Quantum Physics Paper Analysis

We describe an empirical approach to identify low-weight combinations of columns of the decoding matrices of a quantum circuit-level noise model, for which belief-propagation (BP) algorithms converge possibly very slowly. Focusing on the logical-idle syndrome cycle of the low-density parity check gross code, we identify criteria providing a characterization of the Tanner subgraph of such low-weight error syndromes. We analyze the dynamics of iterations when BP is used to decode weight-four and weight-five errors, finding statistics akin to exponential activation in the presence of noise or escape from chaotic phase-space domains. We study how BP convergence improves when adding to the decoding matrix relevant combinations of fault columns, and show that the suggested decoder amendment can result in the reduction of both logical errors and decoding time.

Post-quantum cryptography currently rests on a small number of hardness assumptions, posing significant risks should any one of them be compromised. This vulnerability motivates the search for new and cryptographically versatile assumptions that make a convincing case for quantum hardness. In this work, we argue that decoding random quantum stabilizer codes -- a quantum analog of the well-studied LPN problem -- is an excellent candidate. This task occupies a unique middle ground: it is inherently native to quantum computation, yet admits an equivalent formulation with purely classical input and output, as recently shown by Khesin et al. (STOC '26). We prove that the average-case hardness of quantum stabilizer decoding implies the core primitives of classical Cryptomania, including public-key encryption (PKE) and oblivious transfer (OT), as well as one-way functions. Our constructions are moreover practical: our PKE scheme achieves essentially the same efficiency as state-of-the-art LPN-based PKE, and our OT is round-optimal. We also provide substantial evidence that stabilizer decoding does not reduce to LPN, suggesting that the former problem constitutes a genuinely new post-quantum assumption. Our primary technical contributions are twofold. First, we give a reduction from random quantum stabilizer decoding to an average-case problem closely resembling LPN, but which is equipped with additional symplectic algebraic structure. While this structure is essential to the quantum nature of the problem, it raises significant barriers to cryptographic security reductions. Second, we develop a new suit of scrambling techniques for such structured linear spaces, and use them to produce rigorous security proofs for all of our constructions.

Fair threshold estimation for bivariate bicycle (BB) codes on the quantum erasure channel runs into two recurring problems: decoder-baseline unfairness and the conflation of finite-size pseudo-thresholds with true asymptotic thresholds. We run both uninformed and \emph{erasure-aware} minimum-weight perfect matching (MWPM) surface code baselines alongside BP-OSD decoding of BB codes. With standard depolarizing-weight MWPM and no erasure information, performance matches random guessing on the erasure channel in our tested regime -- so prior work that compares against this baseline is really comparing decoders, not codes. Using 200{,}000 shots per point and bootstrap confidence intervals, we sweep five BB code sizes from $N=144$ to $N=1296$. Pseudo-thresholds (WER = 0.10) run from $p^* = 0.370$ to $0.471$; finite-size scaling (FSS) gives an asymptotic threshold $p^*_\infty \approx 0.488$, within 2.4\% of the zero-rate limit and without maximum-likelihood decoding. On the fair baseline, BB at $N=1296$ has a modest edge in threshold over the surface code at twice the qubit count, and a 12$\times$ lower normalized overhead -- the latter is where the practical advantage sits. All runs are reproducible from recorded seeds and package versions.

Quantum computing experiments and testbeds with large qubit counts have until recently been a privilege afforded only to large companies or quantum technologies where scaling to hundreds or thousands of qubits does not require a substantial increase in quantum control hardware (neutral atoms, trapped ions, or spin defects). Superconducting and spin qubit testbeds critically depend on scaling their control systems beyond what a single electronics board can provide. Multi-board control systems combining RF, fast DC control, bias, and readout require precise synchronization and communication across many hardware and firmware components. To address this, we present XCOM, a network that synchronizes QICK boards and the absolute clocks governing quantum program execution to within 100 ps, free of drift and loss of lock. XCOM also provides deterministic, all-to-all simultaneous data communication with latency below 185 ns. Like QICK itself, XCOM is compatible with a broad range of qubit technologies and is designed to scale to large systems.

The integration of diverse quantum resources and the exploitation of more degrees of freedom provide key operational flexibility for universal fault-tolerant quantum computation. In this work, we propose a flexible Gottesman-Kitaev-Preskill-state-embedded fault-tolerant quantum computation architecture based on a three-dimensional cluster state constructed in polarization, frequency, and orbital angular momentum domains. Specifically, we design optical entanglement generators to produce three diverse entangled pairs, and subsequently construct a three-dimensional cluster state via a beam-splitter network with several time delays. Furthermore, we present a partially squeezed surface-GKP code to achieve fault-tolerant quantum computation and ultimately find the optimal choice of implementing the squeezing gate to give the best fault-tolerant performance (the fault-tolerant squeezing threshold is 11.5 dB). Our scheme is flexible, scalable, and experimentally feasible, providing versatile options for future optical fault-tolerant quantum computation architecture.

We present applications of quantum quadratic residue codes in magic state distillation. This includes showing that existing codes which are known to distill magic states, like the $5$-qubit perfect code, the $7$-qubit Steane code, and the $11$-qutrit and $23$-qubit Golay codes, are equivalent to certain quantum quadratic residue codes. We also present new examples of quantum quadratic residue codes that distill qubit $T$ states and qutrit Strange states with high thresholds, and we show that there are infinitely many quantum quadratic residue codes that distill $T$ states with a non-trivial threshold. All of these codes, including the codes with the highest currently known thresholds for $T$ state and Strange state distillation, are unified under the umbrella of quantum quadratic residue codes.

Quantum error correction (QEC), the lynchpin of fault-tolerant quantum computing (FTQC), is designed and validated against well-behaved Pauli stochastic error models. But in real-world deployment, QEC protocols encounter a vast array of other errors -- coherent and non-Pauli errors -- whose impacts on quantum circuits are vastly different than those of stochastic Pauli errors. The impacts of these errors on QEC and FTQC protocols have been largely unpredictable to date due to exponential classical simulation cost. Here, we show how to accurately and efficiently model the effects of coherent and non-Pauli errors on FTQC, and we study the effects of such errors on syndrome extraction for surface and bivariate bicycle codes, and on magic state cultivation. Our analysis suggests that coherent error can shift fault-tolerance thresholds, increase the space-time cost of magic state cultivation, and can increase logical error rates by an order of magnitude compared to equivalent stochastic errors. These analyses are enabled by a new technique for mapping any Markovian circuit-level error model with sufficiently small error rates onto a detector error model (DEM) for an FTQC circuit. The resulting DEM enables Monte Carlo estimation of logical error rates and noise-adapted decoding, and its parameters can be analytically related to the underlying physical noise parameters to enable approximate strong simulation.

In the presence of qubit losses, the building blocks of fault-tolerant error correction (FTEC) must be revisited. Existing loss-tolerant approaches are mainly architecture-specific, and little attention has been given to optimizing the syndrome measurement sequences under loss. Schemes designed for the standard Pauli error model are not directly applicable because the syndrome patterns differ when both Pauli errors and erasures can occur. Based on recent advances in loss detection units and loss-tolerant syndrome extraction gadgets, we extend the study of adaptive Shor-style measurement sequences to the mixed error model. We begin by discussing how to adaptively convert correctable erasures into located errors. The minimal overhead is quantified by the number of stabilizer measurements, which can be reduced to a subgroup dimension problem for erasures arising in any FTEC circuit for qubits and prime-dimensional qudits. As a byproduct, we provide the construction of the canonical generating set with respect to a given bipartite partition for a stabilizer group on qudits of composite dimension. We then generalize both the weak and strong FTEC conditions. Finally, we present adaptive syndrome-measurement protocols for the mixed error model, generalizing the adaptive protocols for the standard Pauli error model.

We present Quantum Depth Compression (QDC), a general compilation framework that utilizes dynamic circuits to reduce arbitrary quantum circuits to depth linear in the number of non-Clifford gates and to grid connectivity without the need for expensive SWAP-networks. The framework consists of pushing Clifford gates to the end of the circuit, resulting in a sequence of non-Clifford Pauli-phasors followed by an all Clifford sub-circuit, both of which are then reduced to constant depth via dynamic circuits. We show that applying QDC to random Pauli-phasor circuits lowers both their depth and CNOT count compared to a standard alternative compiler.

We propose a general method for preparing stabilizer states with reduced two-qubit gate count and depth compared to the state of the art. The method starts from a graph state representation of the stabilizer state and iteratively reduces the number of edges in the graph using two-qubit Clifford gates to produce a unitary preparation circuit. We explore various heuristic search and AI-based approaches to optimally choose Clifford gates at each step, the most sophisticated of which is a combination of reinforcement learning and Monte Carlo tree search that we call QuSynth. We apply our method to synthesize code states of various quantum error correcting codes including the 23-qubit Golay code and the 144-qubit gross code, the latter of which is significantly beyond the qubit number that is accessible to prior optimal circuit synthesis methods. We demonstrate that our techniques are capable of reducing the required two-qubit gates by up to a factor of 2.5 compared to previous approaches while retaining low circuit depth.

We introduce six independent trivariate bicycle (ITB) codes, which extend the bivariate bicycle framework of Bravyi et al.\ to three cyclic dimensions. Using asymmetric polynomial pairs on three-dimensional tori, we construct four codes including a $[[140,6,14]]$ code with $kd^2/n = 8.40$. In the code-capacity setting, the $[[140,6,14]]$ code achieves a pseudothreshold of $8.0\%$ and $kd^2/n = 8.40$, exceeding the best multivariate bicycle code of Voss et al.\ ($7.9\%$, $kd^2/n = 2.67$). With circuit-level depolarizing noise, pseudothresholds reach $0.59\%$ for $[[140,6,14]]$ and $0.53\%$ for $[[84,6,10]]$. On the SI1000 superconducting noise model, the $[[140,6,14]]$ code achieves a per-round per-observable rate of $5.6 \times 10^{-5}$ at $p = 0.20\%$. We additionally present two self-dual codes with weight-8 stabilizers: $[[54,14,5]]$ ($kd^2/n = 6.48$) and $[[128,20,8]]$ ($kd^2/n = 10.0$). These results expand the design space of algebraic quantum LDPC codes and demonstrate that the third cyclic dimension yields competitive candidates for practical fault-tolerant implementations.

As we are entering an early-FTQC era, circuit execution protocols with logical qubits and certain error-correcting codes are being discussed. Here, we propose a circuit execution protocol for the space-time efficient analog rotation (STAR) architecture. Gate operations within the STAR architecture is based on lattice surgery with surface codes, but it allows direct execution of continuous gates $Rz(θ)$ as non-Clifford gates instead of $T = Rz(π/4)$. $Rz(θ)$ operations involve creation of resource states $|m_θ\rangle = \frac{1}{\sqrt{2}} (|0 \rangle + e^{iθ} |1\rangle ) $ followed by ZZ joint measurements with target logical qubits. While employing $Rz(θ)$ enables more efficient circuit execution, both their creations and joint measurements are probabilistic processes and adopt repeat-until-success (RUS) protocols which are likely to result in considerable time overhead. Our circuit execution protocol aims to reduce such time overhead by parallel trials of resource state creations and more frequent trials of joint measurements. By employing quadratic unconstrained binary optimization (QUBO) in determining resource state allocations within the space, we successfully make our protocol efficient. Furthermore, we proposed performance estimators given the target circuit and qubit topology. It successfully predicts the time performance within less time than actual simulations do, and helps find the optimal qubit topology to run the target circuits efficiently.

The binomial code is renowned for its parity-mediated loss immunity and loss-error recoverability, while geometric phases are widely recognized for their intrinsic resilience against noise. Capitalizing on their complementary merits, we propose a noise-resilient protocol to realize Nonadiabatic geometric quantum computation with binomial codes in a superconducting system composed of a microwave cavity %off-resonantly dispersively coupled to a %three-level qutrit. The control field %geometric quantum computation is designed by %combining geometric phases, integrating reverse engineering and optimal control. This design provides a customized control protocol featuring strong error-tolerance and inherent noise-resilience. Using experimentally accessible parameters in superconducting systems, numerical simulations show that the protocol yields relatively high average fidelity for geometric quantum gates based on binomial code, even in the presence of parameter fluctuations and decoherence. Thus, this protocol may provide a practical approach for realizing reliable Nonadiabatic geometric quantum computation with binomial codes in current technology.

Early demonstrations of fault tolerant quantum systems have paved the way for logical-level compilation. For fault-tolerant applications to succeed, execution must finish with a low total program error rate (i.e., a low program failure rate). In this work, we study a promising candidate for future fault-tolerant architectures with low spatial overhead: the Gross code. Compilation for the Gross code entails compiling to Pauli Based Computation and then reducing the rotations and measurements to the Bicycle ISA. Depending on the configuration of modules and the placement of code modules on hardware, one can reduce the amount of resulting Bicycle instructions to produce a lower overall error rate. We find that NISQ-based, and existing FTQC mappers are insufficient for mapping logical qubits on Gross code architectures because 1. they do not account for the two-level nature of the logical qubit mapping problem, which separates into code modules with distinct measurements, and 2. they naively account only for length two interactions, whereas Pauli-Products are up to length $n$, where $n$ is the number of logical qubits in the circuit. For these reasons, we introduce a two-stage pipeline that first uses hypergraph partitioning to create in-module clusters, and then executes a priority-based algorithm to efficiently assign clusters onto hardware. We find that our mapping policy reduces the error contribution from inter-module measurements, the largest source of error in the Gross Code, by up to $\sim36\%$ in the best case, with an average reduction of $\sim13\%$. On average, we reduce the failure rates from inter-module measurements by $\sim22\%$ with localized factory availability, and by $\sim17\%$ on grid architectures, allowing hardware developers to be less constrained in developing scalable fault tolerant systems due to software driven reductions in program failure rates.

Quantum computing poses significant threats to conventional cryptographic techniques such as RSA and AES, motivating the need for quantum secure communication methods. Quantum Key Distribution (QKD) offers information theoretic security based on fundamental quantum principles. This paper presents a simulation-based analysis of well-known QKD protocols, namely BB84, B92, and E91, using the IBM Qiskit framework. Realistic quantum channel effects, including noise, decoherence, and eavesdropping, are modeled to evaluate protocol performance. Key metrics such as error rate, secret key generation, and security characteristics are analyzed and compared. The study highlights practical challenges in QKD implementation, including hardware limitations and channel losses, and discusses insights toward scalable and robust quantum communication systems. The results support the feasibility of QKD as a promising solution for secure communication in the quantum era.

Large-scale cryogenic quantum systems are constrained by an input-output bottleneck between room-temperature electronics and millikelvin stages, particularly in superconducting qubit platforms. This bottleneck is most acute for output lines, where bulky and expensive microwave components limit scalability. A promising approach for scalable characterization and testing is to perform signal multiplexing directly at the qubit plane. We demonstrate a cryogenic CMOS (cryoCMOS) RF multiplexer operating at 10 millikelvin with record-low static power consumption of 200 pW. The device provides < 2 dB insertion loss and > 30 dB isolation across DC-8 GHz. Direct connection to transmon qubits marginally affects coherence times in the range of 100 microseconds, enabling multiplexing of readout, flux and, in principle, XY drive lines. This work introduces cryoCMOS multiplexers as valuable tools for scalable, high-throughput cryogenic characterization and testing, and advances co-integrated quantum-classical control for future large-scale quantum processors.

We propose an algebraic formulation for two distinct quantum algorithms: a quantum classification algorithm and a quantum search algorithm with a non-uniform initial distribution, both based on Clifford algebras and spinorial representations. In the classification algorithm, we exploit properties of spinorial representations to construct orthogonal quantum states associated with different classes, allowing the identification of an item's class through the evaluation of expectation values of operators derived from the generators of the Clifford algebra. In the quantum search algorithm, we consider a database with prior information in which the oracle is implemented directly using generators of the Clifford algebra, simplifying its realization. The proposed approach provides a unified algebraic description for both algorithms, employing spinorial representations in the construction of quantum states and operators. Computational implementations are presented.

Errors in superconducting qubits that are correlated in time and space can pose problems for quantum error correction codes. Radiation from cosmic and terrestrial sources can increase the quasiparticle (QP) density in a superconducting qubit device, resulting in an increased rate of QPs tunneling across proximal Josephson junctions (JJs) and causing correlated errors. Mechanical vibrations, such as those induced by the pulse tube in a dry dilution refrigerator, are also a known source of correlated errors. We present a method for distinguishing these two types of errors by their temporal, spatial, and frequency domain features, enabling physically motivated error-mitigation strategies. We also present accelerometer data to study the correlation between dilution refrigerator vibrations and the errors. We measure arrays of transmon qubits where the difference in superconducting gap across the JJ is less than the qubit energy, as well as those where the gap is greater than the qubit energy, which has been shown to mitigate radiation-induced errors. We show that these latter devices are also protected against vibration-induced errors.

Quantum state preparation and block encoding are versatile and practical input models for quantum algorithms in scientific computing. The circuit complexity of state preparation and block encoding frequently dominates the end-to-end gate complexity of quantum algorithms. We give algorithms with lower C-NOT counts for both the state preparation and block encoding. For a general $n$-qubit state, we improve the C-NOT count from Plesch-Brukner algorithm, proposed in 2011, from $(23/24)2^n$ to $(11/12)2^n$. For block encoding, our single-ancilla protocol for $2^{n-1}\times 2^{n-1}$ matrices uses the spectral norm as subnormalization and achieves a C-NOT count leading term $(11/48)4^n$. This result even exceeds the lower bound of $(1/4)4^n$ for $n$-qubit unitary synthesis. Further optimization is performed for low-rank matrices, which frequently arise in practical applications. Specifically, we achieve the C-NOT count leading term $(K+(11/12))2^n$ for a rank-$K$ matrix. Our approach builds upon the recursive block-ZXZ decomposition from Krol et al. and introduces a diagonal matrix migration technique based on the commutativity of the diagonal matrix and the uniformly controlled rotation about the $z$-axis to minimize the use of C-NOT gates.

As quantum computing advances toward fault-tolerance through quantum error correction, modular chiplet architectures have emerged to provide the massive qubit counts required while overcoming fabrication limits of monolithic chips. However, this transition introduces a critical compilation gap: existing frameworks cannot handle the scale of fault-tolerant quantum circuits while managing the noisy, sparse interconnects of chiplet backends. We present Chipmunq, the first hardware-aware compiler for mapping and routing fault-tolerant circuits onto modular architectures. Chipmunq employs a quantum-error-correction-aware partitioning strategy that preserves the integrity of logical qubit patches, preventing prohibitive gate overheads common in general-purpose compilers. Our evaluation demonstrates that Chipmunq achieves a 13.5x speedup in compilation time compared to state-of-the-art tools. By incorporating chiplet constraints and defective qubits, it reduces circuit depth by 86.4% and SWAP gate counts by 91.4% across varying code distances. Crucially, Chipmunq overcomes heterogeneous inter-chiplet links, improving logical error rates by up to two orders of magnitude.

Quantum error correction (QEC) is essential for realizing large-scale, fault-tolerant quantum computation, yet its practical implementation remains a major engineering challenge. In particular, QEC demands precise real-time control of a large number of qubits and low-latency, high-throughput and accurate decoding of error syndromes. While most prior work has focused primarily on decoder design, the overall performance of any QEC system depends critically on all its subsystems including control, communication, and decoding, as well as their integration. To address this challenge, we present an open-source, fully integrated QEC system built on RISC-Q, a generator for RISC-V-based quantum control architectures. Implemented on RFSoC FPGAs, our system prototype integrates real-time qubit control, a scalable distributed multi-board architecture, and the state-of-the-art hardware QEC decoder within a low-latency, high-throughput decoding pipeline, forming a complete hardware platform ready for deployment with superconducting qubits. Experimental evaluation on a three-board prototype based on AMD ZCU216 RFSoCs demonstrates an end-to-end QEC decoding-feedback latency of 446 ns for a distance-3 surface code, including syndrome aggregation, network communication, syndrome decoding, and error distribution. Extrapolating from measured subsystem performance and state-of-the-art decoder benchmarks, the architecture can achieve sub-microsecond decoding-feedback latency up to a distance-21 surface code ($\sim$881 physical qubits) when scaled to larger hardware configurations.

Monolithic three-dimensional (3D) Paul traps combine the high-precision microfabrication of two-dimensional (2D) chip traps with the deep trapping potentials and low heating rates characteristic of macroscopic Paul traps, which are typically manually assembled. However, achieving low motional heating rates and optical access with a high numerical aperture (NA) while maintaining the high radio-frequency (RF) voltages required for heavy ionic species, such as Yb$^{+}$ and Ba$^{+}$, remains a significant technical challenge. In this work, we present a segmented, monolithic 3D fused silica blade trap, featuring an ion-electrode distance of 250 $μ$m with stable operation at high RF voltages. We benchmark the performance of the trap using Yb$^{+}$ ions, demonstrating axially homogeneous trapping potentials for 200 $μ$m around the axial center of the trap, high multi-directional optical access (up to 0.7 NA), and radial motional heating rate as low as 1.1 $\pm$ 0.1 quanta/s at radial trap frequencies about 3 MHz near room temperature. Furthermore, we observe a motional Ramsey coherence time, $T_{2}$, of around 95 ms for the radial center-of-mass mode. We demonstrate a two-qubit gate fidelity of ${99.3}^{+ 0.7}_{- 1.5}$$\%$ with state preparation and measurement correction. These results establish fused-silica monolithic blade traps as a scalable, modular platform for quantum simulation, computation, metrology, and networking with heavy ionic species.

I introduce a method to generate families of CSS codes with interesting code parameters. The object of study is Coxeter groups, both finite and infinite (reducible or not), and a geometrically motivated partial order of Coxeter group elements named after Bruhat. The Bruhat order is known to provide a link to algebraic topology -- it doubles as a face poset capturing the inclusion relations of the $p$-dimensional cells of a regular CW~complex and that is what makes it interesting for QEC code design. Assisted by the Bruhat face poset interval structure unique to Coxeter groups I show that the corresponding chain complexes can be turned into multitudes of CSS codes. Depending on the approach, I obtain CSS codes (and their families) with controlled stabilizer weights, for example $[6006, 924, \{{\leq14},{\leq7}\}]$ (stabilizer weights~14 and 9) and $[22880,3432,\{{\leq8},{\leq16}\}]$ (weights 16 and 10), and CSS codes with highly irregular stabilizer weight distributions such as $[571,199,\{5,5\}]$. For the latter, I develop a weight-reduction method to deal with rare heavy stabilizers. Finally, I show how to extract four-term (length three) chain complexes that can be interpreted as CSS codes with a metacheck.

