We therefore examine whether the large uncertainty in $δ_{CP}$ originates from intrinsic reasons, either of the neutrino quantum state or of flavor measurements, or if it instead stems from experimental limitations. By comparing quantum and classical Fisher information, we demonstrate that the limited sensitivity to $δ_{CP}$ originates primarily from the information content of flavor measurements. Furthermore, we show that targeting the second oscillation maximum, as in the ESS$ν$SB proposal, substantially enhances $δ_{CP}$ information compared to experiments centered on the first maximum.

We present the experimental implementation of a three-time-bin phase-encoded Twin-Field Quantum Key Distribution (TF-QKD) protocol using a Sagnac-based star-topology plug-and-play architecture. The proposed encoding method leverages the relative phases of three consecutive time bins to encode two bits per signal. The Sagnac loop configuration enables self-compensation for both phase and polarisation drifts, eliminating the need for active stabilisation. However, field deployments are subject to rapid phase fluctuations caused by external vibrations, which can degrade interference visibility. We used the first time bin for real-time phase-fluctuation monitoring. Although this monitoring reduces the effective key generation rate, the system achieved a secure key rate of approximately 1.5e-5 bits per pulse, with a corresponding visibility of up to 87% over a 50 km asymmetric optical fibre channel. These results demonstrate the practicality, stability, and scalability of the proposed three-time-bin TF-QKD protocol for real-world quantum communication networks.

We propose a model of binary random number generator (RNG) based on a Brillouin optomechanical system. The device uses a hard excitation mode in a Brillouin optomechanical system, where thermal noise induces spontaneous transitions between two stable states in the hard excitation mode. We demonstrate the existence of an amplitude criterion for observing these transitions and show that the probability distribution of their occurrence in the non-generating and generating states can be precisely controlled by the amplitude of an external pump wave. At the same time, the use of a low-intensity seed wave allows for the control of the transition times between states. We demonstrate that the proposed random number generator successfully passes the standard tests NIST SP 800-22. The obtained result opens a way for development of an all-optical integrated True RNG, generating a sequence of random bits with equal probability.

The proposed vacuum beam guide (VBG) represents an innovation in the field of quantum channel technology, guaranteeing an ultra-low level of attenuation and a broad transmission linewidth, which offers an unprecedented quantum capacity exceeding Tera-qubits per second on a continental scale. However, its stability in terms of interferometry remains unexamined. To address this gap, we have developed a comprehensive error model that captures the intrinsic phase noise power spectral density associated with VBG, thereby revealing the advantages of VBG for interferometry over existing techniques. This model facilitates a comprehensive characterization of VBG as a photonic quantum channel, thereby facilitating a detailed investigation of its potential. Our theoretical analysis demonstrates the feasibility of VBG and its expected performance in a wide range of quantum applications.

Fast coherent state transport is essential to quantum computation and quantum information processing. While an adiabatic transport of atomic qubits guarantees a high fidelity of the state preparation, it requires a long timescale that defies efficient quantum operations. Here, we propose an adaptable and fast bang-bang-bang (BBB) protocol, utilizing a combination of forwardand backward-moving trap potentials, to expedite the coherent state transport. This protocol approaches the quantum speed limit under a harmonic trap potential, surpassing the performance by the forward-moving-only potential protocols. We further showcase the advantage of applying squeezed coherent state evolution under a deeper potential followed by a weaker one, where a design of symmetric squeezing potential transports promotes an even shorter timescale for genuine state preparation. Our protocols outperform conventional forward-moving-only methods, providing new insights and opportunities for rapid state transport and preparation, ultimately advancing the capabilities of quantum control and quantum operations.

Quantum computing is a promising technology that accelerates the partial differential equations solver for practical problems. The reconstruction of solutions (i.e., the readout of quantum states) remains a crucial problem, although numerous efficient quantum algorithms have been proposed. In this paper, we propose and compare several efficient readout methods in the real and the Fourier space. The Fourier space readout (FSR) and the proposed approximate real space readout (ARSR) methods are currently the most efficient and practical ones for the purpose of reconstructing continuous real-valued functions. In contrast, the quantum amplitude estimation (QAE) based methods (especially in the Fourier space) are favorable for mid-term/far-term quantum devices. Besides, we apply the methods for benchmark solutions in computational fluid dynamics (CFD) and demonstrate great improvements compared to the conventional sampling method for large grid numbers. Equipped with efficient readout methods, we further show that a 2D Burgers' equation can be solved efficiently without using the expensive strategy of linearization. It suggests the potential quantum advantages for some practical applications on mid-term quantum devices.

