Quantum Physics Paper Analysis

The increasing number of qubits in quantum processors necessitates a corresponding increase in the number of control lines between the processor, which is typically operated at cryogenic temperatures, and external electronics. Scaling poses significant challenges in terms of the thermal loads, forming a major bottleneck in the realization of large-scale quantum computers. In this study, we analyze simultaneous gate operations on multiple qubits using microwaves transmitted via a single cable in a frequency-division multiplexing (FDM) scheme. By employing rectangular control microwave pulses, we reveal the contribution of drive frequency spacing to gate fidelity. Through theoretical and numerical analyses, we demonstrate that orthogonal and quasi-orthogonal microwave signals suppress interference in simultaneously driven qubits, thereby ensuring high gate fidelity. Additionally, we provide design guidelines for key parameters, including pulse length, number of multiplexed microwave signals, and rotation angle, to achieve precise qubit operations. Our findings enable a scalable FDM-based microwave control scheme suitable for quantum processors with a large number of qubits.

We present quantum circuits with a brick wall structure using the optimal number of parameters and two-qubit gates to parametrize $SU(2^n)$, and provide evidence that these circuits are universal for $n\leq 5$. For this, we successfully compile random matrices to the presented circuits and show that their Jacobian has full rank almost everywhere in the domain. Our method provides a new state of the art for synthesizing typical unitary matrices from $SU(2^n)$ for $n=3, 4, 5$, and we extend it to the subgroups $SO(2^n)$ and $Sp^\ast(2^n)$. We complement this numerical method by a partial proof, which hinges on an open conjecture that relates universality of an ansatz to it having full Jacobian rank almost everywhere.

Neutral atom quantum computers and to a lesser extent trapped ions may suffer from atom loss. In this work, we investigate the impact of atom loss in long chains of trapped ions. Even though this is a relatively rare event, ion loss in long chains must be addressed because it destabilizes the entire chain resulting in the loss of all the qubits of the chain. We propose a solution to the chain loss problem based on (1) a quantum error correction code distributed over multiple long chains, (2) beacon qubits within each long chain to detect the loss of a chain, and (3) a decoder adapted to correct a combination of circuit faults and erasures after beacon qubits convert chain losses into erasures. We verify the chain loss correction capability of our scheme through circuit level simulations with a distributed $[[72,12,6]]$ BB code with beacon qubits.

Neutral-atom quantum computers encode qubits in individually trapped atoms arranged in optical lattices. Achieving defect-free atom configurations is essential for high-fidelity quantum gates and scalable error correction, yet stochastic loading and atom loss during rearrangement hinder reliable large-scale assembly. This work presents ATLAS, an open-source atom transport algorithm that efficiently converts a randomly loaded $W \times W$ lattice into a defect-free $L \times L$ subarray while accounting for realistic physical constraints, including finite acceleration, transfer time, and per-move loss probability. In the planning phase, optimal batches of parallel moves are computed on a lossless virtual array; during execution, these moves are replayed under probabilistic atom loss to maximize the expected number of retained atoms. Monte Carlo simulations across lattice sizes $W=10$--$100$, loading probabilities $p_{\mathrm{occ}}=0.5$--$0.9$, and loss rates $p_{\mathrm{loss}}=0$--$0.05$ demonstrate fill rates above $99\%$ within six iterations and over $90\%$ atom retention at low loss. The algorithm achieves sublinear move scaling ($\propto M^{0.55}$) and linear growth of required initial size with target dimension, outperforming prior methods in robustness and scalability -- offering a practical path toward larger neutral-atom quantum arrays.

Quantum circuits will experience failures that lead to computational errors. We introduce Medusa, an automated compilation method for lowering a circuit's failure rate. Medusa uses flags to predict the absence of high-weight errors. Our method can numerically upper bound the failure rate of a circuit in the presence of flags, and fine tune the fault-tolerance of the flags in order to reach this bound. We assume the flags can have an increased fault-tolerance as a result of applying surface QECs to the gates interacting with them. We use circuit level depolarizing noise to evaluate the effectiveness of these flags in revealing the absence of the high-weight stabilizers. Medusa reduces the cost of quantum-error-correction (QEC) because the underlying circuit has a lower failure rate. We benchmark our approach using structured quantum circuits representative of ripple-carry adders. In particular, our flag scheme demonstrates that for adder-like circuits, the failure rate of large-scale implementations can be lowered to fit the failure rates of smaller-scale circuits. We show numerically that a slight improvement in the local fault-tolerance of the flag-qubits can lead to a reduction in the overall failure rate of the entire quantum circuit.