Code-switching offers a route to universal, fault-tolerant quantum computation by circumventing the limitation implied by the Eastin-Knill theorem against a universal transversal gate set within a single quantum code. Here, we present a fault-tolerant code-switching protocol between two versions of the $[[8, 3, 2]]$ code. One version supports weakly fault-tolerant single-qubit Clifford gates, while the other supports a logical $\overline{\mathrm{CCZ}}$ gate via transversal $T/T^\dagger$ together with logical $\overline{\mathrm{CZ}}$, $\overline{\mathrm{CNOT}}$, and $\overline{\mathrm{SWAP}}$ gates. Because both codes have distance 2, the protocol operates in a postselected, error-detecting regime: single faults lead to detectable outcomes, and accepted runs exhibit quadratic suppression of logical error rates. This yields a universal scheme for postselected fault-tolerant computation. We validate the protocol numerically through simulations of state preparation, code switching, and a three-logical-qubit implementation of Grover's search.

Useful quantum information processing ultimately requires operations over large Hilbert spaces, where logical information can be encoded efficiently and protected against noise. Harmonic oscillators naturally provide access to such high-dimensional spaces and enable hardware-efficient, error-correctable bosonic encodings. However, direct entangling operations between oscillators remains an outstanding challenge. Existing strategies typically rely on parametrically activating interactions that populate the excited states of an ancillary nonlinear element. This induces an effective interaction between the oscillators, at the expense of introducing additional dissipation channels and potential leakage from the encoded manifold. Here, we engineer a Raman-assisted cross-Kerr interaction between microwave photons hosted in two superconducting cavities, without exciting the nonlinear element, thereby suppressing coupler-induced decoherence.This approach generates a direct coupling between microwave photons that is exploited to implement a controlled-phase gate within the single- and two-photon subspaces of two oscillators, directly entangling them. Finally, we harness this dynamics to map the photon-number parity of a storage cavity onto an auxiliary oscillator rather than a nonlinear element, enabling error detection while protecting the storage mode from measurement-induced decoherence. Our work expands the bosonic circuit quantum electrodynamics (cQED) toolbox by enabling coherence-preserving direct photon-photon interactions between oscillators. This realizes an entangling gate that operates entirely within a bosonic code space while suppressing decoherence from nonlinear ancilla excitations, providing a key primitive for fault-tolerant bosonic quantum computing.

We propose a Monte Carlo based method for simulating the open system dynamics of multiple exchange-only (EO) qubits. In the EO encoding, the total spin projection quantum number along the $z$-axis of the three constituent spins remains unchanged under exchange operations, in contrast to the open system (or multi-qubit miscalibration) setting where coherent and incoherent mixing of states with different quantum numbers occurs. In our approach, we choose to measure the total spin component along the $z$-axis of each EO qubit after every logical quantum operation, which decoheres coherent mixtures of states with different spin projection quantum numbers. Independent simulations thus give different trajectories of the system in the associated subspaces, so we refer to this method as the Subspace Monte Carlo method. With each EO qubit having a definite spin projection quantum number, the density matrix of $n$ qubits can be represented by a vector of dimension $3^{2n}$, instead of $8^{2n}$, with an additional vector of dimension $n$ to label the quantum number of each qubit. We show that this approximation of the dynamics remains faithful to the true dynamics when the simulated circuits twirl the noise, converting coherent errors to stochastic errors, which can be achieved using randomized compiling. We use this simulation approach to study how correlations in measurement outcomes of circuits with reset-if-leaked gadgets, such as a multi-round Bell state stabilization circuit that uses 6 EO qubits, are affected by the choice of CNOT implementations.

Realizing error-corrected logical qubits is a central goal for the current development of digital quantum computers. Neutral atoms offer the opportunity to coherently shuttle atoms for realizing efficient quantum error correction based on long-range connectivity and parallel atom transport. Nevertheless, time overheads in shuttling atoms and complex control hardware pose challenges to scaling current architectures. Here, we introduce atom velocity as a new degree of freedom in neutral-atom architectures tailored to quantum error correction. Through controlled Doppler shifts, we demonstrate velocity-selective mid-circuit state preparation and measurement on moving atoms, leaving spectator atoms unaffected. Furthermore, we achieve on-the-fly local single-qubit rotations by mapping micron-scale atom displacements to the spatial phase of global control beams. Complementing these techniques with CZ entangling gates with a fidelity of 99.86(4)%, we experimentally implement key primitives for quantum error correction and measurement-based quantum computing. We generate an eight-qubit entangled cluster state with an average stabilizer value of 0.830(4), realize an [[4,2,2]] error-detection code with 99.0(3) % logical Bell-state fidelity, and perform stabilizer measurements using a flying ancilla. By enabling selective operations on continuously moving atoms using only global beams, this velocity-enabled architecture reduces hardware overhead while minimizing shuttling and transfer delays, opening a new pathway for fast, large-scale atom-based quantum computation.

Bosonic codes offer hardware-efficient approaches to logical qubit construction and hosted the first demonstration of beyond-break even logical quantum memory.However, such accomplishments were done for idling information, and realization of fault-tolerant logical operations remains a critical bottleneck for universal quantum computation in scaled systems. Error-transparent (ET) gates offer an avenue to resolve this issue, but experimental demonstrations have been limited to phase gates. Here, we introduce a framework based on dynamic encoding subspaces that enables simple linear drives to accomplish universal gates that are error semi-transparent (EsT) to oscillator photon loss. With an EsT logical gate set of {X, H, T}, we observe a five-fold reduction in infidelity conditioned on photon loss, demonstrate extended active-manipulation lifetimes with quantum error correction, and construct a composite EsT non-Clifford operation using a sequence of eight gates from the set. Our approach is compatible with methods for detectable ancilla errors, offering an approach to error-mitigated universal control of bosonic logical qubits with the standard quantum control toolkit.

We examine exact and approximate error correction for multi-mode Fock state codes protecting against the amplitude damping noise. Based on a new formalization of the truncated amplitude damping channel, we show the equivalence of exact and approximate error correction for Fock state codes against random photon losses. Leveraging the recently found construction method based on classical codes with large distance measured in the $\ell_1$ metric, we construct asymptotically good (exact and approximate) Fock state codes. These codes have an additional property of bounded per-mode occupancy, which increases the coherence lifetime of code states and reduces the photon loss probability, both of which have a positive impact on the stability of the system. Using the relation between Fock state code construction and permutation invariant (PI) codes, we also obtain families of asymptotically good qudit PI codes as well as codes in monolithic nuclear state spaces.

The next frontier in device-independent quantum information lies in the certification of scalable and parallel quantum resources, which underpin advanced quantum technologies. We put forth a simultaneous self-testing framework for maximally entangled two-qudit state of local dimension $m_*=2^{\lfloor n/2 \rfloor}$ (equivalently $\lfloor n/2 \rfloor$ copies of maximally entangled two-qubit pairs), together with $n$ numbers of anti-commuting observables on one side. To this end, we employ an $n$-settings Bell inequality comprising two space-like separated observers, Alice and Bob, having $2^{n-1}$ and $n$ number of measurement settings, respectively. We derive the local ontic bound of this inequality and, crucially, employ the Sum-of-Squares decomposition to determine the optimal quantum bound without presupposing the dimension of the state or observables. We then establish that any physical realisation achieving the maximal quantum violation must, up to local isometries and complex conjugation, correspond to a reference strategy consisting of a maximally entangled state of local dimension of at least $2^{\lfloor n/2 \rfloor}$ and local observables forming an irreducible representation of the Clifford algebra. This construction thereby demonstrates that the minimal dimension compatible with $n$ mutually anticommuting observables is naturally self-tested by the maximal violation of the proposed Bell functional. Finally, we analyse the robustness of the protocol by establishing quantitative bounds relating deviations in the observed Bell value to the fidelity between the realised and the ideal strategies. Our results thus provide a scalable, dimension-independent route for the certification of high-dimensional entanglement and Clifford measurements in a fully device-independent framework.

A complete architecture for cavity-free quantum networking based on collective enhancement in Rydberg atom ensembles is presented. The protocol exploits Rydberg blockade and phase-matched directional emission to eliminate optical cavities without sacrificing performance. The architecture comprises three steps: (i) local control-ensemble entanglement via Rydberg blockade with fidelity $F_{\mathrm{gate}} \approx 99.93\%$; (ii) atom-photon conversion via Raman transitions, achieving directional emission ($η_{\mathrm{dir}} \approx 35\%$) and single-node efficiency $η_{\mathrm{node}} \approx 19\%$; and (iii) remote atom-atom entanglement via Hong-Ou-Mandel interference, producing Bell states with fidelity $F > 97.5\%$. With quantum memories enabling retry protocols, entanglement generation rates exceed $600$ Hz at 20 km separation. This cavity-free approach provides a practical and scalable pathway for distributed quantum computing and secure quantum communication.

Quantum computing provides the feasible multi-layered security challenges to classical blockchain systems. Whereas, quantum-secured blockchains relied on quantum key distribution (QKD) to establish secure channels can address this potential threat. This paper presents a scalable quantum-resistant blockchain architecture designed to address the connectivity and distance limitations of the QKD integrated quantum networks. By leveraging the twin-field (TF) QKD protocol within a measurement-device-independent (MDI) topology, the proposed framework can optimize the infrastructure complexity from quadratic to linear scaling. This architecture effectively integrates information-theoretic security with distributed consensus mechanisms, allowing the system to overcome the fundamental rate-loss limits inherent in traditional point-to-point links. The proposed scheme offers a theoretically sound and feasible solution for deploying large-scale and long-distance consortium.

In realistic hardware for quantum computation that possesses fault-tolerance, non-stationary noise and stochastic drift lead to logical failure from the temporal accumulation of errors, not from independent events. Static decoding and fixed calibration techniques are structurally incompatible with this situation because they do not take into account temporal correlations between errors or control-induced back-action of errors. These effects motivate control policies that must track noise evolution across correction cycles, rather than respond to individual syndromes in isolation. We treat fault-tolerant quantum computation as a stochastic control problem, modelled using reduced quantum dynamics in which Pauli error processes are governed by latent noise parameters that vary temporally. From this perspective, logical failure arises through the accumulation of a hazard variable, and the corresponding control objective depends on the full history of observations. Operating under these conditions, a Chronological Deep Q-Network (Ch-DQN) maintains an internal belief state that tracks both noise evolution and accumulated hazard. During training, backward refinement of trajectories is used to sample slowly drifting modes of operation, while runtime inference remains strictly causal. A fractional meta-update stabilizes learning in the presence of non-stationary, control-coupled dynamics. Through multi-distance simulations that incorporate stochastic drift and feedback from decision-making, Ch-DQN suppresses hazard accumulation and extends logical survival time relative to static and recurrent baselines. Error correction in this regime is therefore no longer a static decoding task, but a control process whose success is determined over time by the underlying noise dynamics.

In this work, we characterize the $t$-th order commutants of fermionic Gaussian unitaries and of their particle-preserving subgroup acting on $n$ fermionic modes. These commutants govern Haar averages over the corresponding groups and therefore play a central role in fermionic randomized protocols, invariant theory, and resource quantification. Using Howe dualities, we show that the particle-preserving commutant is generated by generalized copy-hopping operators, while that for general Gaussian commutant is generated by generalized quadratic Majorana bilinears together with parity. We then derive closed formulas for the dimensions of both commutants as functions of $t$ and $n$, and develop constructive Gelfand--Tsetlin procedures to obtain explicit orthonormal bases, with detailed low-$t$ examples. Our framework also clarifies the structure of replicated fermionic states and connects naturally to measures of fermionic correlations, generalized Plücker-type constraints, and the stabilizer entropy of fermionic Gaussian states. These results provide a unified algebraic description of higher-order invariants for fermionic Gaussian dynamics.

Whether the complex numbers of standard quantum theory are experimentally indispensable has remained open for decades. Real quantum theory (RQT), obtained by replacing complex amplitudes with real ones while retaining the usual Kronecker-product composition rule, reproduces all single-party and bipartite Bell correlations of quantum theory (QT), but its lack of local tomography suggested that the two theories might diverge in more general local experiments. This possibility appeared to be confirmed by Renou et al., who argued that a bilocal network experiment can falsify RQT without falsifying QT. Here we show that this conclusion relies on an experimentally untestable assumption. The key distinction is between product-state independence, which constrains the mathematical form of source states, and operational independence, which is defined entirely by the absence of observable cross-source correlations. We prove that, once source independence is imposed operationally, every finite network correlation achievable in QT is also achievable in RQT with the same locality structure of the measurements. We then extend this equivalence to arbitrary finite sequential multipartite protocols involving channels and measurements with prescribed locality structure. Thus, as long as no violation of QT is observed, RQT cannot be experimentally falsified. Our results restore the empirical indistinguishability of QT and RQT, while showing that they support markedly different pictures of the correlation structure underlying the same observed world.

We introduce a measurement-induced quantum neural network (MINN), an adaptive monitored-circuit architecture in which mid-circuit measurement outcomes determine the entangling gates in subsequent layers. In contrast to standard monitored circuits where sites and gates are sampled randomly, the gates are parametrized and variational, producing correlated history-dependent dynamics and injecting nonlinearity through measurement back-action. A generic MINN is not expected to be efficiently classically simulable. To demonstrate feasibility, we study a matchgate MINN that admits exact fermionic simulation and can be trained with gradient estimators. We apply the architecture to continuous optimization, image classification, and ground-state search in the Sherrington-Kirkpatrick spin glass, finding effective training and performance over a broad range of monitoring rates.

Matrix product states (MPS) provide a powerful framework for characterizing one-dimensional symmetry-protected topological (SPT) phases of matter and for formulating Lieb-Schultz-Mattis (LSM)-type constraints. Here we generalize the MPS formalism to translationally invariant systems with general modulated symmetries. We show that the standard symmetry "push-through" condition for conventional global symmetry must be revised to account for symmetry modulation, and we derive the appropriate generalized condition. Using this generalized push-through structure, we classify one-dimensional SPT phases with modulated symmetries and formulate LSM-type constraints within the same MPS-based framework.

We connect partition logic with Generative Logic by translating finite partition logics into Prolog-based Simple Generative Logic Grammars. As a proof of concept, we use the five-atom V-logic L_{12} to generate a modular visual artifact, the \emph{Quantum Square}. The approach separates logical structure from its visual, textual, or sonic realization. This makes partition logic useful both as a generative design resource and as a tool for communicating complementarity.

Quantum block encoding (QBE) is a crucial step in the development of most quantum algorithms, as it provides an embedding of a given matrix into a suitable larger unitary matrix. Historically, the development of efficient techniques for QBE has mostly focused on sparse matrices; less effort has been devoted to data-sparse (e.g., rank-structured) matrices. In this work we examine a particular case of rank structure, namely, one-pair semiseparable matrices. We present a new block encoding approach that relies on a suitable factorization of the given matrix as the product of triangular and diagonal factors. To encode the matrix, the algorithm needs $2\log(N)+7$ ancillary qubits. This process takes polylogarithmic time and has an error of $\mathcal{O}(N^2)$, where $N$ is the matrix size.

In this work, we review quantum approaches to combinatorial optimization, with the aim of bridging theoretical developments and industrial relevance. We first survey the main families of quantum algorithms, including Quantum Annealing, the Quantum Approximate Optimization Algorithm (QAOA), Quantum Reinforcement Learning (QRL), and Quantum Generative Modeling (QGM). We then examine the problem classes where quantum technologies currently show evidence of quantum advantage, drawing on established benchmarking initiatives such as QOBLIB, QUARK, QASMBench, and QED-C. These problem classes are subsequently mapped to representative industrial domains, including logistics, finance, and telecommunications. Our analysis indicates that quantum annealing currently exhibits the highest level of operational maturity, while QAOA shows promising potential on NISQ-era hardware. In contrast, QRL and QGM emerge as longer-term research directions with significant potential for future industrial impact.

We investigate the quantum advantage that can arise in typical two-party communication scenarios, where the sender and the receiver are allowed to share prior correlations. Focusing on communication tasks constrained by the distinguishability of the sender's inputs, we demonstrate that entanglement-assisted communication, both classical and quantum, can outperform classical communication supplemented with shared randomness. We begin by developing a general framework for communication tasks with pre-shared correlations. We identify certain communication tasks that exhibit an advantage under entanglement assistance compared to classical communication. Through these results, we establish a connection between quantum communication and entanglement-assisted classical communication, and also show an equivalence between entanglement-assisted classical communication and entanglement-assisted quantum communication. We then consider the simplest scenarios in which the receiver has no input and demonstrate that entanglement-assisted strategies still offer advantages over both classical communication and quantum communication without prior entanglement. Finally, by constructing a class of communication tasks, we show that a non-maximally entangled state can, in some cases, be more useful than a maximally entangled state as a pre-shared resource.

We introduce and characterize different models for an active quantum particle where activity arises from engineered dissipation-- specifically, from a suitably coupled nonequilibrium environment. These include a model of a particle moving on a lattice with coherent and dissipative hopping, as well as quantum generalizations of well-studied models of active behavior, such as the active Ornstein-Uhlenbeck process, run-and-tumble dynamics, and the active Brownian particle. Despite the different microscopic mechanisms at play, we show that all these models display key features of active motion. Notably, we observe a crossover from diffusive to active-diffusive behavior at long times, leading to an effective Péclet number, as well as a strong sensitivity to boundary conditions which, in our open quantum system context, arises from the Liouville skin effect. We discuss the role of quantum fluctuations and experimental realizations with superconducting circuits or cold gases, closing with perspectives for many-body effects in quantum active matter.

Models of interacting quantum spins are used in many areas of physics ranging from the study of magnetism and strongly correlated materials to quantum sensing. In this work, we study coherent many-body dynamics of interacting spin models realized using polar molecules trapped in rearrangeable optical tweezer arrays. Specifically, we encode quantum spins in long-lived rotational states and use the electric dipolar interaction between molecules, together with Floquet Hamiltonian engineering, to realize $1/r^3$ XXZ and XYZ models. We microscopically probe several types of coherent dynamics in these models, including quantum walks of single spin excitations, the emergence of magnon bound states, and coherent creation and annihilation of magnon pairs. Our results establish molecular tweezer arrays as a new quantum simulation platform for interacting quantum spin models.

Incorporating sample efficiency, by requiring the number of states consumed by broadcasting does not exceed that of a naive prepare-and-distribute strategy, gives rise to the no practical quantum broadcasting theorem. To navigate this limitation, we introduce approximate and probabilistic virtual broadcasting and derive analytic expressions for their optimal sample complexity overheads. Allowing deviations at the receivers restores sample efficiency even in the 1-to-2 approximate setting, whereas probabilistic protocols obey a stronger no-go theorem that excludes all sample efficient 1-to-2 implementations for arbitrary dimension and success probability. Rather counterintuitive, this obstruction does not persist at larger receiver numbers: for qubit systems, practical 1-to-6 virtual broadcasting becomes attainable. These results elevate sample complexity from a technical constraint to a defining operational principle, opening an unexplored route to the efficient distribution of quantum information.

Chemistry and materials science are widely regarded as potential killer application fields for quantum hardware. While the dream of unlocking unprecedented simulation capabilities remains compelling, quantum algorithm development must adapt to the evolving constraints of the emerging quantum hardware in order to accomplish any advantage for the computational chemistry practice. At the same time, the continuous advancement of classical wavefunction-theory methods narrows the window for a broad quantum advantage. Here, we explore potential benefits of quantum computation from the broader perspective of utility-scale applications. We argue that quantum algorithms need not only enable accurate calculations for a few challenging, that is strongly correlated, molecular structures, that might be hard to describe with traditional methods. Instead, they must also support the practical integration of quantum-accelerated computations into high-throughput pipelines for routine calculations on arbitrary molecules, ultimately delivering a tangible value to society.

The short quantum link regime, where the photon travel time $τ$ is comparable to the emitter lifetime $1/γ$, is experimentally relevant but theoretically underexplored: existing few-mode descriptions lose validity as retardation and multimode effects become significant. Using a Delay Differential Equation (DDE) framework that admits exact analytical solutions from the single-mode cavity limit to the multimode waveguide continuum, we show that emitters coupled to a short link spontaneously lock into self-synchronized Rabi oscillations driven by coherent photon echoes, breaking the link's discrete time-displacement symmetry. The resulting spectral structure -- persistent quasi-dark states and vacuum Rabi splitting, including in the superstrong coupling regime -- enables efficient quantum state transfer (QST): benchmarking three protocols across the full $γτ$ parameter space, we find that STIRAP exploits the quasi-dark-state structure to achieve a quadratic infidelity floor $\mathcal{O}((γτ)^2)$, outperforming both SWAP (linear error $\mathcal{O}(γτ)$) and wavepacket engineering for $γτ\lesssim 1.44$, even in regimes where retardation cannot be neglected. These results establish photon-echo synchronization as an engineering resource for quantum state transfer, with DDE modeling providing the exact analytical predictions needed to design and optimize short-link experiments on current circuit-QED hardware.

Classical reverse diffusion is generated by changing the drift at fixed noise. We show that the quantum version of this principle obeys an exact law with a sharp phase boundary. For Gaussian pure-loss dynamics -- the canonical model of continuous-variable decoherence in optical attenuation channels, squeezed-light interferometric sensing, and superconducting bosonic architectures -- complete positivity, the requirement that the dynamics remain physical even for systems entangled with an ancilla, creates an exact phase boundary at which the minimum reverse cost vanishes, fixes the reverse-noise budget on both sides, and makes pure nonclassical targets dynamically singular. The minimum reverse cost vanishes exactly at a critical squeezing-to-thermal ratio and is strictly positive away from it, with a sharp asymmetry: below the boundary, standard reverse prescriptions such as the fixed-diffusion Bayes reverse remain feasible at mild cost; above it, these prescriptions become infeasible, the covariance-aligned generator remains CP-feasible and uniquely optimal, and the cost can be severe. The optimal reverse noise is locked to the state's own fluctuation geometry and simultaneously minimizes the geometric, metrological, and thermodynamic price of reversal. For multimode trajectories, the exact cost is additive in a canonical set of mode-resolved data, and a globally continuous protocol attains this optimum on every mixed-state interval. If a pure nonclassical endpoint is included, the same pointwise law holds for every $t>0$, but the optimum diverges as $2/t$: exact reversal of a pure quantum state is dynamically unattainable. These results establish an exact law of quantum reversibility in the canonical pure-loss setting and provide a sharp benchmark for broader theories of quantum reverse diffusion.