Decoded Quantum Interferometry (DQI) promises superpolynomial speedups for structured optimization; however, its practical realization is often hindered by significant sensitivity to hardware noise and spectral dispersion. To bridge this gap, we introduce Kernelized Decoded Quantum Interferometry (k-DQI), a unified framework that integrates spectral engineering directly into the quantum circuit architecture. By inserting a unitary kernel prior to the interference step, k-DQI actively reshapes the problem's energy landscape, concentrating the solution mass into a ``decoder-friendly'' low-frequency head. We formalize this advantage through a novel robustness metric, the noise-weighted head mass $Σ_K$, and prove a Monotonic Improvement Theorem, which establishes that maximizing $Σ_K$ guarantees higher decoding success rates under local depolarizing noise. We substantiate these theoretical gains in Optimal Polynomial Interpolation (OPI) and LDPC-like problems, demonstrating that kernel tuning functions as a ``spectral lens'' to recover signal otherwise lost to isotropic noise. Crucially, we provide explicit, efficient circuit realizations using Chirp and Linear Canonical Transform (LCT) kernels that achieve significant boosts in effective signal-to-noise ratio with negligible depth overhead ($\tilde{O}(n)$ to $\tilde{O}(n^2)$). Collectively, these results reframe DQI from a static algorithm into a tunable, noise-aware protocol suited for near-term error-corrected environments.

Virtual maps allow the simulation of quantum operations by combining physical processes with classical post-processing. Recent work on virtual unitary covariant broadcasting has shown, however, that such maps remain impractical for observable estimation tasks due to poor sample efficiency. Here we investigate whether relaxing the symmetry requirements can improve operational performance, focusing on virtual phase-covariant quantum broadcasting for qubits. We show that imposing phase-covariance, flip covariance, permutation invariance, and classical consistency fully determines the structure of the broadcasting map. Within this family, we identify the unique map that minimizes the simulation cost, and we prove that both the simulation cost and the distance to the closest CPTP map are strictly smaller than in the unitary covariant setting. We also demonstrate that the closest physical map is the optimal phase-covariant cloning channel, mirroring the relation between unitary covariant broadcasting and universal cloning. Despite these improvements, the resulting virtual broadcasting map remains sample-inefficient and is therefore still operationally impractical.

We prove that the PARITY protocol is optimal for a general class of non-adaptive distillation protocols of all $n$ player nonlocal boxes (NLBs) based on XOR games. The conditional distributions generated by these NLBs are assumed to have trivial local marginals. We also show that already for $n=2$, PARITY is no longer optimal if the local marginals are non-trivial. The OR protocol is shown to perform better and in the process also slightly extend the known correlations that collapse communication complexity. This emphasizes again the need to understand the local properties of nonlocal systems in order to obtain a better characterization of the global behavior. We conclude by showing an equivalence between adaptive distillation protocols that use identical NLBs and PARITY protocol using nonidentical NLBs.

A recent paper by Aziz and Howl (Nature 2025) argues that, once quantum matter is described at the level of quantum field theory and coupled to a classical gravitational field, higher order processes can generate entanglement between two spatially separated masses. A contemporaneous critical note (Marletto, Oppenheim, Vedral, Wilson, arXiv:2511.07348v1) shows that, in the actual nonrelativistic limit employed there, the interaction becomes ultra local, the total unitary factorizes, and no entanglement is generated from a product input. In this comment we (i) restate the core point of that critique, (ii) give a channel theoretic reformulation that makes the conclusion model independent, and (iii) clarify the distinction between activation of entanglement in already quantum matter and genuine mediation of entanglement by a classical field. Once these clarifications are in place, the standard BMV inference that observation of gravity mediated entanglement strongly indicates nonclassical gravitational degrees of freedom remains intact.