Quantum computing faces a key challenge: balancing the need for low circuit depth (crucial for fault tolerance) with the high accuracy required for complex computations like quantum chemistry and error correction, which typically require deeper circuits. We overcome this trade-off by introducing a novel reinforcement learning approach featuring engineered reward functions, called \textbf{QASER}, that take into account seemingly contradictory optimization goals. This reward enables the compilation of circuits with lower depth and higher accuracy, significantly outperforming state-of-the-art techniques. Benchmarks on quantum chemistry state preparation circuits demonstrate stable compilations. We achieve up to 50\% improved accuracy, while reducing 2-qubit gate counts and depths by 20\%. This advancement enables more efficient and reliable quantum compilation.

An important proof technique in the random oracle model involves reprogramming it on hard to predict inputs and arguing that an attacker cannot detect that this occurred. In the quantum setting, a particularly challenging version of this considers adaptive reprogramming wherein the points to be reprogrammed (or the output values they should be programmed to) are dependent on choices made by the adversary. Some quantum frameworks for analyzing adaptive reprogramming were given by Unruh (CRYPTO 2014, EUROCRYPT 2015), Grilo-Hövelmanns-Hülsing-Majenz (ASIACRYPT 2021), and Pan-Zeng (PKC 2024). We show, counterintuitively, that these adaptive results follow from the \emph{nonadaptive} one-way to hiding theorem of Ambainis-Hamburg-Unruh (CRYPTO 2019). These implications contradict beliefs (whether stated explicitly or implicitly) that some properties of the adaptive frameworks cannot be provided by the Ambainis-Hamburg-Unruh result.

Quantum low-density parity check (QLDPC) codes can significantly reduce the overhead of quantum computing, provided the methods for performing logical operations do not require substantial space and time resources. A popular method for performing logical operations is by measuring logical Pauli operators. We present a simple, explicit construction for fixed gadgets that can measure arbitrary logical Pauli operators on QLDPC codes when dynamically connected to the code block. We apply this construction to a family of generalised bicycle codes with distances relevant to utility-scale quantum computation ($10\leq d \leq 24$) and show that it reduces the space overhead by at least an order of magnitude compared to corresponding surface code architectures, without increasing the time overhead.

We propose high-fidelity single-qubit spin-dependent kicks (SDKs) for trapped ions using nanosecond Raman pulses via amplitude modulation of a continuous-wave laser with a tunable beat frequency. We develop a general method for maintaining SDK performance in the presence of micromotion by identifying optimal choices of the RF phase and frequency that suppress unwanted backward kicks. The proposed scheme enables SDK infidelities as low as $10^{-9}$ in the absence of micromotion, and below $10^{-5}$ with micromotion. This study lays the foundation for the realization of sub-trap-period and high-fidelity two-qubit gates based on SDKs.

The ensemble-averaged dynamics of open quantum systems are typically irreversible. We show that this irreversibility need not hold at the level of individually monitored quantum trajectories. Our main results are quantum stochastic differential equations for reverse diffusion, along with corresponding stochastic master equations. These equations describe the exact and approximate stochastic reverse processes for continuously monitored Pauli channels, including time-dependent depolarizing noise. The exact SDEs admit closed-form solutions that can be implemented online without the need for variational techniques. Importantly, the reverse SDEs and corresponding processes are generalizations of their forward counterparts. One can recover the forward process from its reverse, meaning that the reverse process experiences the same decoherence and noise effects as the forward process. This establishes an analytical framework for noise-resilient quantum gates, quantum tomography via forward-reverse cycles, and potential paradigms for quantum error correction based on reverse diffusion.