We investigate the multiparameter quantum estimation and quantum thermodynamics properties of a gravitational cat state (gravcat) system composed of two interacting massive particles confined in double-well potentials. The system is described by an effective Hamiltonian involving the energy splitting parameter $ω$ and the gravitational coupling strength $γ$, while the interaction with a thermal environment is modeled through a Gibbs thermal state. Within the framework of quantum parameter estimation theory, we employ the quantum Fisher information matrix (QFIM) to analyze the precision limits for estimating the three fundamental parameters of the model, namely the gravitational coupling $γ$, the energy splitting $ω$, and the temperature $T$. Utilizing the symmetric logarithmic derivative (SLD) formalism within the QFIM framework, we derive the analytical expressions of the estimation bounds and evaluate the corresponding minimal variances associated with the quantum Cramér-Rao bound. Both simultaneous and individual estimation strategies are investigated, and their performances are compared in different parameter regimes. Our results reveal the existence of optimal estimation regions where the precision is significantly enhanced and show that the relative efficiency of the estimation schemes strongly depends on the interaction strength, the energy gap, and the thermal environment. In addition, the thermodynamic behavior of the system is analyzed within the framework of a quantum Stirling cycle. The internal energy, entropy, heat exchanges, and work production are examined, allowing us to evaluate the efficiency of the gravcat-based quantum heat engine. The obtained results highlight the interplay between quantum metrology and quantum thermodynamics.

Simulations of chemical dynamics are a powerful means for understanding chemistry. However, classical computers struggle to simulate many chemical processes, especially non-adiabatic ones, where the Born-Oppenheimer approximation breaks down. Quantum computers could simulate quantum-chemical dynamics more efficiently than classical computers, but there is currently no complete quantum algorithm for calculating dynamical observables to within a known error. Here, we develop an efficient, end-to-end quantum algorithm for simulating chemical dynamics that avoids all uncontrolled approximations (including the Born-Oppenheimer approximation) and whose error is bounded subject to mild assumptions. To do so, we treat the nuclei and the electrons on an equal footing and simulate the full molecular wavefunction on a momentum-space grid in first quantization, including all algorithmic steps: initial-state preparation, time evolution using qubitization, and measurement of chemical observables such as reaction yields and rates. Our work gives the first algorithm for quantum simulation of chemistry whose end-to-end complexity achieves sublinear scaling in the size of the grid. We achieve this by developing an exponentially faster method for initial-state-preparation. Photochemistry is a likely early application of our algorithm and we estimate resources required for end-to-end simulations of non-adiabatic dynamics of atmospherically important molecules. Classically intractable photochemical computations could be performed using resources comparable to those required for other chemical applications of quantum computing.

We study non-equilibrium steady states and recurrence times in noisy, stroboscopically monitored qubit systems using complete measurements. In the noiseless limit, recurrence times are integer-quantized, with dips to lower integers when sampling approaches revival conditions associated with ergodicity breaking. Using an IBM quantum platform, we find that quantization is robust when sampling far from revivals, but breaks down dramatically near revivals: even weak noise produces large deviations and can invert the expected dips into pronounced peaks. To explain this behavior, we formulate a statistical-physics model of monitored noisy circuits in which monitoring drives an effective infinite-temperature steady state while thermal-like relaxation competes to favor a low-temperature limit. We show that the sampling time tunes a crossover between these regimes, near revivals stabilizing low-temperature behavior, and far from revivals restoring infinite-temperature behavior -- with noise strength and detuning acting as coupled small parameters near resonance.

Spectral statistics probe integrability versus chaos and have recently been extended to Markovian open quantum systems described by Lindbladians, whose quantum-trajectory unraveling decomposes the evolution into no-jump dynamics generated by an effective non-Hermitian Hamiltonian and recycling jumps. In this work, we perform spectrum-statistics diagnostics for Lindbladians and their effective non-Hermitian Hamiltonians. We show that recycling processes, symmetry constraints, and the Liouville-space structure crucially shape the spectral correlations. In particular, we identify a family of spectrally separable Lindbladians whose spectra exhibit robust Poisson statistics, despite the effective non-Hermitian Hamiltonian varying from regular to chaotic. Our work establishes a unified spectral-statistics characterization for Lindbladians and their associated effective non-Hermitian Hamiltonians, deepening our understanding of integrable and chaotic spectral properties in open many-body systems.

Low-altitude drones can serve as dynamic nodes apparently mitigating terrain-induced impacts for quantum networks. However, it is extremely hard to establish a sable quantum link in a drone-based dynamic platform, which requires centimeter-level positioning techniques and high-precision time synchronization technologies. In this paper, we develop a single-ended polarization adaptive correction technology at both the transmitting and receiving ends. Based on this, we present the world's first kilometer-scale drone-based QKD network, achieving an 1.2 km free-space QKD link with a secure key rate of 2.76 kbps, suitable for urban quantum network deployment. We validate the feasibility of QKD between dynamic drone and ground unmanned vehicle at a relative speed of 1 m/s over a distance of 100 m, attaining a secure key rate of 70.94 kbps. This work advances drone-based QKD from static demonstrations to practical dynamic network, boasting great development potential for an airborne quantum internet.

Interfacing materials with electromagnetic cavities offers a route to modify equilibrium properties through structured vacuum fluctuations. The coupling of light with correlated electrons lacks a characteristic energy scale, making vacuum induced modifications of such systems inherently off-resonant and sensitive to the full photon mode structure. Here, we present a non-perturbative calculation of the cavity induced modification of the magnetic exchange interaction $J$ of the half-filled Hubbard model, including all cavity modes and with parameters determined from first principles. We show that the strength of the modification is controlled by a generalized Purcell factor, proportional to the frequency integrated photonic density of states. This result identifies polaritonic surface cavities as promising platforms to modify correlated systems, while standard Fabry-Pérot resonators produce negligible effects due to spectral weight cancellations upon integration. To perform the calculation, we develop a consistent quantization scheme for materials coupled to a dielectric substrate, in the Coulomb gauge, which reveals a competition between static Coulomb screening and dynamical effects arising from the vector potential. Including both effects is essential to obtain even qualitatively correct predictions. For a gold substrate the light-matter interactions lead to a net enhancement of $J$, whose magnitude is large enough to be observable in two-magnon Raman spectroscopy. Our framework establishes a concrete design principle linking cavity geometry to material response in the off-resonant regime, which will guide future experimental and theoretical explorations.

Aerodynamic drag reduction on highways through vehicle platooning is a well-known concept, but it has not yet seen systematic uptake, arguably because of significant technological and legislative obstacles. As a low-tech entry point to real multi-vehicle platooning, "Windbreaking-as-a-Service" (WaaS) was introduced recently. Here we use a QUBO formulation to study classical metaheuristics such as simulated annealing and tabu search, together with emerging quantum heuristics including quantum annealing and variants of the Quantum Approximate Optimization Algorithm (QAOA). These heuristic solvers do not guarantee optimality, but they traverse the same higher-order landscape using polynomial memory. They can also be parallelized aggressively, and efficient classical post-processing can be used in hybrid workflows to return only valid schedules. This paper therefore positions QUBO as a common language that allows heterogeneous classical, quantum, and hybrid solvers to address the optimization of highway platooning.

Fermionic Gaussian circuits can be simulated efficiently on a classical computer, but become universal when supplemented with non-Gaussian operations. Similar to stabilizer circuits augmented with non-stabilizer resources, these non-Gaussian circuits can be simulated classically using rank- or extent-based methods. These methods decompose non-Gaussian states or operations into Gaussian ones, with runtimes that scale polynomially with measures of non-Gaussianity such as the rank and the extent -- quantities that typically grow exponentially with the number of non-Gaussian resources. Current fermionic rank- and extent-based simulators are limited to Gaussian circuits with magic-state injection. Extending them to mixed states and non-unitary channels has been hindered by the lack of known extent-optimized decompositions for physically relevant gates and noisy channels. In this work, we address this gap. First, we derive analytic decompositions for key non-Gaussian gates and channels, including decompositions for arbitrary two-qubit fermionic gates which are provably optimal for diagonal gates or those acting on Jordan-Wigner-adjacent qubit pairs. Second, we show that stochastic Pauli noise can reduce the effective extent of non-Gaussian rotation gates, but that fermionic magic is substantially more robust to such noise than stabilizer magic. Finally, we demonstrate how these decompositions can accelerate classical sampling from the output distribution of a quantum circuit. This involves a generalization of existing sparsification methods, previously limited to convex-unitary channels, to circuits involving intermediate measurements and feed-forward. Our decompositions also yield speedups for emulating noisy Pauli rotations with quasiprobability simulators in the large-angle/arbitrary-strength-noise and small-angle/low-noise parameter regimes.

Ergotropy, the maximum work extractable from a quantum system, is a central resource in quantum physics. Computing ergotropy is well established when the system state is fully known, but its estimation under partial information remains an open problem. Here we introduce a general certification framework that lower bounds ergotropy using only the expectation values of a limited set of arbitrary observables. The method naturally applies in the finite-statistics regime, yielding confidence-certified bounds that explicitly incorporate shot noise. We benchmark our approach on both synthetic data and experimental measurements from an IBM quantum processor. This establishes a robust and experimentally accessible tool for certifying extractable work in realistic quantum settings.

We review the recent quantum advantage experiments by IBM, D-Wave, and Google, focusing on cases where efficient classical simulations of the experiment were demonstrated or attempted using tensor network methods. We assess the strengths and limitations of these tensor network-based approaches and examine how the interplay between classical simulation and quantum hardware has advanced both fields. Our goal is to clarify what these results imply for the next generation of quantum advantage experiments. We identify regimes and system features that remain challenging for current tensor network approaches, and we outline directions where improved classical methods could further raise the standard for claiming quantum advantage. By analyzing this evolving competition, we aim to provide a clear view of where genuine, scalable quantum advantage is most likely to emerge.

Quantum metrology enables parameter estimation beyond classical limits by exploiting nonclassical resources such as squeezing and entanglement. In distributed quantum sensing, Heisenberg scaling has been extended from $1/N^2$ to $1/(NM)^2$ through entanglement across both particles and spatial modes, where $N$ denotes the photon number and $M$ the number of spatially distributed modes. However, the overall sensitivity has remained limited to linear scaling with the number of measurement repetitions $R$. Here, we show that exploiting entanglement across temporal modes via time-domain multiplexing enables a scaling advantage with respect to $R$. As a result, the sensitivity can asymptotically approach simultaneous Heisenberg scaling in photons, spatial modes, and repetitions, yielding an overall sensitivity approaching $Δ^2 φ\propto 1/(NMR)^2$. Using the Bogoliubov transformation formalism, we prove the optimality of the protocol within the class of Gaussian states and show that the scaling is realizable via homodyne detection and maximum-likelihood estimation. We further show that the advantage persists under optical loss and propose an experimentally feasible loop-based photonic sensing scheme. Our results open a route to incorporating time-multiplexing techniques into quantum metrology.

The standard approach to quantum measurements is to assume that they lead to effectively instantaneous collapse of the quantum state. However, if we assume that we are unable to enforce at what exact moment of time the measurement occurs due to a finite resolution of any time measurement device, at the level of the ensemble, the measurement would lead to an effectively nonunitary evolution involving a mixed state. Each individual ensemble member would face an instantaneous collapse at different moments of time. This process is completely indistinguishable from fundamental nonunitary evolution at the level of each individual ensemble member, within the framework of strong projective measurements. In this paper, we show that weak postselected measurements can distinguish these two types of evolution. An experimental protocol for determining the nature of quantum collapse is described, and the example of a hydrogen atom is analyzed in detail.

We report a comparative study on transmon qubit control using (i) conventional attenuated coaxial microwave line and (ii) an optical control system using modulated laser light delivered over telecommunications optical fiber to a photodiode located at the 1K stage of a dilution cryostat. During each experiment, we performed repeated measurements of the energy relaxation and coherence times of a transmon qubit using one of the control signal delivery methods. Each measurement run spanned 20 hours of measurement time and from these datasets we observe no measurable effect on coherence of the qubit compared to random coherence fluctuations. Our results open up the possibility of large scale integration of the optical qubit control system.

The study of spontaneous supersymmetry breaking (SSB) on the lattice is obstructed by a severe sign problem. Quantum computing provides a promising alternative approach. In particular, properties of supersymmetry relate SSB to the ground-state energy, which can be probed using hybrid quantum--classical algorithms such as the variational quantum eigensolver (VQE). In this work we present VQE analyses for supersymmetric quantum mechanics with various superpotentials. A key new feature is an adaptive ansatz construction algorithm that reduces the number of variational parameters within our ansätze. This lowers the resource burden on both the classical optimizer and the noisy quantum processor, thereby improving the feasibility of these calculations in the NISQ era. Additionally, we present preliminary VQE results obtained from real IBM quantum devices, highlighting accuracy, resource constraints, and computational cost, both with and without the application of error mitigation techniques.

We present a framework for computing the solution to Hamiltonian eigenproblems in a subspace defined by bit-strings sampled from a quantum computer. Hamiltonians are represented using an extended alphabet that includes projection and ladder operators, yielding a unified solution method for qubit and fermionic systems. Operators are grouped and sorted so that only non-zero terms are evaluated and a minimal number of subspace lookup operations are performed. Bit-strings are expressed using bit-sets to reduce memory consumption and allow for evaluating operators with no intrinsic limitation on the number of qubits. Subspaces defined over bit-sets are stored in a hash map format that allows for efficient indexing and lookup operations. Our method can be used to directly construct sparse matrix representations or obtain matrix-free solutions. Users are free to utilize these in their eigensolver of choice. We show the benefits of our framework by computing the ground-state solution to examples from condensed matter physics and quantum chemistry with less memory and runtime compared to existing techniques, in some cases by an order of magnitude or more. This work provides a flexible interface for performant quantum-classical eigensolutions for candidate quantum advantage applications.

Single-Molecule Magnets (SMMs) exhibit slow magnetic relaxation as a result of axial magnetic anisotropy inhibiting spin-phonon transitions. In order to establish a direct link between physical observables and the microscopic theory of magnetic relaxation, we here develop and numerically implement a first-principles linear-response theory for open quantum systems that provides access to the complex a.c. magnetic susceptibility in the presence of an oscillating a.c. magnetic field. Once combined with density functional theory and multiconfigurational electronic structure simulations, this formalism is applied in a fully first-principles fashion to three cyanido-bridged Ln/Y-based coordination polymers with general formula {Ln$^{III}_x$ Y$^{III}_{1-x}$ [Co(CN)$_6$]}, where Ln = Yb (1), Tb (2), and Dy (3). The method is able to reproduce the low-temperature direct relaxation process and its field dependence, as well as the high-temperature Orbach relaxation regime for all the investigated compounds. These results demonstrate the feasibility of ab initio simulations of magnetic a.c.susceptibility in lanthanide-based SMMs and support the potential of further development of ab initio open quantum systems methods towards the completion of a magnetization dynamics theory.

Fast electrons in partially ionized plasmas lose energy through inelastic collisions with bound electrons. While the mean energy loss is well described by stopping-power theory, fluctuations associated with discrete excitation and ionization events produce energy straggling and an additional longitudinal diffusion in momentum space. We incorporate this effect into fast-electron kinetics through a derived Fokker-Planck operator whose coefficients are obtained from ab initio quantum many-body simulations. We demonstrate that neglecting inelastic energy diffusion in partially ionized D-Ar plasmas can underestimate primary runaway-electron generation by several orders of magnitude.

In their paper (arXiv:2402.09879), Aredes and Saldanha analyze several paradoxes related to weak values and present a "general argument" that aims to show that "realistic interpretations ...of weak values lead to inconsistencies". Although we agree with the identified inconsistencies for the specific weak values analyzed there, in this Comment we demonstrate that the origin of these inconsistencies is not their general argument, which is formally incorrect. We use Bohmian mechanics as a counterexample to confirm that their conclusions are not valid for all weak values and quantum theories. In particular, we show that weak values postselected in position can in fact be interpreted within Bohmian mechanics as properties of quantum systems, detached from any measuring devices, in a consistent and meaningful way.

The use of Bohmian mechanics as a practical tool for modeling non-relativistic quantum phenomena of matter provides clear evidence of its success, not only as a way to interpret the foundations of quantum mechanics, but also as a computational framework. In the literature, it is frequently argued that such a realistic view-based on deterministic trajectories cannot account for phenomena involving the "creation" and "annihilation" of photons. In this paper, by revisiting and rehabilitating earlier proposals, we show how quantum optics can be modeled using Bohmian trajectories for electrons in physical space, together with well-defined electromagnetic fields evolving in time. By paying special attention to an experiment demonstrating partition noise for photons, and to how the Born rule emerges in this context, the paper pursues two main goals. First, it vindicates the pedagogical use of this simple Bohmian framework to compute, understand, and visualize quantum electrodynamics phenomena. Second, given that measurements are ultimately indicated on matter pointers, it clarifies what it means to measure photon or electromagnetic-field properties, even when they are considered non-ontic elements.

We propose a quantum teleportation scheme for transmitting a single qutrit state by adopting a 2-qudit entangled state as the quantum channel. The measurement basis for Alice has been carefully and systematically constructed, which is essential for the successful implementation of the teleportation protocol. Based on Alice's measurement outcomes, we design the corresponding collective unitary transformations to be performed by Bob on an auxiliary qubit and information particle. After implementing the collective unitary transformation, Bob performs a von Neumann measurement on the auxiliary qubit. The single qutrit state is then teleported to the distant receiver Bob with a finite success probability. We obtain the achievable success probabilities of the proposed teleportation scheme for different quantum channels. The obtained results not only enrich the theory of quantum teleportation over high-dimensional entangled channels but also provide a novel and feasible approach to implementing qutrit teleportation.

In microwave-based quantum circuits, including double quantum dots (DQDs), superconducting qubits and spin qubits, parametric amplifiers are indispensable in achieving high-fidelity qubit readouts. Despite its importance, the application of parametric amplifiers is hampered by several challenges, such as high insertion losses, constrained tunability, and a pronounced vulnerability to magnetic fields. Here, we demonstrate an on-site single-atom parametric amplifier (SAPA) within a reconfigurable quantum circuit, which consists of a superconducting microwave cavity and two GaAs gate-defined DQDs. Leveraging the inherent nonlinearity of the DQD, a parametric gain exceeding 11 dB is achieved. This gain contributes to enhance the qubit readout, as evidenced by exceeding two times improvement in the signal-to-noise ratio (SNR) when employing the DQD-based amplifier for reading out another DQD. Our work not only presents a versatile experimental platform with enhanced readout capabilities in quantum computing, but also introduces alternative choices of parametric amplifiers for a variety of microwave-based quantum circuits.

Bayes' rule is widely regarded as the canonical prescription for belief updating. We show, however, that one can arbitrarily preserve pre-specified beliefs while appearing to perform Bayesian updates via "prior hacking": engineering a reference prior distribution such that, for a fixed channel and evidence, the update matches a chosen target distribution. We prove that this is generically possible in both classical and quantum settings whenever Bayesian inversions are well-defined (with the Petz recovery map as the quantum analogue to Bayes' rule), and provide constructive algorithms for doing so. We further establish a duality between prior hacking and Schrödinger bridge problems (a key object in statistical physics with applications in generative modelling), yielding in the quantum setting a unique, inference-consistent selection among candidate bridges. This formally establishes the Bayes-like updating that Schrödinger bridges are performing with respect to the process as opposed to the reference prior, both in classical and quantum settings.

We investigate the distribution of fidelity zeros in two-band topological models by extending the phase transition driving parameter into the complex plane. Within the biorthogonal formulation, we unveil that fidelity zeros are related to momentum modes for which the real part of the energy gap vanishes. Guided by this relation, we analyze the Kitaev chain, the Haldane model, and the Qi-Wu-Zhang (QWZ) model. In finite-size systems the zeros form discrete lines parallel to the imaginary axis, while in the thermodynamic limit they accumulate into extended regions in the complex parameter plane. For the Kitaev and Haldane models, the accessible interval of the real part of the complexified parameter is bounded by the critical points of the corresponding topological transitions. For the QWZ model, the transitions at $u = \pm2$ are identified in the same way, whereas the critical point at $u = 0$ is signaled by fidelity zeros crossing the real axis. These results extend the fidelity-zero framework to topological quantum phase transitions and clarify how critical information is encoded in complexified parameter space.

Quantum Generative Adversarial Networks (QGANs) offer a promising path for learning data distributions on near-term quantum devices. However, existing QGANs for image synthesis avoid direct full-image generation, relying on classical post-processing or patch-based methods. These approaches dilute the quantum generator's role and struggle to capture global image semantics. To address this, we propose ReQGAN, an end-to-end framework that synthesizes an entire N=2^D-pixel image using a single D-qubit quantum circuit. ReQGAN overcomes two fundamental bottlenecks hindering direct pixel generation: (1) the rigid classical-to-quantum noise interface and (2) the output mismatch between normalized quantum statistics and the desired pixel-intensity space. We introduce a learnable Neural Noise Encoder for adaptive state preparation and a differentiable Intensity Calibration module to map measurements to a stable, visually meaningful pixel domain. Experiments on MNIST and Fashion-MNIST demonstrate that ReQGAN achieves stable training and effective image synthesis under stringent qubit budgets, with ablation studies verifying the contribution of each component.

Traversable wormhole teleportation in the Sachdev-Ye-Kitaev (SYK) model links quantum channel integrity to black hole interior dynamics, using teleportation fidelity to probe holographic scrambling. We subject the SYK boundary to a gravitational-wave (GW)-inspired periodic Floquet deformation, mimicking a leading-order metric-strain perturbation from the JT-gravity dictionary. We characterize the channel response via exact numerical time evolution with disorder averaging at $βJ = 2$. The drive produces a coherent, frequency-selective fidelity suppression, yielding four main results: (i) two amplitude regimes separated near $\varepsilon \sim J$ (perturbative sensing vs.\ strong-drive); (ii) the channel acts as a low-pass filter, most sensitive at $ω\lesssim β^{-1}$ with monotone recovery above the thermal scale; (iii) an inspiral chirp drive delays the fidelity peak by $Δt_{\rm scr}^{(\rm fid)} = +0.11\, J^{-1}$, corroborated by an out-of-time-order correlator (OTOC) diagnostic ($Δt_{\rm scr}^{(\rm OTOC)} = +0.20\, J^{-1}$), establishing a genuine scrambling delay; and (iv) the effects persist across $N \in \{10, 12, 14, 16\}$ Majorana modes, indicating no systematic finite-size suppression. These results establish that holographic teleportation channels degrade gracefully under GW-inspired boundary deformations, with direct implications for near-term quantum processor implementations of traversable wormholes.

Parameterized quantum circuits (PQCs) are central to quantum machine learning and near-term quantum simulation, but their scalability is often hindered by barren plateaus (BPs), where gradients decay exponentially with system size. Prior explanations, including expressivity, entanglement, locality, and noise, are often presented in ways that conflate two distinct issues: concentration of the measured observable and loss of parameter sensitivity caused by circuit dynamics. We develop a unified statistical framework that separates these mechanisms. We show that several standard BP explanations, including locality- and entanglement-related effects, can be understood through a single phenomenon that we term observable concentration (OC). Importantly, we prove that avoiding OC is necessary but not sufficient for trainability. Beyond OC, we identify two distinct mid-circuit sources of gradient suppression. First, mid-circuit information loss occurs when parameter perturbations propagate into degrees of freedom that are inaccessible to the final measurement, yielding little or no response. Second, mid-circuit information scrambling occurs when local perturbations rapidly spread across the system and become effectively undetectable on the measured subsystem. We support our theory with explicit constructions and numerical evidence, including quantum convolutional neural network architectures that exhibit information-loss-induced barren plateaus despite the absence of observable concentration.