This paper develops a unified framework for quantum wavelet shrinkage, extending classical denoising ideas into the quantum domain. Shrinkage is interpreted as a completely positive trace-preserving process, so attenuation of coefficients is carried out through controlled decoherence rather than nonlinear thresholding. Phase damping and ancilla-driven constructions realize this behavior coherently and show that statistical adaptivity and quantum unitarity can be combined within a single circuit model. The same physical mechanisms that reduce quantum coherence, such as dephasing and amplitude damping, are repurposed as programmable resources for noise suppression. Practical demonstrations implemented with Qiskit illustrate how circuits and channels emulate coefficientwise attenuation, and all examples are provided as Jupyter notebooks in the companion GitHub repository. Encoding schemes for amplitude, phase, and hybrid representations are examined in relation to transform coherence and measurement feasibility, and realizations suited to current noisy intermediate-scale quantum devices are discussed. The work provides a conceptual and experimental link between wavelet-based statistical inference and quantum information processing, and shows how engineered decoherence can act as an operational surrogate for classical shrinkage.

Ultrafast quantum matter experiments have validated predictions from Floquet theory - notably, the dynamical modification of the electronic band structure and the light-induced anomalous Hall effect, via monotonic modulation of the driving amplitude. Here, we demonstrate how new physics is uncovered by leveraging quantum optimal control techniques to design Floquet amplitude modulation profiles. We discover a fundamentally different regime of topological transport, whereby the optimal oscillatory preparation protocol functions as a non-adiabatic topological pump: as a result, ultrahigh time-averaged anomalous Hall conductivities emerge, that reach up to around seventy times the values one would expect from the Chern number of the targeted Floquet state. The optimal protocols achieve >99% fidelity at the topological energy gap closing point - a twenty-fold improvement over standard monotonic approaches in as little as ten Floquet cycles - while unexpectedly generating the predicted ultrahigh conductivities. Our findings demonstrate that optimally prepared non-equilibrium quantum states can access transport regimes not achievable in the corresponding equilibrium system or even by applying conventional Floquet approaches, opening new avenues for ultrafast quantum technologies and topological device applications.

Quantum sensors based on the nitrogen-vacancy (NV) center in diamond are leading platforms for high-sensitivity magnetometry with nanometer-scale resolution. State-of-the-art implementations, however, typically rely on bulky free-space optics or sacrifice spatial resolution to achieve high sensitivities. Here, we realize an integrated platform that overcomes this trade-off by fabricating monolithic whispering-gallery-mode cavities from a diamond chip containing a high density of NV centers and by evanescently coupling excitation to and photoluminescence from the cavity using a tapered optical fiber. Employing a lock-in-amplified Ramsey magnetometry scheme, we achieve a photon-shot-noise-limited DC sensitivity of $58\,\text{nT}/\sqrt{\text{Hz}}$ -- the best sensitivity reported to date for a nanofabricated cavity-based magnetometer. The microscopic cavity size enables sub-micrometer-scale spatial resolution and low-power operation, while fiber-coupling provides a path to scalable on-chip integration. Arrays of such sensors could enable NV-NMR spectroscopy of sub-nanoliter samples, new magnetic-gradient imaging architectures, and compact biosensing platforms.

We investigate the emergence of an exciton condensate and associated collective modes in a bilayer configuration of $\text{MnBi}_2\text{Te}_4$, an antiferromagnetic topological insulator and van der Waals material, recognized for hosting axion physics. Utilizing a minimal low-energy Hamiltonian for the two layer system which is gapped by the intrinsic Néel order, we first employ mean-field theory to establish the conditions for exciton condensation. Our analysis identifies a nonzero, spin-singlet exciton order parameter which is tuned by external displacement field, temperature, and Coulomb attraction. Beyond the mean-field, we explore collective mode fluctuations in the uncondensed phase via many-body perturbation theory and the random phase approximation. From this, we derive the exciton spectral function which allows for a direct comparison between theoretical prediction and experimental observation. We detail how the softening of the collective mode peak is a function of the competition between interlayer detuning and thermal fluctuations. This work elucidates how the unique topological and magnetic environment of $\text{MnBi}_2\text{Te}_4$ offers a tunable platform for the realization and manipulation of exciton condensates and the corresponding collective excitations. Our findings contribute to understanding the interplay of topology and bosonic condensates, which could inspire application in optically accessing topological properties, dissipationless transport, and gate-tunable optoelectronics.