Modular trapped-ion quantum computing hardware, known as QCCDs require shuttling operations in order to maintain effective all-to-all connectivity. Each module or trap can perform only one operation at a time, resulting in low intra-trap parallelism, but there is no restriction on operations happening on independent traps, enabling high inter-trap parallelism. Unlike their superconducting counterparts, the design space for QCCDs is relatively flexible and can be explored beyond current grid designs. In particular, current grid-based architectures significantly limit the performance of many promising, high-rate codes such as HGP codes and BB codes, suffering from numerous trap to trap ``roadblocks", forcing serialization and destroying the inherent parallelism of these codes.. Many of these codes are highly parallelizable, meaning that with appropriate hardware layouts and matching software schedules, execution latency can be reduced. Faster execution, in turn, reduces error accumulation from decoherence and heating, ultimately improving code performance when mapped to realistic hardware. To address this, we propose Cyclone, a circular software-hardware codesign that departs from traditional 2D grids in favor of a flexible ring topology, where ancilla qubits move in lockstep. Cyclone eliminates roadblocks, bounds total movement, and enables high levels of parallelism, resulting in up to ~4$\times$ speedup in execution times. With HGP codes, Cyclone achieves up to a 2$\times$ order of magnitude improvement in logical error rate, and with BB codes, this improvement reaches up to a 3$\times$ in order of magnitude.Spatially, Cyclone reduces the number of required traps and ancilla qubits by $2\times$.The overall spacetime improvement over a standard grid is up to $\sim 20 \times$, demonstrating Cyclone as a scalable and efficient alternative to conventional 2D QCCD architectures.

Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge theories induced by automorphisms of the gauge group, when the gauge theories have nontrivial topological actions in different spacetime dimensions. We discover the automorphism symmetry can be extended, become a higher group symmetry, and/or become a non-invertible symmetry. We illustrate the discussion with various models in field theory and on the lattice. In particular, we use automorphism symmetry to construct new transversal non-Clifford logical gates in topological quantum codes. In particular, we show that 2+1d $\mathbb{Z}_N$ qudit Clifford stabilizer models can implement non-Clifford transversal logical gate in the 4th level $\mathbb{Z}_N$ qudit Clifford hierarchy for $N\geq 3$, extending the generalized Bravyi-König bound proposed in the companion paper [arXiv:2511.02900] for qubits.

Magic is a non-classical resource whose efficient manipulation is fundamental to advancing efficient and scalable fault-tolerant quantum computing. Quantum advantage is possible only if both magic and entanglement are present. Of particular interest is non-local magic- the fraction of the resource that cannot be distilled (or erased) by local unitary operations - which is a necessary feature for quantum complex behavior. We perform the first experimental demonstration of non-local magic in a superconducting Quantum Processing Unit (QPU). Direct access to the QPU device enables us to identify and characterize the dominant noise mechanisms intrinsic to the quantum hardware. We observe excellent agreement between theory and experiment without the need for any free parameter in the noise modeling of our system and shows the experimental capability of harnessing both local and non-local magic resources separately, thereby offering a promising path towards more reliable pre-fault-tolerant quantum devices and to advance hardware-aware research in quantum information in the near term. Finally, the methods and tools developed in this work are conducive to the experimental realization of efficient purity estimation (featuring exponential speedup) and the decoding of Hawking radiation from a toy-model of a Black Hole.

The security of future large-scale IoT networks is critically threatened by the ``Harvest Now, Decrypt Later'' (HNDL) attack paradigm. Securing the massive, long-lived data streams from these systems requires protocols that are both quantum-resistant and highly scalable. Existing solutions are insufficient: post-quantum classical protocols rely on computational assumptions that may not hold for decades, while purely quantum protocols are too resource-intensive for the sheer scale of IoT. This paper introduces the Quantum Anonymous Data Reporting (QADR) protocol, a hybrid framework that provides a theoretical benchmark and high-performance architecture for this challenge, designed for future fully-connected quantum networks. The protocol achieves scalable, quantum-resistant anonymity through a hybrid security model; it leverages information-theoretically secure keys from Quantum Key Distribution (QKD) to seed a quantum-secure pseudorandom function (QS-PRF), grounding its long-term data protection in well-established computational hardness assumptions. We also propose and analyze an automated slot reservation mechanism by making a deliberate trade-off: achieving high performance by accepting a quantifiable information leak during the anonymous slot reservation phase while maintaining strong unlinkability for the final data submission. Our security analysis formally quantifies the anonymity reduction caused by the leak and discusses pathways to fully mitigate it at a significant performance cost. We prove the protocol's critical advantage as a performance benchmark: its primary communication cost scales as $O(n^2)$, a dramatic improvement over quantum-native alternatives ($O(n^4)$), establishing a high-performance goal for future quantum-secured anonymity systems.