The generation of a trapping potential for dark-state polaritons in a two-dimensional electromagnetically induced transparency system is theoretically studied. We show that such a trap can arise from a spatially inhomogeneous effective mass of the dark-state polariton. Because this mass inhomogeneity can be engineered by tuning the parameters of the control fields, the motion, spatial profile, and coherent behavior of bound dark-state polaritons can be tailored accordingly. Our results enable spatial controls of optical information and provide a possible route toward realizing Bose-Einstein condensation of dark-state polaritons in a trapping potential.

We investigate multipartite quantum correlations by analyzing the mutual information of N-partite states for both free bosonic and fermionic fields in the background of a Garfinkle-Horowitz-Strominger (GHS) dilaton black hole. Focusing on multipartite GHZ and W states, we examine how the Hawking effect influences the N-partite mutual information when one observer hovers near the event horizon while the remaining observers stay in the asymptotically flat region. By tracing over the inaccessible modes inside the event horizon, we derive analytical expressions for the N-partite mutual information in dilaton spacetime for both bosonic and fermionic fields. Our results show that fermionic mutual information is larger than its bosonic counterpart under the influence of the dilaton black hole, whereas the fermionic relative entropy of coherence (REC) is smaller than the bosonic REC. Moreover, the mutual information of GHZ states is consistently larger than that of W states, while the REC of GHZ states is smaller than that of W states in curved spacetime. These findings indicate that the choice of quantum resources should be tailored to the particle species and state structure in relativistic quantum information tasks to optimize their operational efficiency.

Negativities in quasiprobability distributions, a foundational concept originating in quantum optics, serve as a fundamental signature of quantum nonclassicality, with entanglement quasiprobabilities offering a necessary and sufficient criterion for entanglement. However, practical reconstruction of entanglement quasiprobabilities conventionally requires full quantum state tomography, severely limiting scalability. Here, we propose a deep-learning framework that reconstructs entanglement quasiprobabilities directly from incomplete local projective measurements, bypassing full state reconstruction. Using a residual neural network, partial measurement outcomes are mapped to high-fidelity entanglement quasiprobabilities. Numerical benchmarks up to three qubits show more than a $30\times$ reduction in reconstruction error compared with state-of-the-art tomographic methods. Experimental validation on photonic entangled states demonstrates reconstruction and entanglement detection with substantially reduced measurement resources. Our results establish machine-learning-assisted reconstruction of entanglement quasiprobabilities as a scalable and practical tool for entanglement characterization in quantum optical systems.

We introduce the CaRBM algorithm for fixed-depth thermal state preparation. Our algorithm is based on thermal state purification and uses the Restricted Boltzmann Machine (RBM) block-encoding scheme to implement the imaginary-time propagator $e^{-βH}$, which is implemented in the quantum circuit in a fixed-depth manner via Cartan decomposition. Our algorithm performs best at high temperatures, with the success probability of the block encoding decreasing as the temperature decreases. To increase the success probability, we have devised a correction scheme for the block-encoding that increases the temperature range our algorithm reliably probes. We demonstrate our algorithm by calculating the partition function zeros of the XXZ model and the phase diagram of the Gross-Neveu model, which is a model of strongly interacting relativistic fermions.

Extracting energy spectra from quantum Hamiltonians is a fundamental task for quantum simulation, yet remains challenging on noisy intermediate-scale quantum (NISQ) devices. We propose Measured Quantum Time Evolution (MQTE), an ancilla-free algorithm that estimates energy gaps by applying real-time evolution to a reference state and measuring time-resolved probabilities via repeated projective measurements. Spectral analysis of these signals reveals oscillation frequencies corresponding to eigenvalue differences. Crucially, MQTE exhibits inherent robustness to quantum hardware noise and sampling errors: these disturbances manifest as a white-noise background, which does not distort the underlying spectral structure but rather obscures the frequency information. By increasing the number of measurement samples, the intensity of the background white noise can be suppressed, thereby recovering the original spectral content. We validate the algorithm's performance via numerical simulations on one- and two-dimensional Heisenberg models, demonstrating accurate extraction of energy gaps and resilience against both sampling and circuit-level noise. Experimental implementation on the superconducting quantum processor Tianyan-176-II further confirms the practical feasibility and noise tolerance of MQTE under real hardware conditions. This work provides a robust and scalable framework for quantum spectral estimation in the NISQ era.

As early as 1935, Schrödinger recognized entanglement as ``not one but rather the characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought''. Indeed, most remarkable phenomena in quantum information science, such as quantum computing and quantum teleportation, spring from clever uses of entanglement. Among them, pseudotelepathy enables two or more players to win systematically at some cooperative games with no need for communication between them, a restriction that would make the task impossible in a classical world. We investigate the power of multipartite entanglement for pseudotelepathy. Some known games that can be won with tripartite entanglement cannot be won with bipartite entanglement, but they can be won with bipartite nonsignalling resources such as the so-called Popescu--Rohrlich nonlocal box. We exhibit a five-player game that can be won with tripartite entanglement, but not with arbitrary bipartite nonsignalling resources even in the presence of arbitrary five-partite classical resources. This illustrates both the power of bipartite nonsignalling resources (over bipartite entanglement) and the even superior power of tripartite entanglement.

I propose a physical measurement scheme on multiple independent and identically distributed quantum objects to approach the Holevo--Nagaoka bound for quantum multiparameter estimation. The scheme entails a physical interaction of the objects with bosonic ancillas, followed by a general-dyne measurement of the ancillas. The proposal offers a more concrete description of the experimental setup needed to achieve the ultimate precision limit set by the bound.

This paper introduces Witnessed Quantum Time Evolution (WQTE), a novel quantum algorithm for efficiently computing the eigen-energy spectra of arbitrary quantum systems without requiring eigenstate preparation-a key limitation of conventional approaches. By leveraging a single ancillary qubit to control real-time evolution operators and employing Fourier analysis, WQTE enables parallel resolution of multiple eigen-energies. Theoretical analysis demonstrates that the algorithm achieves Heisenberg-limited precision and operates with only a non-zero wavefunction overlap between the reference state and target eigenstates, significantly reducing initialization complexity. Numerical simulations validate the algorithm's effectiveness in molecular systems (e.g., H4 chains) and lattice models (e.g., Heisenberg spin systems), confirming that computational error scales inversely with maximum evolution time while maintaining robustness against sampling errors and quantum noise. Experimental implementation on an NMR quantum processor further verifies its feasibility in real-world noisy environments. Compared to existing quantum algorithms (e.g., VQE, QPE and their variants), WQTE exhibits superior circuit depth efficiency, resource economy, and noise resilience, making it a promising solution for eigen-energy computation on noisy intermediate-scale quantum (NISQ) devices.

Non-Markovian dynamics is ubiquitous in both quantum and classical systems, but the numerical computation of the time-delay dynamics is demanding. In this work, we propose an efficient quantum algorithm for solving linear distributed delay differential equations and identify the condition under which it applies. Using the linear chain trick, the distributed delay differential equations can be embedded into ordinary differential equations augmented with auxiliary variables, when the kernel function is characterized by a phase-type distribution. Employing the Schrödingerization method, the resulting equations can be embedded into the Schrödinger equation and efficiently solved by Hamiltonian simulation. Although this embedding requires the augmented differential equation to be semi-stable, we show that it is satisfied if and only if the original distributed-delay differential equations are semi-stable. The query complexity to obtain the normalized solution state of the $N$-dimensional delay system $|\mathbf{x}(t)\rangle\equiv\mathbf{x(t)}/\vert\vert\mathbf{x}(t)\vert\vert$ is $\mathcal{O}((st\vert\vert H\vert\vert_{\max}+\logε^{-1}/\log\logε^{-1})\vert\vert\mathbf{x}(0)\vert\vert/\vert\vert\mathbf{x}(t)\vert\vert)$ with $ε$, $g$, $H$, and $s$ being the allowable error, the dimension of the auxiliary variables associated with each kernel function, the Hamiltonian operator, and its sparsity, respectively. The gate complexity is given by this quantity multiplied by $\mathcal{O}(m+\log(N(1+gs)))$, where $m$ is the number of precision bits. To demonstrate the efficacy of our method, we present its applications to the generalized master equation and to the Redfield equation of the dephasing model.

We study the cross-resonance effect in capacitively-coupled fluxonium qubits and devise a simple formula for their maximum ZX interaction strength. By going beyond the perturbative regime, we find that a CNOT gate can generally be realized in under 200 ns with residual ZZ limited to 50 kHz, for fluxonium qubits with frequencies below 1 GHz. Our analysis relies on a semi-analytical method: we first numerically diagonalize the Floquet Hamiltonian of the strongly-driven control qubit and then perturbatively incorporate the weak qubit-qubit coupling to obtain an effective Hamiltonian. We also derive frequency collision windows around harmful control-target and control-spectator transitions. For large fluxonium devices, we predict a collision-free yield that is considerably less sensitive to junction variability compared to transmons in the same layout. These results support the viability of an all-fluxonium cross-resonance architecture with only capacitive couplings.

The quantum Zeno and anti-Zeno effects describe how frequent measurements can either suppress or accelerate quantum dynamics. While extensively studied in various platforms, their manifestation in dark-state dynamics remains largely unexplored. Here we investigate the stability of dark states in a cavity QED system consisting of two atoms coupled to a single-mode cavity, subject to thermal dephasing that models continuous quantum non-demolition monitoring. Using the Tavis--Cummings model within a Lindblad master equation framework, we numerically analyze how measurement-induced dephasing affects dark-state retention and stabilization time. We identify distinct parameter regimes corresponding to Zeno and anti-Zeno behavior: at low dephasing intensities, increasing the measurement strength accelerates the loss of dark-state coherence (anti-Zeno regime), while at higher intensities, it slows down the dynamics and partially recovers dark-state weight (Zeno regime). The transition between these regimes is controlled by the dephasing rates, the cavity photon exchange, and the asymmetry in atom-field couplings. We show that even under strong dephasing, a finite dark-state component persists, demonstrating remarkable robustness. Our results provide insights into the interplay between measurement back-action and decoherence in open quantum systems, with implications for quantum control and information storage.

We consider damped driven Maxwell-Bloch equations for a single-mode Maxwell field coupled to a two-level molecule. The equations are used for semiclassical description of the laser action. Our main result is the construction of solutions with single-frequency asymptotics of the Maxwell field in the case of quasiperiodic pumping. The asymptotics hold for solutions with harmonic initial values which are stationary states of averaged reduced equations in the interaction picture. We calculate all harmonic states and analyse their stability. Our calculations rely on the Hopf reduction by the gauge symmetry group U(1). The asymptotics follow by application of the averaging theory of Bogolyubov--Eckhaus--Sanchez-Palencia.

Accurate contraction of tensor networks beyond one dimension is essential in various fields including quantum many-body physics. Existing approaches typically rely on approximate contraction schemes and do not provide certified error bars. We introduce a numerical bootstrap framework which casts the problem of tensor-network contractions into a convex optimization problem, thereby yielding certified lower and upper bounds on expectation values of physical observables. As a proof-of-principle, we construct such constraints explicitly for translationally invariant matrix product states and demonstrate that, assuming a canonical form, second-order-cone relaxation can provide tight bounds on the contraction result. We further demonstrate that when the requirement on canonical form is lifted, a more general semidefinite-programming approach could yield similar tight bounds at higher but still polynomial computational cost. Our work suggests numerical bootstrap could be a possible way forward for the rigorous contractions of tensor networks.

Fourier representations play a central role in operator learning methods for partial differential equations and are increasingly being explored in quantum machine learning architectures. The classical fast Fourier transform (FFT), particularly in its Cooley--Tukey decomposition, exhibits a structure that naturally matches continuous-variable quantum circuits. This correspondence establishes a direct structural isomorphism between the Cooley-Tukey butterfly network and Gaussian photonic gates, enabling the FFT to be realized as a native optical computation in continuous-variable quantum computing. Building on this observation, we introduce a continuous-variable Quantum Fourier Layer (CV--QFL) based on a bipartite Gaussian encoding and a Cooley-Tukey quantum Fourier transform, enabling exact two-dimensional spectral processing within a Gaussian photonic circuit. We test the CV--QFL on two representative tasks: spectral low-pass filtering and Fourier-domain integration of the heat equation. In both cases, the results match the classical reference to machine precision. Beyond these examples, our method naturally extends to optical-input settings in which the signal is already available as a Gaussian optical field. In such scenarios, coherent light coupled into single-mode waveguides can be processed directly by the CV--QFL, bypassing the need for an explicit classical-to-quantum encoding stage. This enables native spectral processing of light and lays the groundwork for new approaches to quantum scientific machine learning, in particular for future neural operator architectures within the CV framework.

We derive an exact uncertainty relation for arbitrary quantum states of finite-dimensional Hilbert spaces. For any given $k$-partition of a $d$-dimensional multipartite system, we introduce the total uncertainty as the sum of the uncertainties associated with all possible tensor products of local $\mathrm{SU}(N)$ observables, where each observable acts on the corresponding subsystem. We show that the total uncertainty exactly equals the algebraic sum of the global state purity and the purities of all possible state reductions. For systems containing at least one single-qubit subsystem, this equality implies saturation of the Robertson-Schrödinger uncertainty inequality, with the missing term needed for saturation equal to the bipartite qubit-environment entanglement for a pure global state, or to the qubit two-Rényi entropy for a mixed global state. Leveraging on these results, we show how for any finite-dimensional multipartite system the Hilbert-Schmidt squared norm of the correlation matrix $t$ can be expressed exclusively in terms of the global and reduced state purities. We then derive a correlation matrix-based necessary condition for $k$-separability of arbitrary finite-dimensional quantum states and show, in the case of $n$ qubits, how it is related to a necessary criterion for Bell nonlocality in scenarios with two dichotomic measurements per party. For sufficiently large systems the purity-based formulation of the $k$-separability criterion always yields an exponential advantage over the direct evaluation of the $t$-matrix norm, allowing for a more efficient practical verification of multipartite entanglement and nonlocality via simple experimental schemes based on purity measurements. Our results shed some further light on the intimate and intricate relation between correlations, entropies, uncertainties, and the entanglement certification and detection problem.

We study the Heisenberg spin-1/2 model on a semi-infinite chain - or, equivalently, a trotterized unitary SU(2) symmetric six-vertex quantum circuit - with a boundary defect where the interaction between the two spins nearest the edge differs from that in the bulk. For sufficiently strong boundary interaction we explicitly construct a conserved operator quasi-localized near the boundary using a matrix-product ansatz. This quasi-local edge mode leads to non-decaying boundary correlation functions, corresponding to a nonzero boundary Drude weight. The correlation length of the edge mode diverges at a finite critical value of the boundary interaction, signaling a transition to ergodic boundary dynamics for subcritical interactions.

One-dimensional crystals serve as a versatile platform for engineering nontrivial states, which can be easily explored in transport configurations. In this work, we analyze the properties of a periodic structure composed of an H-shaped unit cell, which forms a periodic ladder-shaped system. Using tight-binding models, group-theoretical considerations, and standard band topology, we uncover the influence of bound states in the continuum (BICs) and quasi-BICs formed in the original finite geometry on the creation of nontrivial band states. By designing various textures for the onsite energies, we discovered a topological band inversion between quasi-BIC-induced bands, leading to the emergence of topologically protected edge states that are characterized by a quantized Zak phase. Additionally, we found an on-site configuration that exhibits robust flat bands, induced by a symmetry-protected BIC and linked to special one-sided localized edge states. We present a detailed analysis of the mechanisms driving both effects and discuss the crucial role of symmetry in characterizing the topological phases of these systems.

To treat a problem with a Quantum Processing Unit (QPU), it must be transformed into a sequence of quantum operations, or gates: this is the quantum description of the problem. These operations are either packed into a query (i.e. quantum algorithm primitive) that encodes the problem, or used to construct the cost function for Variationnal Quantum Algorithm (VQA). Typical queries are the problem Hamiltonian Simulation (HS) and the problem Block-Encoding (BE). To construct the circuits associated with the quantum description, the problem must be mapped as a Linear Combination of Hermitian (LCH) or a Linear Combination of Unitary (LCU) matrices. All the summed Hamiltonian matrices or unitary matrices must have a known decomposition in basic gates. The complexity of this query should be incorporated into the quantum algorithm's query complexity, thereby limiting the processing possibilities of QPU for many problems. Qubitization constructs a specific query that respects single-qubit behavior when expressed in the appropriate basis. In this work, we extend the notion of qubitization to Hamiltonian matrices used to map the problem of interest. These methods concern almost all the problems implemented on QPUs: from second-quantization chemistry operators to graphs associated with Partial Differential Equations (PDE), or sparse matrices. This work underlines interesting properties associated with the qubitized Hamiltonian basic gate decomposition. It includes the ability to switch from LCH to LCU, to map non-Hermitian problems, and to construct the different quantum circuit primitives (queries) needed for the quantum description of the problem. We also provide a list of qubitized Hamiltonians that are used for the matrix decomposition of many structured matrices. These structured matrices are associated with graph adjacency matrices that can be combined to implement structured matrices.

Integrating quantum mechanics into drug discovery marks a decisive shift from empirical trial-and-error toward quantitative precision. However, the prohibitive cost of ab initio molecular dynamics has historically forced a compromise between chemical accuracy and computational scalability. This paper identifies the convergence of High-Performance Computing (HPC), Machine Learning (ML), and Quantum Computing (QC) as the definitive solution to this bottleneck. While ML foundation models, such as FeNNix-Bio1, enable quantum-accurate simulations, they remain tethered to the inherent limits of classical data generation. We detail how High-Performance Quantum Computing (HPQC), utilizing hybrid QPU-GPU architectures, will serve as the ultimate accelerator for quantum chemistry data. By leveraging Hilbert space mapping, these systems can achieve true chemical accuracy while bypassing the heuristics of classical approximations. We show how this tripartite convergence optimizes the drug discovery pipeline, spanning from initial system preparation to ML-driven, high-fidelity simulations. Finally, we position quantum-enhanced sampling as the beyond GPU frontier for modeling reactive cellular systems and pioneering next-generation materials.

Characterizing the relation between entanglement and Bell nonlocality is a long-standing open problem, notably challenging in the multipartite case. Here we investigate the effect of superactivation of genuine multipartite nonlocality. Specifically, we show that starting from multipartite states that feature only two-party entanglement (hence almost fully separable), it is possible to obtain GMNL in the many-copy regime. This represents the weakest possible resource for GMNL superactivation. On the technical side, we develop an efficient and practical criterion for certifying GMNL superactivation based on network entangled states, as well as a perfect parallel repetition result for the Khot-Vishnoi Bell game, which are of independent interest.

These lecture notes contain an introduction to quantum simulation of bosonic systems in the continuum, focusing on weakly interacting Bose-Bose mixtures with competing mean-field interactions. When the values of such interactions are fine-tuned to almost completely cancel the mean-field energy, quantum fluctuations become apparent and dominate the behavior of the system, stabilizing an ultradilute quantum liquid phase. An analogous situation appears in single-component dipolar quantum gases. We review the mechanism that gives rise to this exotic quantum liquid, which can form droplets that are self-bound in the absence of any external confinement, and discuss their properties and dynamics in both the mixture and the dipolar cases. In dipolar gases, arrays of dipolar droplets stabilized by quantum fluctuations can establish global phase coherence and form supersolids. In bosonic mixtures, supersolidity can emerge already at the mean-field level through spin-orbit coupling. We discuss the properties of such spin-orbit-coupled supersolids, comparing them to their dipolar counterparts. Specifically, we focus on their periodic density modulation, phase coherence, and peculiar excitation spectrum, which hosts both superfluid and crystal excitations. Finally, we conclude by discussing open research directions in the areas of quantum liquid droplets and spin-orbit-coupled supersolids, in particular at the interface of the two research topics.

Experimental implementations of Hamiltonian dynamics are often affected by dissipative noise arising from interactions with the environment. This raises the question of whether one can detect the presence or absence of such dissipation using only access to the observed time evolution of the system. We consider the following decision problem: given black-box access to the time-evolution channels $e^{t\mathcal{L}}$ generated by an unknown time-independent Lindbladian $\mathcal{L}$, determine whether the dynamics are purely Hamiltonian or contain dissipation of magnitude at least $ε$ in normalized Frobenius norm. We give a randomized procedure that solves this task using total evolution time $\mathcal{O}(ε^{-1})$, which is information-theoretically optimal. This guarantee holds under the assumptions that the Lindblad generator has bounded strength and its dissipative part is of constant locality with bounded degree. Our work provides a practical method for detecting dissipative noise in experimentally implemented quantum dynamics.

Structured light in the quantum regime has garnered considerable attention due to the opportunities it offers when mixing light's internal degrees of freedom, for high-dimensional and multi-dimensional quantum states of light. A popular example is to harness polarisation and spatial entangled photons with a shared topological invariant that is robust against numerous families of noisy quantum channels. Yet, producing such states with high purity and adaptability remains challenging. Here we introduce a compact, self-locking Mach-Zehnder interferometer that integrates digital spatial light modulators with static beam displacers to map spatial-mode entanglement from a parametric down-conversion source onto topological entanglement with high fidelity. The device also mimics the action of a reprogrammable controlled-unitary gate, digitally driven by the spatial light modulator. This approach is an enabling platform and provides a practical route to generating reliable, high-purity quantum-structured light with topological features, both at the single-photon level and as entangled states, a direction of growing topical interest.

TENSO is a versatile and powerful open-source software package for numerically exact simulations of the dynamics of quantum systems immersed in structured thermal environments. It is based on a tree tensor network decomposition of the hierarchical equations of motion (HEOM) that efficiently curbs its curse of dimensionality with bath complexity. As such, TENSO enables exact non-Markovian open quantum dynamics simulations even with complex environments typical of chemistry and quantum information science. TENSO allows for time-dependent drive in the system, and for non-commuting fluctuations. More generally, TENSO efficiently propagates the dynamics for any method with a generator of the dynamics that can be expressed in a sum-of-products form, including the HEOM and multi-layer multiconfigurational time-dependent Hartree methods. TENSO enables simulations using tensor trees and trains of arbitrary order, and implements three propagation strategies for the coupled master equations; two fixed-rank methods that require a constant memory footprint during the dynamics and one adaptive rank method with a variable memory footprint controlled by the target level of computational error. In contrast to the accompanying theory and algorithmic paper [J. Chem. Phys. 163, 104109 (2025)] the focus here is on the practical usage and applications of TENSO with underlying theoretical concepts introduced only as needed.