The Landau paradigm is a central dogma for understanding phase and phase transitions in condensed matter systems, yet for decades it has been known that a variety of quantum phases exist beyond the framework. Is there a more general framework that provides a systematic understanding of phase and phase transitions in quantum many-body systems? Recent developments of the notion of generalized symmetry and generalized gauging seem to point to a way to generalize the Landau Paradigm. In this essay, we discuss how `beyond Landau' phases and phase transitions can be captured by a generalized Landau paradigm in terms of the breaking of generalized symmetries, often induced by the generalized gauging procedure facilitated through the topological holography formalism. We also discuss what needs to be understood to make the generalized Landau paradigm useful in the study of quantum phase and phase transitions.

We consider the phase space of the Maxwell field as a simplified framework to study the quantisation of holonomies (Wilson line operators) on lightlike (null) surfaces. Our results are markedly different from the spacelike case. On a spacelike surface, electric and magnetic fluxes each form a commuting subalgebra. This implies that the holonomies commute. On a lightlike hypersurfaces, this is no longer true. Electric and magnetic fluxes are no longer independent. To compute the Poisson brackets explicitly, we choose a regularisation. Each path is smeared into a thin ribbon. In the resulting holonomy algebra, Wilson lines commute unless they intersect the same light ray. We compute the structure constants of the holonomy algebra and show that they depend on the geometry of the intersection and the conformal class of the metric at the null surface. Finally, we propose a quantisation. The resulting Hilbert space shows a number of unexpected features. First, the holonomies become anti-commuting Grassmann numbers. Second, for pairs of Wilson lines, the commutation relations can continuously interpolate between fermionic and bosonic relations. Third, there is no unique ground state. The ground state depends on a choice of framing of the underlying paths.

This work presents exact solutions of the Kemmer equation for spin-1 particles in $(1+1)$-dimensional Rindler spacetime, motivated by the need to understand vector bosons under uniform acceleration, including non-inertial effects and the Unruh temperature, which distinguish them from spin-0 and spin-1/2 systems. Starting from the free Kemmer field in an accelerated reference frame, we establish eigenvalue equations resembling those of the Klein--Gordon equation in Rindler coordinates. By introducing the Dirac oscillator interaction through a momentum substitution, we derive an exact closed-form spectrum for the Kemmer oscillator, revealing how the acceleration parameter modifies the characteristic length, shifts the discrete energy spectrum, and lifts degeneracies. In the Minkowski limit $a\to 0$, the standard Kemmer oscillator spectrum is recovered, ensuring consistency with flat-spacetime results. These findings provide a tractable framework for analyzing acceleration-induced effects, with implications for quantum field theory in curved spacetime, quantum gravity, and analogue gravity platforms.

In this work, we investigate the microlocal properties of the evolutions of Schrödinger equations using metaplectic Wigner distributions. So far, only restricted classes of metaplectic Wigner distributions, satisfying particular structural properties, have allowed the analysis of microlocal properties. We first extend the microlocal results to all metaplectic Wigner distributions, including the well-known Kohn-Nirenberg quantization, and examine these findings in the framework of Fourier integral operators with quadratic phase. Finally, we analyze the phase space concentration of the (cross) Wigner distribution arising from the interaction of two states, with particular attention to interactions generated by certain Schrödinger evolutions. These contributions enable a more refined study of the so-called ghost frequencies.

Timing and phase resolution in satellite QKD, kilometre-scale gravitational-wave detectors, and space-borne clock networks hinge on quantum-speed limits (QSLs), yet benchmarks omit relativistic effects for coherent and squeezed probes. We derive first-order relativistic corrections to the Mandelstam-Tamm and Margolus-Levitin bounds. Starting from the Foldy-Wouthuysen expansion and treating $-p^{4}/(8 m^{3} c^{2})$ as a harmonic-oscillator perturbation, we propagate Gaussian states to obtain closed-form QSLs and the quantum Cramér-Rao bound. Relativistic kinematics slow evolution in an amplitude- and squeezing-dependent way, increase both bounds, and introduce an $ε^{2} t^{2}$ phase drift that weakens timing sensitivity while modestly increasing the squeeze factor. A single electron ($ε\approx 1.5\times 10^{-10}$) in a $5.4\,\mathrm{T}$ Penning trap, read out with $149\,\mathrm{GHz}$ quantum-limited balanced homodyne, should reveal this drift within $\sim 15\,\mathrm{min}$ -- within known hold times. These results benchmark relativistic corrections in continuous-variable systems and point to an accessible test of the quantum speed limit in high-velocity or strong-field regimes.