The gauge field formalism, or operator-valued cochain formalism, has recently emerged as a powerful framework for describing quantum Calderbank-Shor-Steane (CSS) codes. In this work, we extend this framework to construct a broad class of logical gates for general CSS codes, including the S, Hadamard, T, and (multi-)controlled-Z gates, under the condition where fault-tolerance or circuit-depth optimality is not necessarily imposed. We show that these logical gates can be expressed as exponential of polynomial functions of the electric and magnetic gauge fields, which allows us to derive explicit decompositions into physical gates. We further prove that their logical action depends only on the (co)homology classes of the corresponding logical qubits, establishing consistency as logical operations. Our results provide a systematic method for formulating logical gates for general CSS codes, offering new insights into the interplay between quantum error correction, algebraic topology, and quantum field theory.

The ultimate goal of quantum error correction is to create logical qubits with very low error rates (e.g. 1e-12) and assemble them into large-scale quantum computers capable of performing many (e.g. billions) of logical gates on many (e.g. thousands) of logical qubits. However, it is necessarily difficult to directly assess the performance of such high-quality logical qubits using standard Monte Carlo sampling because logical failure events become very rare. Building on existing approaches to this problem, we develop three complementary techniques to characterize the rare-event regime for general quantum low-density parity-check (qLDPC) codes under circuit noise. (I) We propose a well-motivated, low-parameter ansatz for the failure spectrum (the fraction of fault sets of each size that fail) that empirically fits all the QEC systems we studied and predicts logical error rates at all physical error rates. (II) We find min-weight logical operators of syndrome measurement circuits and exactly compute the number of min-weight failing configurations. (III) We generalize the splitting method to qLDPC codes using multi-seeded Metropolis sampling to improve convergence for systems with many inequivalent logical operators. We apply these tools to distance-6, -12, and -18 bivariate bicycle codes under circuit noise, observing strong low-error-rate performance with the recently proposed Relay decoder but also considerable scope for further improvement.

Micromotion in radio-frequency ion traps is generally considered detrimental for quantum logic gates, and is typically minimized in state-of-the-art experiments. However, as a deterministic effect, it can be incorporated into quantum control frameworks aimed at designing high-fidelity quantum logic controls. In this work, we demonstrate that micromotion can be beneficial to the design of fast gates utilizing the radial modes of a two-ion crystal, particularly in the sub-trap-period regime where high-fidelity control sequences are identified with operation times ranging from hundreds of nanoseconds to microseconds. Through analysis of select fast gate solutions, we uncover the physical origin of micromotion enhancement and further study the induced gate error under experimental noises and control imperfections. This analysis establishes the feasibility of realising high-fidelity entangling gates in hundreds of nanoseconds using the micromotion-sensitive radial modes of trapped-ion crystals.

We propose a variational alternative to the Trotter-Suzuki decomposition that provides greater control over errors while preserving the unitary structure of time evolution. The variational parameters in our ansatz are derived from a global action principle, where Euler-Lagrange equations govern their optimal dynamics. Unlike conventional wavefunction-based variational methods, our approach specifically targets the time evolution operation and this allows a single set of optimized parameters to be applied to any initial state for a fixed Hamiltonian avoiding costly optimization procedures. Our method outperforms the standard Trotter-Suzuki formulas, typically achieving higher accuracy than higher-order Suzuki schemes. This translates directly to quantum computing applications, where it enables the design of quantum circuits with fewer gates which reduces noise and improves precision. Although we focus on quantum dynamics, the method is broadly applicable to problems involving general time-evolution operators. Applied to various model Hamiltonians, our approach reduces errors by factors of 2 to 5 compared to Trotter-Suzuki decompositions, demonstrating its promise for accurate quantum simulation with improved efficiency. In certain cases, the variational ansatz achieves higher accuracy than more complex higher-order Suzuki formulas while reducing the gate count by nearly half within a single circuit layer. Furthermore, we derive approximate analytical expressions for the variational parameters up to cubic order in time, valid for generic Hamiltonians. These approximations enable long-time quantum simulations with improved accuracy over equivalent Suzuki decompositions, providing ready-to-use evolution formulas that match Suzuki's gate complexity while delivering better performance.