Robust laser delivery and stabilization are key components in atom-based quantum technologies, such as quantum computing. Moving these technologies towards product-like deployment requires scalable, compact, cost-effective, and upgradable modules. Here we describe laser systems consisting of application-flexible modules, and demonstrate their performance by characterizing key metrics and by integration with ion trap systems. The laser system is confined to a single server rack and a compact locking station. Both are Class 1 laser products with fiber in-out and electronic control of the laser light. This is achieved through precision manufacture of optical boards that are designed to reduce the degrees of freedom, ease alignment, and increase the robustness to environmental factors. We present a range of 13 wavelengths from 375 nm to 1092 nm: efficiencies from laser source to ion trap range from 21 - 28%, with laser stabilization line widths below 1 MHz.

We consider the Bethe ansatz integrable Russian Doll (RD) model of superconductivity with time-reversal symmetry breaking, which exhibits a cyclic renormalization group. By obtaining an exact solution for the renormalization group flows, we investigate the phase structure in the one-pair sector, which includes localized, fractal, and delocalized phases. We show that the quantum number Q, arising from the Bethe ansatz equations, counts the number of cycles and parametrizes the towers of states. Using the action of the renormalization group on the eigenstates, we demonstrate that Q serves as an order parameter, providing a new mechanism for the formation of the fractal phase in the deterministic systems and an example of the interplay between fractality and cyclic RG.

In the context of Rydberg anti-blockade, this paper proposes a new scheme for a high-fidelity controlled-unitary gate based on non-adiabatic holonomic quantum computation. Under specific detuning and interaction conditions, the scheme achieves a suitable evolution path for non-adiabatic holonomic quantum computation through reverse engineering of pulse parameters. Numerical simulations show that the geometric gate maintains high fidelity even in the presence of spontaneous radiation and laser intensity errors. Finally,we extend our designed quantum gates to non-local gates and investigate their use in converting four-qubit entangled states. This finding indicates the potential applicability of our scheme to complex quantum information processing tasks.

We explore the stability of a high-finesse optical cavity at 493 nm in vacuum for cavity QED with Barium ions. A high-finesse Fabry-Perot cavity is built using mirrors with high-reflectivity (HR) coatings that are implemented by stacking multiple thin films of low-loss dielectrics on substrates. Applications of such HR mirrors in the near ultraviolet (UV) range have been hampered by degradation of coatings in vacuum. Here, we explore the degradation of mirrors with HR coatings at 493 nm in vacuum. We study both vacuum-induced and laser-induced effects on oxide-coated cavity mirrors by probing changes in cavity loss using cavity lifetime measurements. We investigate the role of circulating power in the rate of increase in cavity loss and demonstrate methods of reversal of cavity degradation. While we observe no degradation without long exposure or with short exposures at lower circulating powers, we find evidence of degradation on long exposure to high circulating powers. We discuss potential causes and conclude that laser-induced deposition is the likely cause while ruling out thermally activated processes due to laser-induced heating.

Postselection of quantum trajectories is known effectively introduce nonlinearity into dynamics of open quantum systems. We study the effect of such non-linearity in continuous-time quantum walks (CTQWs) on networks with homogeneous and heterogeneous degree distributions. Using the recently proposed nonlinear Lindblad master equation (NLME), we investigate the dynamics under two decoherence mechanisms: Haken-Strobl and quantum stochastic walk (QSW). Our analysis reveals a striking dichotomy: under Haken-Strobl decoherence the nonlinear contributions precisely cancel, yielding a uniform steady state independent of postselection details. In stark contrast, QSW decoherence permits postselection to break dynamical balance on heterogeneous networks, inducing robust localization preferentially at low-degree (peripheral) nodes. Remarkably, this localized state maintains finite quantum coherence. Extending our results to many-body spin systems, we demonstrate that degree heterogeneity similarly stabilizes localization of spin-up excitations in spin-down backgrounds, enhancing entanglement preservation. These findings establish degree heterogeneity and postselection as joint control parameters for engineering quantum transport and localization in dissipative dynamics.

We investigate fractional revival in graphs with respect to the adjacency, Laplacian, and signless Laplacian matrices. We observe that, under certain conditions, fractional revival is preserved under graph complementation. Then we establish a connection between fractional revival in a graph and in its double cover, and obtain a complete characterization of pretty good plus state transfer in cycles and their complements. This leads to characterizations of pretty good vertex state transfer in weighted paths with potential.

Quantum-matter theory (QMT), based on the Schrödinger or Dirac equations, is firmly established for both intra- and intermolecular interactions. However, there are two key issues with QMT. First, its applicability to large molecular complexes is hindered by the relatively high computational cost of the calculations required to achieve high accuracy. Second, fields are also quantum objects that produce many intriguing effects beyond standard QMT approaches to molecular systems. This review focuses on recent developments in quantum-field theory (QFT) approaches to both covalent and non-covalent interactions for molecules in vacuum and subject to environments such as cavities and solvents. QFT provides a rich playground for novel chemical theories and insights. For example, chemical reactions and van der Waals interactions can be manipulated by cavities, boundaries, and optical excitations; novel interactions emerge when molecules interact with quantized fields; systems with millions of atoms could soon be treated with coarse-grained QFT formalisms; and unexpected scaling laws for atomic and molecular properties can emerge when QFT is applied to sets of chemical systems. This review sets the stage for an exciting QFT-driven path for further development of chemical theory.

We take quantum theory and replace $\mathbb{C}$ by $\mathbb{C}[\varepsilon]$ where $\varepsilon^2=0$, i.e. we extend quantum theory to the ring of dual complex numbers. The aim is to develop a common language in which to treat continuous quantum physics and discrete quantum models in a unified manner, including their symmetries. Since quantum theory is linear, introducing $\varepsilon$ is enough to model infinitesimals. A first objection to this programme is that $\mathbb{C}[\varepsilon]$ is not a field, since division by $\varepsilon$ is undefined, while quantum mechanics typically relies on division. A second objection concerns whether unitarity still makes sense given $\varepsilon^2 = 0$. Hence, the core of this work is dedicated to proving that \dual quantum theory remains fully consistent. In particular, norm is preserved at all times, and renormalization never requires dividing by an infinitesimal. An equivalence with conventional quantum theory is demonstrated: the \dual extension of a parametrized quantum operation automatically provides a linear treatment of its first-order variations. As a first example application, we provide a unified description of both the Dirac equation in the continuum and the Dirac Quantum Walk in the discrete. We establish the discrete Lorentz covariance of the latter.

Understanding relaxation dynamics in open quantum systems is a central problem in nonequilibrium quantum physics. Here we investigate the quantum Mpemba effect in the spin-boson model. In the weak-coupling Markovian regime we show that the occurrence of the effect strongly depends on the choice of distance measure at low temperature: while it appears in the trace distance, it can disappear in the quantum relative entropy. Going beyond the weak-coupling approximation, numerically exact simulations of the full system-bath dynamics reveal that increasing coupling enhances the effect in the trace distance and restores it in the quantum relative entropy. For all spin-bath couplings prior to delocalized-localized quantum phase transition, we uncover a simple geometric structure of the effect on the Bloch sphere: within the excited-state hemisphere, pairs of states related by rotations generically exhibit relaxation-order inversion. These results highlight the role of geometry and system-environment correlations in anomalous quantum relaxation.

The article concerns damped driven Jaynes-Cummings equation which describes quantised one-mode Maxwell field coupled to a two-level molecule. We consider a broad class of damping and pumping which are polynomial in the creation and annihilation operators, and their structures correspond to the theory of completely positive and trace preserving generators (CPTP) of Lindblad and Kossakowski & al. Our main result is the construction of global generalised solutions with values in the Hilbert space of nonnegative Hermitian Hilbert-Schmidt operators in the case of time-dependent pumping. The proofs rely on finite-dimensional approximations of the annihilation and creation operators.

Non-Hermitian physics traditionally relies on active gain--loss modulation or non-reciprocal couplings, which often introduce significant complexity, compromise stability, and offer very limited scalability in conservative systems. Here we propose an attenuation-gauge duality paradigm in which non-Hermitian topology emerges within fully passive, conservative systems through coupling to a structured reservoir. We derive that a spatially varying reservoir can establish an attenuation-gauge duality, where the spatial variation manifests as an emergent imaginary gauge field in the effective dynamics. It drives the boundary accumulation of skin modes while preserving energy conservation, analogous to Feshbach projection in quantum open systems. We validate this universal wave paradigm via macroscopic mechanical metamaterials, demonstrating that the direction of the skin effect can be reversed by tuning a single passive coupling parameter$t_\perp$, driven by a topological phase transition characterized by the spectral winding number. This framework also allows for a nonlinear extension, where amplitude-dependent coupling can induce intrinsic topological transitions.

The article addresses the damped driven Jaynes-Cummings for quantised one-mode Maxwell field coupled to a two-level molecule. We consider a broad class of damping and pumping which are polynomial in the creation and annihilation operators. Our main result is the construction of a contraction dynamical semigroup in the Hilbert space of Hermitian Hilbert-Schmidt operators in the case of a nonpositive dissipation operator and time-independent pumping. All trajectories of the semigroup are generalised solutions to the Jaynes-Cummings equations. As a key example, we prove nonpositivity for the basic dissipation operator of Quantum Optics.

We show that anyonic statistics fundamentally reshapes non-Hermitian many-body physics by intrinsically breaking pseudo-Hermiticity, leading to a unique real-complex spectral transition with characteristically dense states in Im$E$. This anyon-induced transition occurs even when bosonic and pseudofermionic counterparts remain entirely real, revealing a form of non-Hermitian criticality driven purely by exchange statistics. The resulting spectrum exhibits enhanced gaps in Im$E$ that dynamically isolate dominant eigenstates, producing anomalously stable short-time quench dynamics for anyons. Our results identify anyonic statistics as an intrinsic mechanism for generating unconventional non-Hermitian critical behavior usually associated with highly non-local systems.

We present an analytical framework for stabilizing second-order correlated tunneling of two spin-orbit-coupled bosons in a periodically driven non-Hermitian double-well potential. By combining Floquet theory with multiple-scale asymptotic analysis, we derive effective second-order dynamics and exact quasienergy spectra in the strongly interacting regime. Our analysis reveals distinct stability mechanisms for three fundamental tunneling channels: interwell spin-conserving, interwell spin-flipping, and intrawell spin-flipping. For balanced gain and loss, we identify discrete, well-defined parameter regions where stable pair tunneling emerges, with the spin-flipping channel exhibiting a characteristic symmetry absent in its spin-conserving counterpart. Under unbalanced gain-loss conditions, stability is achieved only when the gain and loss coefficients satisfy specific parametric relations, enabling dissipation-controlled tunneling. Most notably, stable intrawell spin-flipping, while inherently unstable for an initial Fock state, becomes accessible when the system is prepared in a coherent superposition state, thereby revealing that initial-state coherence can serve as a control parameter for dynamical stability in non-Hermitian systems. These results expand the possibilities for controlling correlated tunneling in many-body systems with engineered dissipation.

Boundary conditions can have dramatic impact in non-Hermitian systems, as exemplified by the non-Hermitian skin effect. Focusing on one-dimensional non-Hermitian quasiperioidic lattices, we show that the interplay of quasiperiodicity and the non-Hermitian skin effect leads to counterintuitive localization properties. On the one hand, for Anderson localized states under the periodic boundary condition, we find that their localization features can be boundary-sensitive, which originates from the incompatibility of the periodic boundary condition with quasiperiodicity. On the other hand, for non-localized states, the well-known extended-localized duality relation can break down, as their counterparts in the dual model can also be nonlocal. We discuss how these remarkable phenomena can be engineered and analyzed from the perspective of Lyapunov exponents. Our findings shed new light on localization in non-Hermitian quasiperiodic systems.

Linear response theory and Green's functions provide a universal framework for understanding how macroscopic and strongly correlated systems respond to weak external perturbations. While the theoretical foundation for non-Hermitian linear response theory has been recently established to describe open quantum systems, generalizing these predictions onto practical quantum computers remains a formidable algorithmic challenge due to the non-unitary nature of the dynamics. In this work, we present a systematic algorithmic mapping that transforms the non-unitary multi-time correlation functions into a unitary form viable for quantum hardware. By mapping the vectorization of the Lindblad master equation into a unitary Schrödinger-like equation using the continuous-variable Schrödingerization technique, we show that generalized non-Hermitian Green's functions can be systematically extracted. This approach bridges the gap between the established physical theory of non-Hermitian linear response and quantum simulation, achieving optimal state preparation cost.

Quantum emitters near the surface of silver nanoparticles undergo Rabi oscillations in electronic population dynamics due to strong coupling with near-field multipole modes that are not radiative. Low-frequency nanoparticle dipole modes are radiative but do not couple strong enough to quantum emitters. These features limit the observation of strong coupling. Using macroscopic quantum electrodynamics theory within a Lorentzian pseudo-mode approximation for the non-Markovian interaction kernel, we demonstrate that by coating spherical silver nanoparticles with a thin molecular J-aggregate layer, the resulting core-shell plexciton resonance restructures the local electromagnetic vacuum at dipole-mode frequencies to enable Rabi oscillations for quantum emitters that otherwise would only undergo exponential population decay. Specifically, we show for quantum dot emitters in the near field of silver nanospheres of 20 nm radius, that weak-to-strong coupling crossovers can be induced using 2 nm J-aggregate shells. Our work demonstrates the potential of molecular aggregates to enable deep sub-wavelength structuring of the vacuum field for the observation of coherent quantum dynamics in optical nanocavities.

The NOON states play a critical role as physical resources in quantum information processing and quantum metrology, yet their preparation efficiency and applicability are often constrained by complicated operational procedures or the requirement for nonlinear interactions. In this paper, we propose an efficient protocol to generate the NOON states within two microwave cavities embedded in a superconducting system, assisted by an auxiliary five-level qudit. The state preparation is accomplished in three steps for an arbitrary photon number $N$ by adjusting only external classical fields, while keeping the qudit-cavity coupling strengths and the qudit level spacings fixed. Based on parameters accessible in superconducting systems, numerical simulations show that the protocol achieves relatively high fidelity for the NOON states preparation even in the presence of parameter fluctuations and decoherence effects. Thus, this protocol may provide a practical approach for preparing the NOON states with current technology. Notably, since nonlinear interactions are not required, the protocol is flexible and has the potential to be applied across various physical systems.

We investigate the effect of nonrelativistic motion on the emission dynamics of a dipole emitter moving next to a reflecting interface. Within the formalism of macroscopic QED, we obtain a general equation of motion for the dipole amplitude in terms of the dyadic Green's function, yielding a dynamical extension of the Drexhage effect. At short dipole-surface distances, the dipole can be described as a parametric oscillator featuring time-dependent dampings and Lamb shifts, both arising from the self-induced modulation of the surrounding electromagnetic environment. Importantly, these time-dependent parameters do not always average out, leading to amplification of the dipole amplitude and the radiated intensity when considering certain sinusoidal trajectories with specific modulation amplitudes and frequencies. We derive threshold modulation amplitudes as function of the relative permittivities at the interface. Qualitatively, in the vicinity of certain epsilon-near-zero materials, amplification is possible purely by modulation of the damping. Our findings open up avenues for the dynamic control of light-matter interaction in nanophotonic environments.

We present a new p-adic version of the Jackiw-Rebbi model. In the new model, the real numeric line is replaced by a p-adic line (the field of p-adic numbers Q_{p}), and the Dirac Hamiltonian is replaced by a non-local operator acting on complex-valued functions defined on Q_{p}. These Hamiltonians admit localized wavefunctions and allow long-range interactions, so spooky action at a distance is allowed. These features are not present in the original model. The new model gives the same predictions as the standard one. The p-adic line serves as a discrete model for the physical space; in this type of space, non-locality emerges naturally.

Two-level systems (TLS) in native Nb and Ta oxides limit superconducting-qubit coherence and SRF-cavity quality factors in the microwave frequency range, yet their microscopic origin remains unclear. We combine MLIP-accelerated sampling of hydrogen configurations and diffusion pathways in amorphous Nb and Ta pentoxides with targeted $\textit{ab initio}$ validation. Hydrogen is the only light interstitial with barrier-distance combinations near the $\sim0.1-10$ GHz tunneling regime, and its ensemble statistics in amorphous oxides produce effective TLS densities and loss estimates consistent with the experimentally observed higher loss in Nb oxide than in Ta oxide. Our results point to H tunneling as a plausible microscopic TLS source in these materials.

We use a Quantum Extreme Learning Machine for characterizing and estimating parameters of quantum dynamics generated by a tunable collision model. The input to the learning protocol consists of quantum states produced by successive system environment interactions, while the reservoir is implemented as a disordered many body quantum system evolving under a fixed Hamiltonian. We systematically explore how extending the QELM feature space, through the inclusion of temporal information and additional observables, affects estimation performance. Our results demonstrate that temporal extensions of the feature vector consistently and significantly enhance estimation accuracy relative to the baseline protocol. Notably, incorporating memory from earlier time steps yields the most substantial and robust improvements, whereas extensions based solely on additional observables offer only marginal gains. Crucially, the advantage conferred by temporal memory becomes increasingly pronounced as the dynamics become more strongly non Markovian, indicating that environmental memory effects serve as a constructive resource for learning.

We present a general protocol for estimating $M$ observables from only $\mathcal{O}(\log (M)/\varepsilon^2)$ copies of a Gibbs state whose Hamiltonian is accessible. The protocol uses single-copy, nonadaptive measurements and uses a total Hamiltonian simulation time of $\widetilde{\mathcal{O}}(βM/\varepsilon^2)$; we show that the sample complexity is optimal in a black-box setting where exponential time Hamiltonian simulation is prohibited. The key idea is a new interpretation of quantum Gibbs samplers as \textit{detailed-balance measurement channels}: measurements that preserve the Gibbs state when outcomes are marginalized. Consequently, shadow tomography of thermal states admits a general efficient algorithm when the Hamiltonian is known, substantially lowering the readout cost in quantum thermal simulation.

We analytically investigate a quantum estimation method for a mechanical oscillator in a detuned cavity system based solely on homodyne measurement records, building on the framework developed by C.Meng et al. (Science Advances 8, 7585 (2022)). Estimation based only on measurement records is important because it enables state verification without assuming knowledge of the true system state. We construct a relative estimate operator from causal and anti-causal quantum Wiener filters and calculate its variance. The deviation from the causal conditional variance is defined as a reconstruction bias, whose magnitude is evaluated analytically. We show that, within experimentally relevant parameter regimes for typical quantum-state preparation, the reconstruction bias is sufficiently small to be neglected. As applications to state verification, we apply the method to proposals for macroscopic quantum entanglement mediated by electromagnetic interactions and for conditional momentum-squeezed states generated by homodyne detection, and clarify the conditions under which the bias remains negligible and when the reconstruction bias becomes significant.

We present implementations of the topological K-theory spectra $KU$ and $KO$ in terms of time evolution operators of irreducible free fermion systems with symmetries, with explicit formulas for the structural suspension maps. We also introduce a geometric definition of weakly interacting time evolution operators, and show how associated spectra $KU^{wi}$ and $KO^{wi}$ deformation retract to $KU$ and $KO$. We thus have a stable homotopy theoretical proof that the tenfold way is stable to weak interactions.

Any quantum state of the radiation field, sliced in small non-overlapping space-time bins is a collection of single-rail qubits, each spanning the vacuum and single-photon Fock state of a mode. Quantum logic on these qubits would enable arbitrary measurements on information-bearing light, but is hard due to the lack of strong nonlinearities. With unentangled ancilla single-rail qubits, an $8$-port interferometer and photon detection, we show any single-rail qubit measurement in the $XY$ Bloch plane is realizable with success probability $147/256$, which beats the prior-known $1/2$ limit.

Quantum signal processing (QSP), originally developed for composite pulse sequences in nuclear magnetic resonance systems, has recently attracted attention as a unified framework for quantum algorithms. A pioneering study applied QSP to nonequilibrium control in integrable many-body systems, enabling the realization of nonequilibrium dynamics with greater flexibility than Floquet engineering. However, extending QSP to nonintegrable systems faces fundamental obstacles arising from the limited number of conserved quantities and thermalization. In this work, we propose a protocol that leverages QSP in systems exhibiting Hilbert space fragmentation (HSF). Specifically, we consider a pair-hopping model with four-fold periodic potentials that exhibits an HSF structure, thereby providing integrable and nonintegrable sectors within a single system. We analytically show that nonequilibrium dynamics can be flexibly designed through QSP engineered by these potentials in the integrable sectors. In contrast, we numerically identify signatures of thermalization in the nonintegrable sectors. Remarkably, by inserting domain walls, we achieve parallel control of multiple quantum dynamics within a single system. This approach sheds light on the control of nonequilibrium dynamics from the perspective of quantum computation by extending the scope of QSP to nonintegrable systems.

Zero modes, understood here as degrees of freedom with vanishing confining frequency, play a central role in the nonequilibrium dynamics of bosonic systems. In Gaussian models, however, they lead to an unbounded, logarithmic growth of entanglement entropy. We show that this divergence is not an intrinsic property of zero modes themselves, but arises specifically for non-compact zero modes. Their non-compact configuration space allows unbounded spreading in position space, while their continuous spectra enable indefinite dephasing in momentum space. By contrast, compact zero modes in compact bosonic systems behave fundamentally differently: Spreading and dephasing are eventually halted, so that compactness caps the entanglement entropy at a finite value, making its dynamical role most transparent in the presence of a zero mode. We demonstrate this mechanism in a minimal setting by comparing two coupled harmonic oscillators with two coupled quantum rotors. We then show that the same physics persists in many-body systems by contrasting an N-site compact rotor chain with the non-compact harmonic chain. Finally, we relate these insights to ultra-cold-atom realizations of compact quantum field theories. In particular, we clarify when a compact free-boson (Tomonaga-Luttinger liquid) description is required and when the commonly used non-compact massless Klein-Gordon model breaks down. Even when the initial state is accurately captured by a non-compact Gaussian description, compactness ultimately governs the late-time quench dynamics, curbing entanglement growth rather than allowing a dynamical divergence.

In a recent paper arXiv:2205.06279, Danielson et al. demonstrated that the mere presence of a black hole causes universal decoherence of quantum superpositions (dubbed the DSW decoherence). This result has profound implications for the interplay of quantum mechanics and gravity. We analyze decoherence in a superconducting analogue arXiv:1709.06154 of the event horizon of a black hole, where Andreev reflection plays the role of Hawking radiation. We consider a normal metal interferometer threaded by an Aharonov-Bohm flux, where one of the arms of the interferometer is coupled to a superconductor by a tunnel coupling of varying strength. At absolute zero and for weak coupling, we find that the scattering states of the interferometer are decohered by Andreev reflection, a nontrivial manifestation of the proximity effect analogous to DSW decoherence from the event horizon of a black hole. However, for increasing coupling strength to the superconductor, we find a reemergence of coherence via resonant tunneling through Andreev bound states. This suggests the existence of an analogue gravitational phenomenon wherein transmission mediated by virtual Hawking radiation leads to a reemergence of coherence in an interferometer placed within a few Compton wavelengths of a black hole's event horizon. Our results open a new path to study black hole quantum physics on earth via analogue studies.