We develop an approach for understanding the dynamics of open quantum systems by analyzing individual quantum trajectories in the eigenbasis of the Liouvillian superoperator. From trajectory-eigenstate overlaps, we construct a quasiprobability distribution that characterizes the degree of localization of the trajectories in the Liouvillian eigenbasis. Contrary to the common wisdom that late-time dynamics are governed solely by the steady state and the slowest-decaying modes, we show that trajectories can remain well spread over transient eigenstates deep within the bulk of the Liouvillian spectrum even at late times. We demonstrate this explicitly using numerical simulations of interacting spin chains and bosonic systems. Moreover, we find that the delocalization of the trajectory strongly correlates with the purity of the trajectory-averaged steady state, establishing a further link between the trajectory and ensemble pictures of open quantum dynamics.

We investigate how detuning and auxiliary qubits collaboratively enhance quantum synchronization in a dissipative multi-qubit system that is coupled to a structured reservoir. Our findings indicate that while detuning is ineffective in Markovian environments, it emerges as a powerful control parameter in the non-Markovian regime, where environmental memory facilitates long-lived phase coherence. It is shown that adding more auxiliary qubits amplifies this effect by strengthening the collective coupling and enhancing memory, resulting in robust phase locking within the system. Analysis using the Husimi Q-function, synchronization measures, and Arnold tongue structures reveals a detuning-induced enhancement of phase locking, which significantly improves stability compared to the resonance case. These results establish a cooperative control strategy where detuning actively engineers phases, while auxiliary qubits provide the necessary memory for sustained synchronization.

Absorption spectroscopy is a fundamental tool for probing molecular structure. However, performing absorption spectroscopy on individual molecules is challenging due to the low signal-to-noise ratio. Here, we report on a nondestructive absorption spectroscopy on a mid-infrared vibrational transition in a single molecular ion that is co-trapped with an atomic ion. The absorption of a single photon is detected via the momentum transfer from the absorbed photon onto the molecule. This recoil signal is amplified using a non-classical state of motion of the two-ion crystal and subsequently read out via the atomic ion. We characterize the recoil detection method and use it to investigate the interaction between femtosecond laser pulses and the O-H stretching vibration in individual CaOH+ molecular ions. Furthermore, we present the single-photon absorption spectrum obtained for the vibrational transition. This method represents a milestone towards quantum non-demolition measurements of complex polyatomic molecules, providing high-fidelity methods for preparation and measurement of the quantum state of a wide range of molecular species.

Harnessing rare-earth ions in oxides for quantum networks requires integration with bright emitters in III-V semiconductors, but local disorder and interfacial noise limit their optical coherence. Here, we investigate the microscopic origins of the ensemble spectrum in Er$^{3+}$:TiO$_2$ epitaxial thin films on GaAs and GaSb substrates. Ab initio calculations combined with noise-Hamiltonian modeling and Monte Carlo simulations quantify the effects of interfacial and bulk spin noise and local strain on erbium crystal-field energies and inhomogeneous linewidths. Photoluminescence excitation spectroscopy reveals that Er$^{3+}$ ions positioned at increasing distances from the III-V/oxide interface produce a systematic blue shift of the $Y_1\rightarrow Z_1$ transition, consistent with strain relaxation predicted by theory. Thermal annealing produces a compensating redshift and linewidth narrowing, isolating the roles of oxygen-vacancy and gallium-diffusion noise. These results provide microscopic insight into disorder-driven decoherence, offering pathways for precise control of hybrid quantum systems for scalable quantum technologies.