Drawing on the analogy between intrinsic and extrinsic geometry, we define an intrinsic quantum code as a subspace of a group representation. We show how this abstract code rules over any physical (extrinsic) realization by dictating its error-correction properties. By finding one intrinsic code, we simultaneously uncover properties of all its realizations. This approach brings diverse codes into a unified framework and binds them through a single underlying symmetry.

We present an architecture for the generation of GKP states in which quadrature squeezing operations are used to control the average photon number statistics of probabilistic photon number measurements on Gaussian resource states. Specifically, we present an architecture employing a teleportation-based squeezing protocol and polynomial-gate applications integrated into a time-multiplexed multi-mode cluster state to generate cat states with high amplitudes, which are consequently used to generate GKP states with high quadrature effective squeezing. Compared to our previous work, in addition to using squeezing as a resource, the present architecture reduces damping and noise by minimizing the number of homodyne measurements required in GKP state generation. We demonstrate the effectiveness of these improvements - including dynamic input-state resetting and an improved breeding algorithm - by achieving a fault-tolerance threshold of 11.5 dB cluster squeezing using the RHG surface code for error correction, without requiring active switching or photon-number resource states.

The recently introduced tile codes are a promising alternative to surface codes, combining two-dimensional locality with higher encoding efficiency. While surface codes are well understood in terms of their logical operators and boundary behavior, much less is known about tile codes. In this work, we establish a natural and precise description of their logical operator space. We prove that, under mild assumptions, any tile code admits a canonical symplectic basis of logical operators supported along lattice boundaries, which can be generated efficiently by a simple cellular automaton with the number of update rules only depending on the non-locality of the tile code. Further, we develop algebraic and algebro-geometric frameworks for tile codes, by resolving them by translationally invariant Pauli stabilizer models and showing that they arise as derived sections of a Koszul complex on $\mathbb{P}^1 \times \mathbb{P}^1$. Finally, we introduce the concept of derived automorphisms for quantum codes. These are automorphism-like operations that can exist even for codes that do not have symmetries. We explain how derived automorphisms can be implemented for tile codes in a low-overhead and fault-tolerant manner by extending the lattice on one side and shrinking it on the other. While this operation is trivial for the surface code, it induces a product of logical CNOT gates on the encoded information. Our results provide new structural insights into tile codes and lay the groundwork for tile codes as building blocks for fault-tolerant quantum computation.

As quantum computers continue to improve and support larger, more complex computations, smart control hardware and compilers are needed to efficiently leverage the capabilities of these systems. This paper introduces a novel approach to enhance the execution of quantum algorithms on distributed quantum systems. The proposed method involves the development of a hardware design that supports parallel instruction execution and a compiler that modifies the order of instructions to increase parallelism opportunities. The hardware design can be flexibly configured to facilitate parallel execution of instructions that have identical parameters. Furthermore, the compiler uses the underlying hardware constraints to intelligently reorder and decompose instructions to avoid dependencies. The compiler, hardware, and their combination are evaluated using a runtime calculator and a benchmark quantum algorithm set. The results demonstrate a significant speedup, achieving a maximum average speedup of 16.5x and a maximum single-benchmark speedup of 56.2x relative to a baseline, serial execution model. Furthermore, we show a speedup can be obtained across all benchmarks using any of the proposed hardware schemes, although the degree of speedup is largely dependent on the type of quantum algorithm. Taken together, the results of this paper represent a significant step towards realizing high-performance quantum computing systems.