Quantum digital signatures (QDS) offer information-theoretic security for message integrity, authenticity, and non-repudiation, and constitute a fundamental cryptographic primitive for future quantum networks. Despite significant progress, the practical deployment of QDS has been severely constrained by limited signature rates and poor tolerance to channel loss, particularly in long-distance and metropolitan-scale networks. Here, we report a high-rate, loss-resilient QDS system that overcomes these two key bottlenecks simultaneously. Our implementation combines intrinsically phase-stable polarization modulation based on a Sagnac interferometer with gigahertz-rate quantum state encoding and low-timing-jitter superconducting nanowire single-photon detectors, enabling robust and continuous operation at high repetition frequencies. By integrating this hardware platform with a one-time universal hashing-based QDS protocol, we achieve a signature rate improvement of more than two orders of magnitude compared with existing QDS implementations under comparable channel-loss conditions. Notably, the system maintains a non-zero effective signature rate of approximately 1.25 times per second at a total channel loss of up to 49.05 dB, representing the highest loss tolerance reported for QDS to date. These results establish a practical and scalable technological pathway for deploying QDS in real-world quantum communication networks.

Fermionic Gaussian states are a fundamental tool in many-body physics, faithfully representing non-interacting quantum systems and allowing for efficient numerical simulations. Given a many-body wave function, it is therefore interesting to ask how much it differs from that of a Gaussian state, as quantified by the notion of non-Gaussianity. In this work, we relate measures of non-Gaussianity with the Shannon entropy of the particle-number distribution, coinciding with the particle-number asymmetry for pure states. We derive a lower bound on the relative entropy of non-Gaussianity in terms of the exponential of the Shannon entropy, and study numerically its tightness for large system sizes. Our bound is non-trivial for large values of the asymmetry and relies on the concentration of the particle-number distribution of (mixed) fermionic Gaussian states. Since the Shannon entropy of the particle-number distribution is often efficient to compute or experimentally measure, our results can be viewed as a practical way to lower bound non-Gaussianity, highlighting a non-trivial interplay with particle-number asymmetry.

We obtain two new additivity results of quantum channels. The first one is the additivity of the channel Rényi information associated with the sandwiched Rényi divergence of order $α\in[\frac{1}{2},1)$. To prove this, we introduce the completely bounded $1\toα$ quasi-norms for completely positive maps, with $α\in[\frac{1}{2},1)$, and show that it is multiplicative. The additivity/multiplicativity derived here extends and complements the results of Devetak {\it et al} (Commun Math Phys 266:37-63, 2006) and Gupta and Wilde (Commun Math Phys 334:867-887, 2015), which deal with the case $α>1$. The second one is the additivity of the channel dispersion, which is a quantity related to the second-order behavior of quantum information tasks.

The Kibble-Zurek mechanism provides a universal framework for predicting defect formation in non-equilibrium phase transitions. While Markovian dissipation typically degrades universal scaling, the impact of non-Markovian memory remains largely unexplored. We demonstrate that an Ohmic bath induces a Berezinskii-Kosterlitz-Thouless transition in the open quantum Rabi model. Using simulations based on Matrix Product States, we show that the excitation energy strictly follows universal Kibble-Zurek power-law scaling when evaluated at the freeze-out time. Crucially, we find that since the environment defines the universality class, dissipation does not inherently compete with adiabatic dynamics, in stark contrast to Markovian regimes. Our results establish the Kibble- Zurek mechanism as a robust witness of universality in open quantum systems, revealing that non-Markovian memory preserves the integrity of non-equilibrium scaling.

Fast and high-fidelity qubit readout requires strong coupling between the readout resonator and the feedline. However, such coupling unavoidably enhances qubit decay through the Purcell effect. We present a four-pole broadband Purcell filter implemented on a 3D flip-chip platform to overcome this trade-off. The filter provides a flat 1 GHz passband centered at 7.68 GHz and achieves more than 45 dB suppression at typical qubit frequencies. We demonstrate the filter's compatibility with multiplexed readout using a test chip that integrates six floating readout resonators strongly coupled within the passband. The chip is fabricated using a 150 nm Niobium (Nb) thin-film process and characterized at 20 mK in a cryogenic measurement setup. We also develop an analytical model that accurately captures the filter response and determines the resonance frequencies and external quality factors of the floating resonators directly from their physical geometry, enabling rapid circuit synthesis and design optimization. The proposed design is compact and fabrication-tolerant, making it a practical solution for large-scale superconducting quantum processors.

As spin-based quantum systems scale, their setup and control complexity increase sharply. In semiconductor quantum dot (QD) experiments, device-to-device variability, heterogeneous control-electronics stacks, and differing operational modalities make it difficult to reuse characterization, calibration, and control logic across laboratories. We present FAlCon, an open-source software ecosystem for portable, automated characterization and tuning measurement workflows. FAlCon provides (i) a lightweight domain-specific language for expressing state-based tuning logic in a hardware-agnostic form; (ii) specialized transmittable libraries of physics-informed QD data structures (``tuning vernacula''); and (iii) extensible libraries of shared measurement protocols enabling an interoperable lab-agnostic measurement stack. By separating algorithm intent from instrument realization, while preserving traceability and supporting typed scripting, FAlCon enables researchers and engineers to exchange, adapt, and deploy characterization and autotuning routines across heterogeneous QD setups. The framework supports all users, ranging from end users running prebuilt algorithms with custom initial conditions to developers extending instrumentation support and contributing new tuning strategies. Although the present release targets QD experiments, other qubit modalities and scientific experiments could reuse FAlCon's modular abstractions by providing new tuning data types and instrument control templates.

We present a quantum dynamical study of pulsed few-photon scattering from a single artificial atom, consisting of a two-level system (TLS) or qubit, in a waveguide QED system, directly comparing and contrasting two different quantum theoretical simulation methods: (i) an input-output scattering approach that uses frequency-dependent scattering matrices, and (ii) a matrix product states (MPS) approach, which uses quantum noise operators in time bins and a tensor network technique to solve the time-dependent waveguide function for the entire system. Beginning with pulsed excitation using one-photon and two-photon Fock state pulses, we first show how to compute time-dependent observables with the scattering matrix approach, in terms of frequency integrals that encode the pulse spectrum, including how to extract the population dynamics of the excited quantum emitter, as well as the linear and nonlinear contributions. We present solutions for both symmetric and chiral TLS coupling. We then show how to compute the qubit and field observables in a more direct way using MPS, and obtain the characteristic bird-like shape for the two-photon correlation function at two times, which has been observed in recent experiments. We compare and contrast both of these methods, for one and two-photon excitation pulses, and show excellent agreement. We also present a study of the linear and nonlinear contributions, which can easily be calculated using scattering theory, and show the important role of pulse duration. Finally, we demonstrate the clear advantages of MPS by easily going to higher N-photon excitations, and show selected example population dynamics of up to eight-photon Fock-state pulses, manifesting in clear nonlinear population oscillations during the pulse interaction, similar to classical Rabi oscillations, but with quantum input fields that have a vanishing electric field expectation value.

Quantum state preparation is a central primitive in many quantum algorithms, yet it is generally resource intensive, with efficient constructions known only for structured families of states. This work introduces a method for preparing quantum states whose amplitudes are given by a degree$-d$ polynomial, using circuits with logarithmic depth in the number $n$ of qubits and only $\mathcal O(n)$ ancilla qubits, improving previous approaches that required linear-depth circuits. The construction first relies on a block-encoding of an affine diagonal operator based on its Pauli-basis decomposition, which involves only $n$ terms. A modified linear-combination-of-unitaries (LCU) technique is introduced to implement this decomposition in logarithmic depth, together with a novel circuit for the EXACT-one oracle that flags basis states in which exactly one qubit is in the state $|1\rangle$. It then uses a generalized quantum eigenvalue transformation (GQET) to promote this affine operator to an arbitrary degree polynomial. Theoretical analysis and numerical simulations are reported along with a proof-of-principle implementation on a trapped-ion quantum processor using $14$ qubits and more than $500$ primitive quantum gates. Because polynomial approximations are ubiquitous in scientific computing, this construction provides a scalable and resource-efficient approach to quantum state preparation, further improving the potential of quantum algorithms in fields such as chemistry, physics, engineering, and finance.

We present a novel scheme to detect itinerant microwave radiation at the single photon level. Using existing Josephson-photonics devices, where two microwave cavities are coupled by a dc-voltage biased superconducting junction, we theoretically show how to implement a stroboscopically repeated, near-projective measurement of a photon impinging on one of the cavities. Optimizing rate, duration, and strength of the measurement by flux control of the junction and developing a threshold protocol to detect the photon from a homodyne measurement of the radiation output of the other cavity, we achieve highly efficient detection with low dark counts. By cascading the detector with a preamplifier, where a similar two-cavity Josephson-photonics device acts as a photon multiplier, we can further improve the device to reach a detection efficiency of $88.5 \%$ with a dark count rate of $\sim10^{-4} γ_a$, set by the resonance width $γ_a$ of the absorbing cavity. These results for a multiplication factor of two suggest that near-unity efficiencies may be reached for higher multiplication factors.

We investigate the role of the global driving phase $Φ$ in the dynamics of driven few-level quantum systems, a central setting in coherent control of atomic, molecular, and solid-state platforms. In particular, we focus on systems with closed-loop couplings, where external driving fields induce interference effects that strongly influence population transfer and symmetry properties of time-evolution. While full time-reversal symmetry requires $Φ=0,π$, leading to a real Hamiltonian, we focus on a less restrictive transformation, the phase inversion (or complex conjugation of the Hamiltonian), under which population dynamics can remain symmetric even though coherences generally do not. We show that the presence of a dark (spectator) state is a sufficient condition for this population phase symmetry (P$Φ$S), as it constrains the dynamics to reduced subspaces characterized by SU(2) or open-loop SU(3) evolution. We analyze this mechanism in three- and four-level systems and derive general conditions for P$Φ$S that extend to generic $n$-level configurations, with $n$ even. These findings provide practical guidelines for achieving robust control in quantum systems, with potential applications in quantum information processing and quantum computing.

Quantum annealing with the D-Wave Advantage system in the random Ising model on a cubic lattice is simulated using a three-dimensional (3D) tensor network. The Hamiltonian is driven across a quantum phase transition from a paramagnetic phase to a spin-glass phase. The network is represented as a tensor product state, also known-particularly in two dimensions-as a projected entangled-pair state (PEPS). The annealing procedure is repeated for a range of annealing times in order to test the Kibble-Zurek (KZ) power law governing the residual energy at the end of the annealing ramp. For an infinite lattice with periodic nearest-neighbor random Ising couplings, the final energy is evaluated using a deterministic method. For a finite lattice with open boundaries, we introduce a more efficient Monte Carlo sampling approach. In both cases, the residual energy as a function of annealing time approaches the KZ power law as the annealing time increases.

Quantum computing is a rapidly developing field. However, the most commonly used qubits require cryogenic conditions to operate, which increases the costs and puts constraints on the up-scaling. Ambient solid-state qubits provide an alternative with potential for large-scale application. The nitrogen-vacancy (NV) center in diamond is one of the main candidates for solid-state computing architectures at room temperature and has proven to be competitive in terms of gate fidelity, quantum error correction, couplings, etc. Each NV center has an associated electronic spin that is conventionally read out by photoluminescence. However, regarding the creation of small, ambient NV-based quantum processors, the optical readout introduces limitations on the collection efficiency and resolution of the readout as well as the size of the final device and its integration into standard semiconductor architectures. In this work, we investigate the competitiveness of the photoelectric readout versus the traditional optical readout. In particular, we report on using photoelectrical detection to perform quantum state tomography measurements on a single NV center. We achieve the fidelity $0.995 \pm 0.0062$ for state reconstruction, comparable to optical measurements, demonstrating that the fidelity does not suffer from the adapted readout, highlighting the value of photoelectric detection for NV-based quantum processors.

We propose a system to achieve sub-zeptonewton force sensing and robust spin-mechanical entanglement in a levitated diamond system. By coupling a Nitrogen-Vacancy (NV) center spin to the motion of its host diamond within a magnetic trap, we develop a platform designed to surpass the standard quantum limit. We develop and compare three distinct pulse sequences--Ramsey, Hahn echo, and Carr-Purcell-Meiboom-Gill (CPMG)--to create increasing amounts of backaction evasion while mitigating the effects of shot noise and thermal decoherence. Our results show that the CPMG sequences yield the most significant performance gains, reaching a force sensitivity of better than $10^{-23} \text{ N}/\sqrt{\text{Hz}}$ for broadband sensing around $10^4 \text{ Hz}$. Furthermore, we derive an entanglement witness protocol that accounts for pulsed dynamical decoupling, proving that spin-motion entanglement remains detectable even when occurring much faster than the mechanical period. These findings provide a more practical path for using levitated nanodiamonds both as high-precision sensors and as non-classical mechanical systems for fundamental tests of quantum mechanics.

This study demonstrates a significant enhancement in ultra-low-frequency (ULF) electric field sensitivity using Rydberg atoms via an optical chopping amplification (OCA) technique. Conventional Rydberg-based ULF measurements are fundamentally limited by 1/f noise, which severely degrades sensitivity. Our approach modulates the coupling laser with an optical chopper before the vapor cell, inducing periodic Rydberg excitation at the chopping frequency. The photodetector (PD) output signal is demodulated by a lock-in amplifier (LIA) using the optical chopper's signal as the reference. This process effectively improves the signal-to-noise ratio (SNR) by shifting the 1/f noise to a higher frequency band where it can be filtered out. The OCA technique enhanced sensitivity by 19.1 dB for the frequency 7 Hz, which is down to 49.1 uV/cm/rt(Hz). For the frequency range from 10Hz to 1kHz, it also enhanced nearly 7dB. This OCA method for enhancing the sensitivity of Rydberg atoms in ULF electric field measurements enables the Rydberg sensor's detection range to span the entire spectrum from low frequency (LF) to ULF, thereby significantly broadening its application potential.

We derive the quantum Fisher information for entropy estimation in a Gibbs state and show that $F_s = 1/C_v$, dual to the temperature Fisher information $F_S = C_v/T^2$. Their product $F_S\cdot F_T = 1/T^2$ is independent of the Hamiltonian, yielding the universal uncertainty relation $Δ^2 S\,Δ^2 T \geq T^2/n^2$ in which all system-specific quantities such as heat capacity, the Hamiltonian, and the number of degrees of freedom cancel identically. This is the metrological expression of the Legendre conjugacy between $S$ and $T$. We identify energy measurement as the optimal protocol for entropy estimation, analyse critical-point scaling where $F_S \sim |t|^α\to 0$, and connect $F_S$ to the Ruppeiner metric in entropy coordinates. The uncertainty relation is shown to hold for all standard thermodynamic conjugate pairs, and we examine the distinguished role of the von~Neumann entropy within the Rényi family. Generalisations to the grand canonical and generalised Gibbs ensembles are given.

Surface roughness is an important quantity to many engineering and precision manufacturing disciplines. In this paper we investigate the problem of estimating the root-mean-square roughness of a sample by passive linear optical methods. By adopting quantum parameter estimation techniques, we determine the ultimate precision limits on roughness estimation. In particular, we show that the information on the first moment (mean height) and standard deviation (roughness) of the axial profile distribution of multiple incoherent point sources is bounded by a constant. While classical imaging techniques fail to achieve this bound, a quantum inspired imaging technique based on spatial mode demultiplexing is proven to be optimal for estimating the axial standard deviation. Combined with analogous recently investigated methods for estimating radial profiles, this can provide a powerful technique for measuring roughness of nearly smooth surface patches beyond the diffraction limit.

In classical dynamical systems, chaotic behavior is often associated with exponential sensitivity to initial conditions together with global phase-space structure. Translating this geometric concept to the strictly linear framework of quantum mechanics presents a conceptual puzzle. The out-of-time-ordered correlator (OTOC) is often motivated as the quantum analogue of the classical butterfly effect, but this slogan can hide important mathematical distinctions. This tutorial bridges the gap between applied mathematics and quantum information by detailing the mathematical machinery of the OTOC. We explore how classical sensitivity translates to operator non-commutativity, why standard two-point correlation functions fail to cleanly detect this sensitivity, and how the delocalization of quantum observables relates to classical notions of mixing. Crucially, we outline what the OTOC can and cannot diagnose, distinguishing between local instability and global chaos. Ultimately, we provide a precise and usable conceptual map, exploring how the Koopman-von Neumann formalism offers a framework to view classical and quantum dynamics through a shared linear perspective.

Attributing performance gains in quantum machine learning to genuine quantum resources rather than to classical architectural scaling remains an open methodological challenge. We address this by introducing a counterfactual causal mediation framework that decomposes inter-architectural performance differences into direct effects, attributable to circuit parameterization and expressivity, and indirect effects mediated by quantum information-theoretic observables: entanglement entropy, purity, linear entropy, and quantum mutual information. Applying this framework to five circuit topologies and three benchmark datasets (across 43 validated configurations) reveals that direct architectural contributions systematically exceed quantum-mediated effects, with a mean ratio of 13.1:1 and a mean indirect contribution of 0.82%. These results suggest that current variational quantum circuits operate substantially below their quantum potential, and that principled resource-aware circuit design represents a tractable path toward measurable quantum-mediated performance gains.

A degenerate string is a sequence of sets of characters. A generalized degenerate (GD) string extends this notion to the sequence of sets of strings, where strings of the same set are of equal length. Finding an exact match for a pattern string inside a GD string can be done in $O(mn+N)$ time (Ascone et al., WABI 2024), where $m$ is the pattern length, $n$ is the number of strings and $N$ the total length of strings constituting the GD string. We modify this algorithm to work under a quantum model of computation, achieving running time $\tilde{O}(\sqrt{mnN})$.

Cavity optomechanics has enabled slow-to-fast light conversion, but traditional optomechanic systems suffer from limited tunability due to fixed mechanical frequencies. To address this constraint, we introduce a magnon degree of freedom into an optomechanical system, constructing a system that integrates photons, phonons, and magnons. We establish the theoretical model of the optomagnonic-Laguerre-Gaussian rotational system, and present numerical simulations of Fano resonances and group delay. By manipulating the magnon degree of freedom, we not only achieve slow-to-fast light conversion associated with magnons but also successfully realize such conversion effects associated with mechanical rotation-this achievement effectively overcomes the inherent tunability limitations of pure optomechanical systems and expands the frequency coverage of light conversion effects. Notably, we numerically demonstrate bidirectional light speed conversion (slow-to-fast and fast-to-slow) via continuous control field frequency modulation to tune cavity mode detuning. Additionally, our results show that adjusting optomagnonic parameters enables dynamic switching between slow light and fast light at multiple frequencies. This work provides a flexible platform for multi-frequency light speed control, with potential applications in all-optical networks and quantum communications.

We directly observe far-field correlations of x-ray photon pairs generated by spontaneous parametric down-conversion (SPDC). Using an energy-resolved, two-dimensional photon counting detector we record the full ring-shaped emission of both photons across a broad bandwidth and extract pair correlations directly from raw events without imposing angular constraints. The ring radii scale with photon energy, in quantitative agreement with transverse phase matching, providing a stringent momentum-space validation of x-ray SPDC. These observations open a route to leveraging quantum correlations in x-ray imaging and metrology, including correlation-enhanced magnification and reduced blurring.

We investigate the equilibrium properties of a quantum Brownian particle moving in a periodic potential, specifically addressing the nature of the dissipation-driven Schmid transition in the Ohmic regime. By employing World-Line Monte Carlo in the path-integral formalism and introducing a specific binary order parameter, we demonstrate that the transition belongs to the Berezinskii-Kosterlitz-Thouless universality class. This classification is substantiated through finite-size scaling analysis that reveals the characteristic logarithmic decay of the correlation functions associated with the order parameter at the critical point. Quantum phase transition turns out to be extremely fragile: it disappears in both over- and sub-Ohmic dissipation regimes. Crucially, we find that the presence of the periodic potential does not alter the localization properties in the sub-Ohmic and super-Ohmic regimes, where the system exhibits the same qualitative behavior as the free quantum Brownian particle. These findings highlight that the emergence of critical behavior is strictly governed by the low-frequency form of the environmental spectral function, which determines the long-range temporal decay of the dissipative kernel.

We analyze qubit-qubit entanglement from an energetic perspective and reveal an energetic trade-off between quantum coherence and entanglement. We decompose each qubit internal energy into a coherent and an incoherent component. The qubits' coherent energies are maximal if the qubit-qubit state is pure and separable. They decrease as qubit-qubit entanglement builds up under locally-energy-preserving processes. This yields a "coherent energy deficit" that we show is equal to a well-known measure of entanglement, the square negativity. In general, a qubit-qubit state can always be represented as a mixture of pure states. Then, the coherent energy deficit splits into a quantum component, corresponding to the average square negativity of the pure states, and a classical one reflecting the mixedness of the joint state. Minimizing the quantum deficit over the possible pure state decompositions yields the square negativity of the mixture. Our findings bring out new figures of merit to optimize and secure entanglement generation and distribution under energetic constraints.

Non-Hermitian many-body systems can be spectrally unstable, so small perturbations may induce large eigenvalue shifts. The pseudospectrum quantifies this instability and provides a perturbation-robust diagnostic. For inverse-polynomially small $ε$, we show that deciding whether a point $z\in\mathbb{C}$ is $ε$-close to the spectrum is PSPACE-hard for $5$-local operators, whereas deciding whether $z$ lies in the $ε$-pseudospectrum is QMA-complete for $4$-local operators. This identifies pseudospectrum membership as a natural computational target. We then present a concrete end-to-end quantum framework for deciding pseudospectrum membership, which combines a singular-value estimation step with a dissipative state preparation algorithm. Our Quantum Singular-value Gaussian-filtered Search (QSIGS) combines quantum singular value transformation (QSVT) with classical post-processing to achieve Heisenberg-limited query scaling for singular-value estimation. To prepare suitable input states, we introduce an algorithmic Lindbladian protocol for approximate ground right singular vectors and prove its effectiveness for the Hatano--Nelson model. Finally, we demonstrate the full pipeline on a trapped-ion quantum computer and distinguish points inside and outside the target pseudospectrum near the exceptional point of a minimal non-Hermitian qubit model.

Efimov effects arise from scale invariance, a fundamental symmetry with universal implications. While spatial Efimov physics has been extensively studied, realizing its temporal counterpart remains challenging, as it requires a dynamical system that breaks time-translation symmetry yet preserves the essential time-scaling symmetry. Analog cosmology offers a powerful platform to address this challenge, bridging the domains of Efimov physics and cosmology. Here, we predict a temporal Efimov effect in an analog linearly expanding universe realized with a quasi-two-dimensional Bose-Einstein condensate. The invariance of phonon mode equations under time rescaling leads to particle production with two distinct dynamics: power-law growth and log-periodic oscillations, with the latter being the hallmark signature of the Efimov effect. Furthermore, these dynamics map directly onto sub- and super-horizon cosmological modes. Our predictions can be directly verified through time-averaged measurements of the density-fluctuation spectrum $S_{k}(t)$ in current experiments.