Squeezed reservoirs provide a powerful means of engineering nonclassical noise and controlling irreversible dynamics in open quantum systems. Here we develop a comprehensive analysis of two coupled harmonic oscillators driven by independent squeezed baths, focusing on the emergence of coherence-driven entropy flow and the structure of exceptional points (EPs) in the corresponding Lindblad dynamics. Working entirely within the Gaussian formalism, we derive closed-form evolution equations for the covariance matrix and show that squeezing induces entropy generation only at *second order* in the anomalous correlations, a nonlinear mechanism absent in thermal environments. This entropy flow is accompanied by a rich non-Hermitian structure: by scanning the squeezing parameters we uncover a characteristic "exceptional-point fan" in the (M1, M2) plane, which separates a narrow PT-unbroken region of oscillatory dynamics from broad PT-broken sectors in which one normal mode becomes purely overdamped. This geometric organization of EPs reveals that PT symmetry survives only when the two reservoirs squeeze opposite quadratures, and is generically broken for in-phase squeezing. Our analysis establishes squeezed reservoirs as a natural setting where information-bearing noise drives irreversible behavior through coherent pathways, and lays the groundwork for experimentally accessible probes of entropy flow and critical mode behavior in more complex open systems.

We present a high-order splitting method for simulating non-unitary dynamics by sequential real- and imaginary-time Hamiltonian evolutions. Complex-coefficient splitting methods with positive real parts are chosen for stable integration in a quantum circuit, avoiding the unstable, norm-amplifying negative steps that arise from real-coefficient splitting at high orders. The method is most beneficial for dynamics that naturally separate into unitary and dissipative components, with broad applications across science and engineering. These systems frequently admit compact spectral representations of the split operators, which we demonstrate by deriving efficient quantum circuits for simulating the damped-wave equation with up to sixth-order accuracy in time. A single sixth-order step in three dimensions on 35 trillion cells requires 1,562 CNOT gates, which can be executed within the coherence time of modern quantum processors.

Quantum thermometry aims at determining temperature with ultimate precision in the quantum regime. Standard equilibrium approaches, limited by the Quantum Fisher Information given by static energy fluctuations, lose sensitivity outside a fixed temperature window. Non-equilibrium strategies have therefore been recently proposed to overcome these limits, but their advantages are typically model-dependent or tailored for a specific purpose. This Letter establishes a general, model-independent result showing that any temperature-dependent unitary driving applied to a thermalized probe enhances its quantum Fisher information with respect to its equilibrium value. Such information gain is expressed analytically through a positive semi-definite kernel of information currents that quantify the flow of statistical distinguishability. Our results are benchmarked on a driven spin-$1/2$ thermometer, furthermore showing that resonant modulations remarkably restore the quadratic-in-time scaling of the Fisher information and allow to shift the sensitivity peak across arbitrary temperature ranges. Our findings identify external unitary control as a universal resource for precision metrology and pave the way for future implementations in quantum sensing.

The Quantum Approximate Optimization Algorithm (QAOA) requires considered optimization problems to be translated into a compatible format. A popular transformation step in this pipeline involves the quadratization of higher-order binary optimization problems, translating them into Quadratic Unconstrained Binary Optimization (QUBO) formulations through the introduction of auxiliary variables. Conventional algorithms for the selection of auxiliary variables often aim to minimize the total number of required variables without taking the constraints of the underlying quantum computer-in particular, the connectivity of its qubits-into consideration. This quickly results in interaction graphs that are incompatible with the target device, resulting in a substantial compilation overhead even with highly optimized compilers. To address this issue, this work presents a novel approach for the selection of auxiliary variables tailored for architectures with limited connectivity. By specifically constructing an interaction graph with a regular structure and a limited maximal degree of vertices, we find a way to construct QAOA circuits that can be mapped efficiently to a variety of architectures. We show that, compared to circuits constructed from a QUBO formulation using conventional auxiliary selection methods, the proposed approach reduces the circuit depth by almost 40%. An implementation of all proposed methods is publicly available at https://github.com/munich-quantum-toolkit/problemsolver.

We investigate whether sequential unitary circuits can prepare two-dimensional chiral states, using a correspondence between sequentially prepared states, isometric tensor network states, and one-dimensional quantum channel circuits. We establish two no-go theorems, one for Gaussian fermion systems and one for generic interacting systems. In Gaussian fermion systems, the correspondence relates the defining features of chiral wave functions in their entanglement spectrum to the algebraic decaying correlations in the steady state of channel dynamics. We establish the no-go theorem by proving that local channel dynamics with translational invariance cannot support such correlations. As a direct implication, two-dimensional Gaussian fermion isometric tensor network states cannot support algebraically decaying correlations in all directions or represent a chiral state. In generic interacting systems, we establish a no-go theorem by showing that the state prepared by sequential circuits cannot host the tripartite entanglement of a chiral state due to the constraints from causality.