We theoretically propose a scheme to realize a $n$-cavity-magnon polariton blockade in a cavity-magnon system by utilizing the Kerr nonlinearity. Cavity-magnon polaritons are hybrid quasiparticles formed by the strong coupling between cavity photons and magnons. The Kerr nonlinearity introduces anharmonicity into the polariton energy spectrum, which in turn enables the blockade effect. We demonstrate that when the external driving frequency is resonant with the transition to the $n$th polariton excited state, a perfect $n$-polariton blockade is achieved. Moreover, increasing the driving strength enhances higher-order blockade while maintaining high purity. Our work pioneers the field of cavity-magnon polariton blockade, opens a new avenue for the preparation of controllable quantum resources and holds significant potential for applications in the fields of quantum communication and quantum information processing.

We have investigated the geometric phase acquired by a uniformly accelerated two-level atom coupled to vacuum fluctuations of a massless conformal scalar field in Anti-de Sitter (AdS) spacetime. Using the open-quantum-system formalism, we calculate the phase under three boundary conditions (Dirichlet, transparent and Neumann) imposed on the field at the AdS boundary. Our findings reveal a sharp distinction between subcritical and supercritical accelerations. For subcritical accelerations, the atom evolves effectively as an isolated system, and the geometric phase is independent of both the AdS radius and the acceleration. For supercritical accelerations, however, topology-acceleration-induced phase corrections emerge and display pronounced boundary-condition dependence. When the AdS radius is smaller than the atomic proper wavelength, the magnitude of the correction at large accelerations follows the ordering Neumann$>$transparent$>$Dirichlet. Moreover, over a finite interval of the atomic weight parameter, both Dirichlet and Neumann boundary conditions produce a richer peak structure in the phase correction than the transparent case, with the detailed pattern governed by the competition between the acceleration and the atomic energy gap. Finally, for transparent boundary conditions in the supercritical regime, the AdS phase correction closely resembles its de Sitter (dS) counterpart.

We present a theoretical framework that reinterprets Population Annealing (PA) through the lens of the discrete-time Schrödinger Bridge (SB) problem. We demonstrate that the heuristic reweighting step in PA is derived by analytically solving the Schrödinger system without iterative computation via instantaneous projection. In addition, we identify the thermodynamic work as the optimal control potential that solves the global variational problem on path space. This perspective unifies non-equilibrium thermodynamics with the geometric framework of optimal transport, interpreting the Jarzynski equality as a consistency condition within the Donsker-Varadhan variational principle, and elucidates the thermodynamic optimality of PA.

Qudits, the multi-level generalization of qubits, provide a natural extension of the binary paradigm in quantum computation and offer new opportunities to enhance algorithmic performance. Beyond their direct applicability to the simulation of multi-level quantum systems, higher-dimensional ancillae can improve sampling efficiency in quantum algorithms by enabling the simultaneous implementation of multiple control operations, thereby reducing circuit complexity. In this work, we pursue three main objectives. First, we present a formulation of the Rodeo algorithm employing a general $d$-level ancilla qudit. Second, we introduce the concept of the \emph{Rodeo kernel}, defined as a two-frequency interferometer, which acts as a spectral filter in the energy domain. Finally, we propose a microcanonical protocol for the Rodeo algorithm. This protocol enables the estimation of entropic quantities through a single energy sweep and admits a natural interpretation as a Gaussian convolution of the density of states. To support the theoretical analysis, we perform numerical evaluations of the corresponding quantum circuit using ancilla qudits of dimensions three, four, and five. The simulations are performed for the one-dimensional Ising model, considering both spin-$\frac{1}{2}$ and spin-$1$ particles. The ancilla qutrit implementation exhibits an $18\%$ reduction in fluctuations compared to the qubit implementation. Our results show that the qudits provide a framework for spectral analysis and thermodynamic characterization of multi-level quantum systems.

This technical note provides a high-level overview of the present state of basic field electron emission (FE) theory, as suitable for use in the context of technological applications of FE theory. At present there is much theoretical confusion in FE literature, and a partial breakdown of the peer review system. Even in sensitive technological contexts, many papers have stated and used out-of-date theory that makes current-density predictions that are several hundred times less than those of modern FE theory. A primary aim of this note is to help reduce the confusion and error in future published FE literature. It is not intended as a detailed review of FE theory.

We develop a perfectly distributable quantum-classical streaming algorithm that processes signed edges to efficiently estimate the counts of triangles of diverse signed configurations in the single pass edge stream. Our approach introduces a quantum sketch register for processing the signed edge stream, together with measurement operators for query-pair calls in the quantum estimator, while a complementary classical estimator accounts for triangles not captured by the quantum procedure. This hybrid design yields a polynomial space advantage over purely classical approaches, extending known results from unsigned edge stream data to the signed setting. We quantify the lack of balance on random signed graph instances, showcasing how the classical and hybrid algorithms estimate balance in practice.

The exchange interaction is a foundational building block for the operation of spin-based quantum processors. Extracting the exchange interaction coefficient $J(\mathbf{V})$, as a function of gate electrode voltages, is important for understanding disorder, faithfully simulating device performance, and operating spin qubits with high fidelity. Typical coherent measurements of exchange in spin qubit devices yield a modulated cosine of an accumulated phase, which in turn is the time integral of exchange. As such, extracting $J(\mathbf{V})$ from experimental data is difficult due to the ambiguity of inverting a cosine, the sensitivity to noise when unwrapping phase, as well as the problem of inverting the integral. As a step toward obtaining $J(\mathbf{V})$, we tackle the first two challenges to reveal the accumulated phase, $φ(\mathbf{V})$. We incorporate techniques from a wide range of fields to robustly extract and model a 3D phase volume for spin qubit devices from a sequence of 2D measurements. In particular, we present a measurement technique to obtain the wrapped phase, as done in phase-shifting digital holography, and utilize the max-flow/min-cut phase unwrapping method (PUMA) to unwrap the phase in 3D voltage space. We show this method is robust to the minimal observed drift in the device, which we confirm by increasing scan resolution. Upon building a model of the extracted phase, we optimize over the model to locate a minimal-gradient $π$ exchange pulse point in voltage space. Our measurement protocol may provide detailed information useful for understanding the origins of device variability governing device yield, enable calibrating device models to specific devices during operation for more sophisticated error attribution, and enable a systematic optimization of qubit control. We anticipate that the methods presented here may be applicable to other qubit platforms.

Open quantum walks (OQWs) constitute a class of quantum walks whose dynamics are entirely driven by interactions with the environment. It is well known that OQWs provide a general framework for implementing quantum computation. As a proof of principle, we demonstrate the feasibility of running this algorithm within the open quantum walk computation model, and we show that its expected runtime remains finite even in the slower regime.

Particle statistics impose fundamental constraints on nonequilibrium quantum dynamics, yet it remains an open question whether fractional statistics can lead to emergent universal dynamical scaling beyond the conventional Bose-Fermi paradigm. Here we investigate the far-from-equilibrium many-body relaxation of anyons in a one-dimensional lattice and uncover an unconventional yet universal scaling behavior governed by fractional statistics. Based on large-scale numerical simulations and scaling analysis, we identify a distinct separation between particle transport and information spreading: density correlations spread superdiffusively, whereas entanglement entropy grows ballistically. The anomalous particle dynamics can be interpreted intuitively from the statistical-phase-induced quantum interference, which suppresses coherent holon-doublon propagation. In contrast, the entanglement growth turns out to be dominated by its configurational component, which propagates ballistically. Our results establish anyonic statistics as a distinct source of universal nonequilibrium dynamics beyond bosons and fermions, with direct relevance to current quantum simulation experiments.

A scattering event in a quantum field theory is a coherent superposition of all processes consistent with its symmetries and kinematics. While real-time simulations have progressed toward resolving individual channels, existing approaches rely on knowledge of the asymptotic particle wavefunctions. This work introduces an experimentally inspired method to isolate scattering channels in Matrix Product State simulations based on the entanglement structure of the late-time wavefunction. Schmidt decompositions at spatial bipartitions of the post-scattering state identify elastic and inelastic contributions, enabling deterministic detection of outgoing particles of specific species. This method may be used in settings beyond scattering and is applied to detect heavy particles produced in a collision in the one-dimensional Ising field theory. Natural extensions to quantum simulations of other systems and higher-order processes are discussed.

A central goal of quantum computation is the realistic simulation of quantum materials. Although quantum processors have advanced rapidly in scale and fidelity, it has remained unclear whether pre-fault-tolerant devices can perform quantitatively reliable material simulations within their limited gate budgets. Here, we demonstrate that a superconducting quantum processor operating on up to 50 qubits can already produce meaningful, quantitative comparisons with inelastic neutron-scattering measurements of KCuF$_3$, a canonical realization of a gapless Luttinger liquid system with a strongly correlated ground state and a spectrum of emergent spinons. The quantum simulation is enabled by a quantum-classical workflow for computing dynamical structure factors (DSFs). The resulting spectra are benchmarked against experimental measurements using multiple metrics, highlighting the impact of circuit depth and circuit fidelity on simulation accuracy. Finally, we extend our simulations to 1D XXZ Heisenberg model with next-nearest neighbor interactions and a strong anisotropy, producing a gapped excitation spectrum, which could be used to describe the CsCoX$_3$ compounds above the Néel temperature. Our results establish a framework for computing DSFs for quantum materials in classically challenging regimes of strong entanglement and long-range interactions, enabling quantum simulations that are directly testable against laboratory measurements.

In resetting dynamics, a system is repeatedly coupled to and decoupled from ancillary degrees of freedom that are reinitialized between interactions. This provides a versatile route to engineer nonequilibrium steady states and constitutes a powerful and analytically transparent framework for studying nonequilibrium dynamics in quadratic fermionic models. The baseline noninteracting resetting scheme yields an affine evolution for the subsystem single-particle density matrix (SPDM), with a clear operational interpretation: a finite environment block E mediates the interaction between the subsystem S and an ideal external thermal reservoir. In this work, we develop a controlled extension of such a framework to weakly interacting systems. We introduce a Hartree mean-field treatment of density-density interactions that preserves closure of the SPDM dynamics while producing genuinely nonlinear behavior. We further construct a completely positive (CP-safe) Gaussian Lindblad embedding that reproduces the resetting dynamics in the noninteracting limit and yields a continuous-time representation of environmental thermalization when interactions are present. Our analytical results are complemented by numerical studies of a ring segmentation geometry and a minimal two-site model, revealing interaction-enabled steady states that cannot be obtained in any purely quadratic setting. Together, these results establish a general and physically consistent route for incorporating weak interactions ino resetting-based approaches to open quantum system.

We develop a framework that enables direct and meaningful comparison of two early fault-tolerant methods for the computation of eigenenergies, namely \gls{qksd} and \gls{spe}, within which both methods use expectation values of Chebyshev polynomials of the Hamiltonian as input. For \gls{qksd} we propose methods for optimally distributing shots and ensuring sufficient non-linearity of states spanning the Krylov space. For \gls{spe} we improve rigorous error-bounds, achieving roughly a factor $2/3$ reduction of circuit depth. We provide insights into the scalability of and the practical realization of these methods by computing the maximum Chebyshev degree, linearly related to circuit depth, and the respective number of repetitions required for the simulation of molecules with active spaces up to 54 electrons in 36 orbitals by leveraging \gls{mps}/\gls{dmrg}.

In this work we investigate discrete structures in product Hilbert spaces. For monopartite systems of size $d$ one relies on the Weyl-Heisenberg group $WH(d)$, while in the case of composite Hilbert spaces we identify designs covariant with respect to the product group, $[WH(p)]^{\otimes n}$. In analogy with magic -a quantity attaining its maximum for states fiducial with respect to $WH(d)$ -we introduce a similar notion of magick, defined with respect to the product group. The maximum of this quantity over all equimodular vectors yields fiducial states that generate $d$ $\textit{a priori}$ isoentangled mutually unbiased bases (MUBs), which, when supplemented by the identity, form their complete set. Such fiducial states are explicitly constructed in all prime-power dimensions $p^n$ with $p\ge 3$. The result for $p\ge 5$ extends the construction of Klappenecker and Rötteler, whereas for $p=3$ it is mathematically distinct and is based on Galois rings. The global maximum of magick for $d=2^3$ yields fiducial states corresponding to the symmetric informationally complete (SIC) generalized measurement of Hoggar. Our approach feeds into a unifying perspective in which highly symmetric quantum designs emerge from fiducial states with extremal properties via structured group-orbit constructions.

We introduce QiboAgent, a reference implementation designed to serve as a practitioner's guideline for developing specialized coding assistants in Quantum Computing middleware. Addressing the limitations in scientific software development of general-purpose proprietary models, we explore how lightweight, open-source Large Language Models (LLMs) provided with a custom workflow architecture compare. In detail, we experiment with two complementary paradigms: a Retrieval-Augmented Generation pipeline for high-precision information retrieval, and an autonomous agentic workflow for complex software engineering tasks. We observe that this hybrid approach significantly reduces hallucination rates in code generation compared to a proprietary baseline, achieving a peak accuracy of 90.2% with relatively small open-source models of size up to 30B parameters. Furthermore, the agentic framework exhibits advanced coding capabilities, automating the resolution of maintenance issues and new features requests, or by prototyping larger-scale refactors of the codebase, such as producing a compiled Rust module with bindings of an original pure python package, Qibo in our case. The LLM workflows used for our analysis are integrated into a user interface and a Model Context Protocol server, providing an accessible tool for Qibo developers.

Quantum annealing processors typically control qubits in unison, attenuating quantum fluctuations uniformly until the applied system Hamiltonian is diagonal in the computational basis. This simplifies control requirements, allowing annealing QPUs to scale to much larger sizes than gate-based systems, but constraining the class of available operations. Here we expand the class by performing analog-digital quantum computing in a highly-multiplexed, superconducting quantum annealing processor. This involves evolution under a fixed many-body Hamiltonian that, in the weak-coupling regime, is well-described by an effective XY model, together with arbitrary-basis initialization and measurement via auxiliary qubits. Operationally, this is equivalent to implementing single-qubit gates at the beginning and end of an analog quantum evolution. We demonstrate this capability with several foundational applications: single-qubit and two-qubit coherent oscillations with varying initialization and measurement bases, a multi-qubit quantum walk with fermionic dispersion in line with theory, and Anderson localization in a disordered chain. These experiments open the door to a wide range of new possibilities in quantum computation and simulation, greatly expanding the applications of commercially available quantum annealing processors.

Multispectral satellite imagery poses significant challenges for deep learning models due to the high dimensionality of spectral data and the presence of structured correlations across channels. Recent work in quantum machine learning suggests that unitary evolutions and Hilbert-space embeddings can introduce useful inductive biases for learning. In this work, we show that several empirical advantages often attributed to quantum feature maps can be more precisely understood as consequences of geometric structure induced by unitary group actions and the associated quotient symmetries. Motivated by this observation, we introduce a fully classical pooling mechanism that maps latent features to complex projective space via a fixed-reference unitary action. This construction effectively collapses non-identifiable degrees of freedom, leading to a reduction in the dimensionality of the learned representations. Empirical results on multispectral satellite imagery show that incorporating this quantum-inspired pooling operation into a convolutional neural network improves optimization stability, accelerates convergence, and substantially reduces variance compared to standard pooling baselines. These results clarify the role of geometric structure in quantum-inspired architectures and demonstrate that their benefits can be reproduced through principled geometric inductive biases implemented entirely within classical deep learning models.

Recent advances in optical imaging and communication increasingly involve high-dimensional, partially coherent light, creating a growing need for scalable tools to measure and manipulate coherence. Here, we demonstrate the automatic separation of spatially partially coherent light into "coherence modes" -- its orthogonal and mutually incoherent components. To make this separation possible, we exploit variational processing in layered self-configuring interferometer architectures in a silicon photonic circuit. This process formally finds and measures the eigenvectors and eigenvalues of the coherency matrix, hence measuring the partially coherent state, while leaving it intact and separated after optimization. Furthermore, we show that mutually incoherent beams, if spatially orthogonal, can be automatically separated even if they are completely overlapped, hence separating unknown laser beams based only on their mutual incoherence. Our experiment finds and separates the two strongest coherence modes starting from a nine-mode sampling of the partially or fully overlapping fields from two independent lasers. The method requires a number of physical components that scales linearly with the rank $r$ of the coherency matrix and operates through a sequence of $r$ in situ gradient-based optimizations enabled by electronic drive frequency multiplexing of interferometer phase shifters. We benchmark its performance against a mixture-based tomographic method, also implemented on chip. These results establish a scalable framework for programmable coherence analysis and control in imaging, communication, and photonic information processing.

Solving large-scale sparse linear systems is a challenging computational task due to the introduction of non-zero elements, or "fill-in." The Graph Partitioning Problem (GPP) arises naturally when minimizing fill-in and accelerating solvers. In this paper, we measure the end-to-end performance of a hybrid quantum-classical framework designed to accelerate Finite Element Analysis (FEA) by integrating a quantum solver for GPP into Synopsys/Ansys' LS-DYNA multiphysics simulation software. The quantum solver we use is based on Iterative-QAOA, a scalable, non-variational quantum approach for optimization. We focus on two specific classes of FEA problems, namely vibrational (eigenmode) analysis and transient simulation. We report numerical simulations on up to 150 qubits done on NVIDIA's CUDA-Q/cuTensorNet and implementation on IonQ's Forte quantum hardware. The potential impact on LS-DYNA workflows is quantified by measuring the wall-clock time-to-solution for complex problem instances, including vibrational analysis of large finite element models of a sedan car and a Rolls-Royce jet engine, as well as transient simulations of a drill and an impeller. We performed end-to-end performance measurements on meshes comprising up to 35 million elements. Measurements were conducted using LS-DYNA in distributed-memory mode via Message Passing Interface (MPI) on AWS and Synopsys compute clusters. Our findings indicate that with a quantum computer in the loop, amortized LS-DYNA wall-clock time can be improved by up to 15% for specific cases and by at least 7% for all models considered. These results highlight the significant potential of quantum computing to reduce time-to-solution for large-scale FEA simulations within the Noisy Intermediate-Scale Quantum (NISQ) era, offering an approach that is scalable and extendable into the fault-tolerant quantum computing regime.

Simplifying composite open quantum systems through model reduction is central to enable their analytical and numerical understanding. In this work, we introduce a self-consistent approach to eliminate the cavity degrees of freedom of cavity quantum electrodynamics (CQED) devices in the non-adiabatic regime, where the cavity memory time is comparable with the timescales of the atom dynamics. To do so, we consider a CQED system consisting of a two-level atom coupled to a single-mode cavity, both subsystems interacting with the environment through an arbitrary number of ports, within the input-output formalism. A self-consistency equation is derived for the reduced atom dynamics. This allows retrieving an exact expression for the effective Purcell-enhanced emission rate and, under reasonable approximations, a set of self-consistent dynamical equations and input-output relations for the effective two level atom. The resulting reduced model captures non-Markovian features, characterized through an effective Lindblad equation exhibiting two decoherence rates, a positive and a negative one. In the continuous-wave excitation regime, we benchmark our approach by computing effective steady states and output flux expressions beyond the low-power excitation regime, for which a semi-classical treatment is usually applied. We also compute two-time correlations and spectral densities, showing an excellent agreement with full cavity quantum electrodynamics simulations, except in the strong-coupling, high-excitation regime. Our results provide a practical framework for reducing the size of CQED models, which could be generalized to more complex atom and cavity configurations.

We present a general framework for promoting first-order pulse sequences in quantum simulation to higher-order sequences that maintain robustness in the presence of finite pulse-width effects. Our approach maps a given first-order pulse sequence to a first-order Trotter formula, applies higher-order Trotter-formula constructions, and then compiles the resulting evolution back into physically implementable finite-width pulses via dynamically corrected gates. The resulting sequences achieve arbitrarily high-order error scaling with respect to the control cycle time of the underlying first-order sequence while maintaining robustness to finite pulse-width effects. The framework also enables the use of multi-product formulas for more efficient constructions. We apply the framework to several physically motivated quantum-simulation tasks and numerically verify the predicted error scalings.

We present a systematic workflow for the design of one-dimensional photonic crystal nanobeam cavities with non-zero cavity lengths. By simultaneously optimizing the lattice periodicity, air-hole geometry, and cavity length, our approach enables precise control of optical confinement while mitigating radiative losses and linewidth broadening effects. The method is further extended to the design of crossed nanobeam cavities with both matching and mismatched resonance frequencies. This strategy significantly reduces the need for extensive parameter sweeps, providing an efficient route toward optimized cavity designs for integrated quantum photonic applications. Moreover, the resulting structures are inherently compatible with the integration of single-photon emitters.

Preparing low energy states is a central challenge in quantum computing and quantum complexity theory. Several known approaches to prepare low energy states often get stuck in suboptimal states, such as high energy eigenstates (or low variance high energy states). We develop a heuristic method to go past this barrier for local Hamiltonian systems with relatively low frustration, by taking advantage of the fact that such systems come with multiple Hamiltonians that agree on the low-energy subspaces. We establish an energy-based uncertainty principle, which shows that these Hamiltonians in fact do not have common eigenstates in the high energy regime. This allows us to run energy lowering steps in an alternating manner over the Hamiltonians. We run numerical simulations to check the performance of the `alternating' algorithm on small system sizes, for the 1D AKLT model and instances of Heisenberg model on general graphs. We also formulate a version of the energy-based uncertainty principle using sparse Hamiltonians, which shows a quadratically larger variance at higher energies and hence leads to a larger energy change. We use this version to simulate the method on energy profiles with high energy barriers.

We investigate the non-adiabatic quantum dynamics of ultralong-range Rydberg molecules using a vibronically coupled two-channel treatment. The two channels are composed of coupled trilobite and butterfly electronic states, formed as a result of $S$-wave and $P$-wave scattering of high angular momentum Rydberg electrons with perturbing ground state atoms. Within the Born-Oppenheimer treatment, the $P$-wave scattering channel introduces an adiabatic decay pathway that affects the stability and lifetimes of trilobite states. Our numerical results show that the vibronic coupling is dependent on the principal quantum number $n$, and for certain $n$ there is non-adiabatic stabilization against internal molecular decay, facilitating previously studied dynamical effects in pure trilobite molecules. Apart from the internal diffraction effect we also observe interesting multi-well tunneling effects, during low-energy oscillations for certain $n$-values. Our work serves to highlight that the unique $R$-dependent electronic structure of these polar molecules, along with high level densities, promise many exciting dynamical effects.

We present a quantum field theoretic formulation of acoustoelectric interactions in waveguide-like systems of arbitrary cross-section. Building on an open quantum systems approach, we derive a unified description of plasmon-phonon coupling that incorporates dissipation, noise, and the influence of drift currents. Our analysis captures both bulk and surface plasmon modes, highlighting how drift currents Doppler-shift plasmonic resonances and reshape the phonon noise spectrum. The resulting Heisenberg-Langevin equations yield closed-form expressions for frequency shifts, gain, and noise power spectra, enabling direct evaluation of performance metrics such as the noise factor in acoustoelectric amplifiers and oscillators. In the appropriate limits, this framework reproduces known results while extending them to complex geometries.

Compact, customizable, non-magnetic vacuum systems are a key requirement for many field applications of quantum technology based on cold atoms. We report on the development and construction of a compact, low-cost ultra-high vacuum compatible cell using the glass-ceramic MACOR. The cell offers a CF flange connection to commercial vacuum technology, as well as high numerical aperture viewports for precision optical measurements. The presented technology shows stable vacuum pressures of $< 1 \cdot 10^{-10}$ mbar for more than a year since the implementation into the vacuum system of a quantum gas experiment, further proving suitability for general quantum technology applications.

We develop a Bohmian analysis of a two-dimensional ghost Hamiltonian and its mapping to the degenerate Pais-Uhlenbeck model. Using Gaussian wavepackets, we derive the corresponding guidance equations, the centre and width evolution, and the quantum potential. We use these quantities to characterise bounded, quasi-semiclassical, spiral, and runaway regimes. The Bohmian trajectories provide a direct dynamical diagnostic of coherence, packet deformation, and quantum-classical separation. We then compare a bi-Hamiltonian pair consisting of the ghost Hamiltonian and a classically equivalent alternative formulation. While the two descriptions produce identical classical trajectories, they lead to different Bohmian trajectories and different quantum potentials evaluated along those trajectories. This demonstrates that classical equivalence need not extend to Bohmian quantum dynamics and identifies a concrete quantum ambiguity in the degenerate higher-derivative system.

The SU(2) Wigner function represents a quantum state of a spin-$J$ as a real-valued function on the surface of a 2-sphere. For an ensemble of $N$ spin-1/2 particles, this representation is useful when the dynamics is restricted to a single SU(2) irrep, e.g., the symmetric subspace with $J=N/2$. Physically relevant noise sources tend to be local, such as spontaneous emission, depolarizing, and incoherent optical pumping, all of which transfer the state outside of the initial irrep, and as such the SU(2) Wigner function is no longer a useful representation. In this work, we address this issue by encoding a noisy spin ensemble in an SU(3) irrep, and evaluating the SU(3) Wigner function for that irrep. We find that physical constraints enforced by the noise eliminate all but three real parameters from the input to the Wigner function, which can then be interpreted as a polar, azimuthal, and radial component. This interpretation leads us to refer to the resulting Wigner function as the solid spin Wigner function, visualized on a solid ball rather than a hollow sphere.

Quantum heat engines provide attractive means in quantum thermodynamics for studying the fundamentals of the flow of heat and work. Previous experimental implementations of heat engines operating at the level of a few excitation quanta have utilized external driving, which has made the observation of the produced work challenging. Conversely, autonomous quantum heat engines only require a flow of heat to operate and generate work. However, autonomous quantum heat engines have not yet been experimentally demonstrated in any system despite numerous theoretical investigations. Here, we experimentally realize an autonomous quantum heat engine based on superconducting circuits. We construct the engine circuit implementing an approximate Otto cycle by coupling two superconducting resonators with a superconducting quantum interference device, and coupling this system to spectrally filtered hot and cold reservoirs. By varying the experimental conditions, we observe coherent microwave power generation arising from the internal dynamics of the system driven only by the thermal reservoirs. Our results validate previous theoretical predictions for this circuit and pave the way for detailed studies of quantum effects in heat engines and for using heat-generated coherent microwaves in circuit quantum electrodynamics.

Identifying scalable materials systems that exhibit quantum behavior is a central challenge in quantum information science. Point defects in certain wide-bandgap semiconductors are promising in this regard due to the maturity of semiconductor manufacturing and ion implantation technology. Single erbium defect centers in 4H-SiC are examples of such defects that provide access to discrete defect-induced electron energy levels within the bulk material bandgap, which can be utilized for a variety of quantum technologies, such as single-photon emission for secure communication and distributed quantum computing. This work presents a first-principles study of erbium point defects in 4H-SiC using density functional theory. These results provide materials-level support for the development of Er point defects in 4H-SiC as a scalable platform for quantum devices, helping to bridge the gap between quantum physics and the practical realization of quantum networks.

We systematically compare Quantum Liang Information Flow (QLIF) a recently proposed causal information measure with the out-of-time-order correlator (OTOC) as diagnostics of quantum chaos in the one-dimensional mixed-field Ising chain. Using exact diagonalization and MPS-TEBD, we show that the early-time power-law growth and wavefront propagation velocity of QLIF are identical for integrable and chaotic parameters, being controlled solely by the local Hamiltonian structure. The QLIF signal strength depends sensitively on the initial state, spanning four orders of magnitude across product states, ground state eigenstate evolution, and quantum quench protocols. We identify the time-integrated QLIF as a late-time chaos diagnostic: it grows linearly (monotonically) in chaotic systems, reflecting irreversible thermalization, while saturating or oscillating in integrable systems, reflecting reversible quasiparticle dynamics. These findings establish QLIF as a complementary probe to OTOC, with distinct optimal operating regimes.

Extreme-value fluctuations at quantum critical points remain poorly understood in the presence of strong correlations and openness. At the integer quantum Hall transition in the open Chalker--Coddington network, we show that the maximal wave-function amplitude separates into a global gain and an intrinsic extreme component, $|ψ|_{\max}=A\,|\tildeψ|_{\max}$. We introduce extreme-moment scaling for $|ψ|_{\max}$ and observe an approximately parabolic exponent function $τ_{\max}(q)$ over moderate $q$, while $\ln|ψ|_{\max}$ displays an almost Gaussian bulk over the studied sizes. The gain factor is close to log-normal and largely controls the raw extremes. Gain normalization reorganizes the statistics: $\tildeτ_{\max}(q)$ changes qualitatively and $|\tildeψ|_{\max}$ does not support a single-parameter generalized extreme-value collapse under standard centering/scaling in the accessible size window. Extreme observables thus provide a robust probe of correlated criticality in open quantum systems.

We propose a theoretical model of a fully functional nonreciprocal quantum battery inspired by the architecture of bacterial light-harvesting complexes. We assign functional roles to collective quantum optical subradiant and superradiant states and introduce a unimodal cavity to assist storage. The transition rates are obtained from an effective non-Hermitian Hamiltonian, tailored to the battery geometry which are fed into a master equation to unravel the time evolution. We investigate the complete thermodynamic performance including storage, leakage, ergotropy, work extraction, flux, and power. We observe optimization at different ring sizes, each peaking at its specific energetic function. Strong coupling between the ring and central system enhances the battery's ability to store energy but reduces the ability of power output. The ergotropy exceeds capacity and approaches it linearly with increasing system size, with an optimal small-size regime that disappears under strong coupling.

Non-Gaussian bosonic states are ubiquitous in interacting light--matter systems, many-body platforms, and relativistic quantum field settings, but their quantitative characterization is hindered by the infinite-dimensional Hilbert space and by the poor scalability of Fock-space truncation methods. We introduce an exact finite-manifold encoding for states supported on a finite span of Gaussian branches, enabling the use of standard finite-dimensional quantum-information tools directly on an effective density matrix whose entries are determined by Gaussian overlaps. As demonstrations, we obtain closed-form and numerically stable evaluations of entropies and relative-entropy non-Gaussianity, and derive an analytic expression for the bipartite entanglement negativity of arbitrary multimode two-branch Gaussian superpositions, including a minimal which-branch dephasing model. Our framework provides a practical bridge between experimentally accessible continuous-variable resources (e.g., cat-like and measurement-conditioned states) and discrete-variable information measures, with immediate applications to benchmarking non-Gaussian resources in several quantum technology platforms.

Discrete circular convolution over $\mathbb{Z}/N\mathbb{Z}$ is a linear operator and can be implemented on quantum hardware within the linear-combination-of-unitaries (LCU) framework. In this work, we make this connection explicit through an asymmetric-LCU formulation: circular convolution is the postselected block of a circuit whose controlled-shift unitary is modular addition on computational-basis states. The asymmetry is essential: fixing the postselection state to the uniform state $|u\rangle$ while supplying the kernel state $|\mathbf{b}\rangle$ as the input ancilla naturally preserves the complex coefficients $b_i$ within the block, whereas a symmetric overlap would yield $|b_i|^2$ weights and erase their phases. Accordingly, when $|\mathbf{a}\rangle$ and $|\mathbf{b}\rangle$ are supplied by upstream quantum routines, the convolution subroutine requires only the fixed uncompute $\mathrm{PREP}_u^\dagger$, completely avoiding the need for a kernel-dependent inverse preparation $\mathrm{PREP}_b^\dagger$. We then introduce a reversal matrix $J_n=X^{\otimes n}$ and define reflected shifts $\widetilde{L}_{i,n}=L_{i,n}J_n$. This symmetrization yields a recursive operator algebra for convolution that is natively compatible with LCU/block-encoding workflows. The resulting symmetrized operator differs from circular convolution only by one known input-side $J_n$ layer. Crucially, for real-valued kernels, the resulting operator $H_n(\mathbf{b})=\sum_i b_i\widetilde{L}_{i,n}$ is Hermitian, providing a direct Hermitian interface for quantum singular value transformation (QSVT) and related spectral transformations. Based on this framework, we present a transparent recursive construction, paired with an exactly equivalent optimized bitwise compilation of the same $\mathrm{SELECT}$ block. Finally, we evaluate implementation trade-offs and resource scaling under explicit cost-model conventions.

Digital signatures are one of the security cornerstones of the current information age. Compared with classical digital signatures based on computational complexity, quantum digital signatures (QDS) theoretically guarantee data integrity, authenticity, and non-repudiation by quantum mechanics, showing great potential for development in cryptography and thus attracting widespread attention. However, the performance of existing QDS systems are still limited in rate and distance. Here we report the first experimental demonstration of twin-field QDS (TF-QDS) using a GHz system. We achieve a maximum transmission distance of 504 km fiber spools for both single-bit and multi-bit schemes, surpassing all existing state-of-the-art QDS experiments more than 200 km. Furthermore, by combining the one-time universal hash method, we achieve a maximum signature rate of 21.1 times per second for a 1 Mbit file over fiber distances up to 302 km. In this work, the signature rates of both single-bit scheme and multi-bit scheme are more than two orders of magnitude higher than that of previous works at similar distance. Our work provides a new record for long-distance and high-rate QDS, representing a significant step in the development of QDS.

We report a laboratory measurement of how impurities shift Coulomb crystallization in a strongly interacting ionic system. This is achieved by using laser cooled Ca$^+$ crystals doped with a controlled number of Xe$^{12+}$ highly charged ions. We find that the crystallization threshold is unchanged at low impurity concentration, but shows a clear crossover once the impurity content becomes sufficiently large, after which the shift grows approximately linearly. Complementary measurements reveal that this global effect originates from a local pinning of the crystal around the impurities. We further show how the measured shift could impact standard models of crystallization in white dwarfs and neutron stars. Our results provide an experimental route to incorporating impurity effects into models of multicomponent Coulomb matter, relevant to stellar crystallization and strongly coupled plasmas.

We measure event-by-event discrete changes in the net electric charge of an optically levitated silica microsphere arising from individual radioactive decays within the sphere, in coincidence with energy depositions in a nearby scintillation detector. The net charge of the levitated sphere is continuously monitored by measuring its driven response to an oscillating electric field, allowing individual charge-change events to be resolved on millisecond timescales with precision below an elementary charge. Simultaneously, $α$ and $β$ particles emitted during decays of implanted $^{212}$Pb and its daughters are detected using a scintillator read out with an array of silicon photomultipliers. By correlating reconstructed charge-change times with the scintillator response, we can directly attribute abrupt changes in the sphere's net charge to individual nuclear decays, and identify differences in the distribution of charges ejected for $α$ and $β$ decays. These results establish a new approach for studying low energy charged particles emitted by radioactive decays at the single-decay level, and identify showers of radiogenically produced low-energy electrons emitted by $α$-decaying radon daughters implanted near solid surfaces.

Photonic quantum processors naturally produce intrinsically stochastic measurement outcomes, offering a hardware-native source of structured randomness that can be exploited during machine-learning training. Here we introduce Photonic Quantum-Enhanced Knowledge Distillation (PQKD), a hybrid quantum photonic--classical framework in which a programmable photonic circuit generates a compact conditioning signal that constrains and guides a parameter-efficient student network during distillation from a high-capacity teacher. PQKD replaces fully trainable convolutional kernels with dictionary convolutions: each layer learns only a small set of shared spatial basis filters, while sample-dependent channel-mixing weights are derived from shot-limited photonic features and mapped through a fixed linear transform. Training alternates between standard gradient-based optimisation of the student and sampling-robust, gradient-free updates of photonic parameters, avoiding differentiation through photonic hardware. Across MNIST, Fashion-MNIST and CIFAR-10, PQKD traces a controllable compression--accuracy frontier, remaining close to teacher performance on simpler benchmarks under aggressive convolutional compression. Performance degrades predictably with finite sampling, consistent with shot-noise scaling, and exponential moving-average feature smoothing suppresses high-frequency shot-noise fluctuations, extending the practical operating regime at moderate shot budgets.

Dipolar molecules in optical traps are a versatile platform for studying many-body phases of quantum matter in the presence of strong and long-range interactions. The dipolar interactions in such setups can be enabled by microwave driving opposite parity rotational levels of the molecules. We find that the regime where the $N=0,J=1/2,F=1$ state is coupled to the $N=1,J=3/2,F=2$ manifold with circularly polarized microwaves, in the presence of a small magnetic field, can lead to spin-1 quantum magnetic Hamiltonians, due to the decoupling between electron spin and orbit, that is unique to the $^2Σ$ ground state molecules. We demonstrate that in one dimension, the phase diagram associated with this Hamiltonian, computed via tensor network methods, hosts the celebrated Haldane phase. We find that the Haldane phase persists even in the presence of SU(3) correction terms that break the SU(2) algebra of the Hamiltonian. We discuss the feasibility of the proposed scheme for $^2Σ$ molecules with large rotational constants such as the directly laser cooled molecule MgF for future experiments.

The current definition of the SI second is based on the 133Cs ground-state hyperfine transition in the microwave domain, with the most accurate realizations achieving fractional frequency uncertainties of about (1-2)E16. In contrast, state-of-the-art optical clocks now demonstrate estimated uncertainties two to three orders of magnitude lower, prompting discussion on the redefinition of the SI second. Several options for the new definition have been proposed, one of which introduces a constant N defined as the weighted geometric mean of multiple clock transition frequencies. In this work, we investigate how N can be practically realized when not all defining transitions are available and when multiple optical clocks operate with different performance levels and non-overlapping uptimes. We consider two complementary realization and reconstruction routes. One route is based on geometric-mean combinations, and the other is based on arithmetic-mean combinations. We derive consistent uncertainty expressions that incorporate both measurement uncertainties and, where required, uncertainties of recommended frequencies or frequency ratios. Using analytic three-transition case studies, we identify the parameter regimes in which each route yields a lower total uncertainty and provide explicit conditions for the crossover between them. We further address the dominant role of dead time when a hydrogen maser serves as a flywheel reference by introducing a time-segmented, time-weighted combination based on coefficient and covariance matrices, which accounts for overlapping operation and correlations across measurement intervals. Our findings offer practical guidance for minimizing total uncertainty in multi-clock realizations and contribute to ongoing efforts toward redefining the SI second.

We benchmark constrained-path Monte Carlo (CPMC) on the triangular-lattice Hubbard model for several fillings and $U$ values and show that symmetry-adapted trial wave functions are essential for quantitative accuracy. Away from half-filling, simple free-electron-based trials that preserve the ground state symmetry yield energy deviations $\lesssim 1\%$ from exact diagonalization and density matrix renormalization group results. At half-filling, strong frustration in the intermediate to large $U$ regimes necessitates symmetry-projected trials to reach comparable accuracy, where both free-electron and symmetry-broken Hartree-Fock trials incur substantial constraint bias. Since the computational cost of CPMC with symmetry projection scales polynomially with system size, our results motivate its use as a practical route for studying competing ground states in strongly correlated, frustrated systems.

Accurately simulating extended periodic systems is a central challenge in condensed matter physics. Neural quantum states (NQS) offer expressive wavefunctions for this task but face issues with scalability. In this work, we successfully extend the neural network backflow (NNBF) approach to ab-initio solid-state materials. Building on our scalable optimization framework for molecules [Liu et al., PRB 112, 155162 (2025)], we introduce a two-stage pruning strategy to manage the massive configuration space expansions: by utilizing a computationally cheap, physics-informed importance proxy, we devote exact NNBF amplitude evaluations solely to the most relevant determinants, significantly improving optimization efficiency, energy estimation, and convergence. Our framework achieves state-of-the-art accuracy across diverse solid-state benchmarks. For 1D hydrogen chains, NNBF matches or surpasses DMRG and AFQMC, remains robust in strongly correlated bond-breaking regimes where coupled-cluster methods fail, and smoothly extrapolates to the thermodynamic limit. We further demonstrate its scalability by computing ground-state potential energy curves for 2D graphene and 3D silicon. Finally, ablation studies validate the computational savings of our pruning strategy and highlight the dependence of the NNBF energies on basis sets.

Projection games constitute an important class of nonlocal games where, for any answer from the first player, there is a unique correct answer for the second player. This class of games captures nonlocal games arising from constraint satisfaction problems, oracularisations, and unique games. However, due to the asymmetry between the players, projection games are in general not synchronous, and therefore the powerful results constraining the structure of almost perfect strategies for synchronous games do not apply. In this work, we adapt results of Marrakchi and de la Salle for synchronous games to show that, in both the quantum and commuting-operator models, any strategy that wins with probability $1-\varepsilon$ in a projection game gives rise to a tracial strategy that wins with probability $1-O((L\varepsilon)^{1/4})$, where $L$ is the inverse of the minimal conditional probability of a question for the second player being sampled given a question to the first. For constraint system games, this strengthens the rounding result of Paddock by eliminating the dependence on number of constraints and improving the dependence on constraint size, while also generalising to the commuting-operator setting.

Cardinality-constrained binary optimization is a fundamental computational primitive with broad applications in machine learning, finance, and scientific computing. In this work, we introduce a Grover-based quantum algorithm that exploits the structure of the fixed-cardinality feasible subspace under a natural promise on solution existence. For quadratic objectives, our approach achieves ${O}\left(\sqrt{\frac{\binom{n}{k}}{M}}\right)$ Grover rotations for any fixed cardinality $k$ and degeneracy of the optima $M$, yielding an exponential reduction in the number of Grover iterations compared with unstructured search over $\{0,1\}^n$. Building on this result, we develop a hybrid classical--quantum framework based on the alternating direction method of multipliers (ADMM) algorithm. The proposed framework is guaranteed to output an $ε$-approximate solution with a consistency tolerance $ε+ δ$ using at most $ {O}\left(\sqrt{\binom{n}{k}}\frac{n^{6}k^{3/2} }{ \sqrt{M}ε^2 δ}\right)$ queries to a quadratic oracle, together with ${O}\left(\frac{n^{6}k^{3/2}}{ε^2δ}\right)$ classical overhead. Overall, our method suggests a practical use of quantum resources and demonstrates an exponential improvements over existing Grover-based approaches in certain parameter regimes, thereby paving the way toward quantum advantage in constrained binary optimization.

Spontaneous parametric downconversion (SPDC) has been considered as a reliable source of high- dimensional entangled states in orbital angular momentum (OAM) basis. In real-world experiments, the spatial walk-off of the pump often degrades the fidelity of the generated quantum state. Since the walk-off effect breaks the rotational symmetry of the system, the conservation of total OAM is violated. Although the compensation of walk-off effects has become a well-established experimental technique, a systematic modal analysis of the spatial walk-off effect is still incomplete for SPDC. Here, we quantitatively analyze the violation of OAM conservation due to the pump walk-off effect in SPDC processes. We have derived a scaling law of the total OAM distribution with respect to the pump walk-off angle. We have also explored the feasibility of using the spatial walk-off as a mechanism to engineer the generated quantum state. Our study has provided guidelines for the generation of OAM-entangled state under realistic experimental conditions.

Nitrogen-vacancy (NV) centers in diamond are a versatile quantum sensing platform for high sensitivity measurements of magnetic fields, temperature and strain with nanoscale spatial resolution. A common bottleneck is the analysis of optically detected magnetic resonance (ODMR) spectra, where target quantities are encoded in resonance features. Conventional nonlinear fitting is often computationally expensive, sensitive to initialization, and prone to failure at low signal-to-noise ratio (SNR). Here we introduce a robust, efficient machine learning (ML) framework for real-time ODMR analysis based on a one-dimensional convolutional neural network (1D-CNN). The model performs direct parameter inference without initial guesses or iterative optimization, and is naturally parallelizable on graphics processing units (GPU) for high-throughput processing. We validate the approach on both synthetic and experimental datasets, showing improved throughput, accuracy and robustness than standard nonlinear fitting, with the largest gains in the low-SNR regime. We further validate our methods in two representative sensing applications: diagnosing intracellular temperature changes using nanodiamond probes and widefield magnetic imaging of superconducting vortices in a high-temperature superconductor. This deep-learning inference framework enables fast and reliable extraction of physical parameters from complex ODMR data and provides a scalable route to real-time quantum sensing and imaging.

Real-time dynamics of quantum observables provide direct access to excitation spectra and correlation functions in quantum many-body systems, but currently available quantum devices are limited to short evolution times due to decoherence. We propose a neural ordinary differential equation (Neural ODE) framework with physics-driven designs to reconstruct long-time operator dynamics from short-time measurements. By expanding observables in the Pauli basis and exploiting locality and symmetry constraints, the operator evolution is reduced to a tractable set of coefficients whose dynamics are learned from data. Applied to the transverse-field Ising model, the method accurately extrapolates long-time behavior and resolves excitation spectra from noisy short-time signals. Our results demonstrate a scalable and data-efficient strategy for extracting dynamical and spectral information from practical quantum hardware.

How stochastic, microscopic events generate deterministic, macroscopic properties is a fundamental question in physics. We address this question by developing a quantum master equation model for concentrated radical solutions, where random molecular collisions govern the magnetic properties of the system. Our theory reveals a simple mechanism: the first-order exchange contribution averages to zero over collisions, while the second-order term survives as an effective ferromagnetic coupling that enhances magnetization. The model captures the experimentally observed trends in magnetic behavior that deviate from conventional theories. Because the mechanism arises from statistical averaging, it may apply to a broader class of soft matter phenomena, including liquid crystals.