We formulate a continuous-variable quantum computing (CVQC) algorithm to study Berry's phase on photonic quantum computers. We demonstrate that CVQC allows the simulation of charged particles with orbital angular momentum under the influence of an adiabatically changing $\vec{B}$ field. Although formulated entirely in the CVQC setting, our construction uses only passive linear-optical operations (beam splitters and phase shifts), which act identically in single-photon photonic architectures. This enables experimental realisation on the Quandella Ascella platform, where we observe the Berry's phase phenomenon with interferometric measurement. We also generalise the framework to more rapid non-adiabatic evolution. By concatenating Aharonov-Anandan cycles for opposing magnetic fields we demonstrate that one can engineer a circuit in which dynamical phases and leading non-geometric errors cancel by symmetry, leaving the intrinsically robust geometric phase contribution.

We introduce a holographic framework for analyzing the steady states of repeated quantum channels with strong symmetries. Using channel-state duality, we show that the steady state of a $d$-dimensional quantum channel is holographically mapped to the boundary reduced density matrix of a $(d+1)$-dimensional wavefunction generated by a sequential unitary circuit. From this perspective, strong-to-weak spontaneous symmetry breaking (SWSSB) in the steady state arises from the anyon condensation on the boundary of a topological order in one higher dimension. The conditional mutual information (CMI) associated with SWSSB is then inherited from the bulk topological entanglement entropy. We make this duality explicit using isometric tensor network states (isoTNS) by identifying the channel's time evolution with the transfer matrix of a higher-dimensional isoTNS. Built on isoTNS, we further construct continuously tunable quantum channels that exhibit distinct mixed-state phases and transitions in the steady states.

Nonabelian topological orders host exotic anyons central to quantum computing, yet established realizations rely on case-by-case constructions that are often conceptually involved. In this work, we present a systematic construction of nonabelian dihedral quantum double phases based on a continuous $O(2)$ gauge field. We first formulate a topological $S[O(2)\times O(2)]$ BF theory, and by identifying the Wilson loops and twist operators of this theory with anyons, we show that our topological BF theory reproduces the complete anyon data, and can incorporate all Dijkgraaf--Witten twists. Building on this correspondence, we present a microscopic model with $O(2)$ lattice gauge field coupled to Ising and rotor matter whose Higgsing yields the desired dihedral quantum double phase. A perturbative renormalization group analysis further indicates a direct transition from this phase to a $U(1)$ Coulomb or chiral topological phase at a stable multicritical point with emergent $O(3)$ symmetry. Our proposal offers an alternative route to nonabelian topological order with promising prospects in synthetic gauge field platforms.

The monogamy of mutual information (MMI) is a quantum entropy inequality that enforces the non-positivity of tripartite information. We investigate the failure of MMI in graph states as a forbidden-subgraph phenomenon, conjecturing that every MMI-violating graph state is local-Clifford equivalent to one whose graph contains a four-star subgraph. We construct a family of star-like graphs whose states fail a specific class of MMI instances, and extend this analysis to general star topologies. Deriving adjacency matrix constraints that fix the MMI evaluation for these instances and interpreting them physically, we prove the forbidden-subgraph conjecture for this family of graphs. Finally, through an exhaustive search over graph representatives for all $8$-qubit stabilizer entropy vectors, we establish that MMI failure is not reducible to the cases within our scope.

Unlike the rigid, high-volume automation found in industry, academic research requires process flexibility that has historically relied on variable manual operations. This hinders the fabrication of advanced, complex devices. We propose to address this gap by automating these low-volume, high-stakes tasks using a robotic arm to improve process control and consistency. As a proof of concept, we deploy this system for the resist development of Josephson junction devices. A statistical comparison of the process repeatability shows the robotic process achieves a resistance spread across chips close to 2%, a significant improvement over the ~7% spread observed from human operators, validating robotics as a solution to eliminate operator-dependent variability and a path towards industrial-level consistency in a research setting.