We establish a new performance benchmark for the fault-tolerant syndrome extraction of [[7, 1, 3]] Steane code with a dynamic protocol. Our method is built on two highly optimized circuits derived using fault-equivalent ZX-rewrites: a primary fault-tolerant circuit with 14 CNOTs and an efficient non-fault-tolerant recovery circuit with 11 CNOTs. The protocol uses an adaptive response to internal faults, discarding flagged measurements and falling back to the recovery circuit to correct potentially detrimental errors. Monte Carlo simulations confirm the efficiency of our protocol, reducing the logical error rate per cycle by an average of ~14.3% relative to the optimized Steane method [arXiv:2506.17181] and ~17.7% compared to the Reichardt's three-qubit method [arXiv:1804.06995], the leading prior techniques.

Fault tolerant quantum computation over distributed quantum computing (DQC) platforms requires careful evaluation of resource requirements and noise thresholds. As quantum hardware advances toward modular and networked architectures, various fault tolerant DQC schemes have been proposed, which can be broadly categorized into three architectural types. Type 1 architectures consist of small quantum nodes connected via Greenberger-Horne-Zeilinger (GHZ) states, enabling nonlocal stabilizer measurements. Type 2 architectures distribute a large error correcting code block across multiple modules, with most stabilizer measurements remaining local, except for a small subset at patch boundaries that are performed using nonlocal CNOT gates. Type 3 architectures assign code blocks to distinct modules and can perform fault tolerant operations such as transversal gates, lattice surgery, and teleportation to implement logical operations between code blocks. Using the planar surface code and toric code as representative examples, we analyze how the resource requirements, particularly the number of Bell pairs and the average number of generation attempts, scale with increasing code distance across different architectural designs. This analysis provides valuable insights for identifying architectures well suited to fault tolerant distributed quantum computation under near term hardware and resource constraints.

We show that given an instance of a bivariate bicycle (BB) code, it is possible to generate an infinite sequence of new BB codes using increasingly large covering graphs of the original code's Tanner graph. When a BB code has a Tanner graph that is a $h$-fold covering of the base BB code's Tanner graph, we refer to it as a $h$-cover code. We show that for a BB code to be a $h$-cover code, its lattice parameters and defining polynomials must satisfy simple algebraic conditions relative to those of the base code. By extending the graph covering map to a chain map, we show there are induced projection and lifting maps on (co)homology that enable the projection and lifting of logical operators and, in certain cases, automorphisms between the base and the cover code. The search space of cover codes is considerably reduced compared to the full space of possible polynomials and we find that many interesting examples of BB codes, such as the $[[144,12,12]]$ gross code, can be viewed as cover codes. We also apply our method to search for BB codes with weight 8 checks and find many codes, including a $[[64,14,8]]$ and $[[144,14,14]]$ code. For an $h$-cover code of an $[[n,k,d]]$ BB code with parameters $[[n_h = hn, k_h, d_h]]$, we prove that $k_h \geq k$ and $d_h \leq hd$ when $h$ is odd. Furthermore if $h$ is odd and $k_h = k$, we prove the lower bound $d \leq d_h$. We conjecture it is always true that an $h$-cover BB code of a base $[[n,k,d]]$ BB code has parameters $[[n_h = hn, k_h \geq k, d \leq d_h \leq hd]]$. While the focus of this work is on bivariate bicycle codes, we expect these methods to generalise readily to many group algebra codes and to certain code constructions involving hypergraph, lifted, and balanced products.

Dynamical decoupling (DD) is a key technique for suppressing decoherence and preserving the performance of quantum algorithms. We introduce a measurement-based DD (MDD) protocol that determines control unitary gates from partial measurements of noisy subsystems, with measurement overhead scaling linearly with the number of subsystems. We prove that, under local energy relaxation and dephasing noise, MDD achieves the maximum entanglement fidelity attainable by any DD scheme based on bang-bang operations to first order in evolution time. On the IBM Eagle processor, MDD achieved up to a $450$-fold improvement in the success probability of a $14$-qubit quantum Fourier transform, and improved the accuracy of ground-state energy estimation for $N_2$ in the $56$-qubit sample-based quantum diagonalization compared with the standard XX-pulse DD. These results establish MDD as a scalable and effective approach for suppressing decoherence in large-scale quantum algorithms.

We analytically investigate the switching rate in a two-photon driven Kerr oscillator with finite detuning and two-photon dissipation. This system exhibits quantum bistability and supports a logical manifold for a bosonic qubit. Using Kramer's theory together with the $P$-representation, we derive an analytical expression for the bit-flip error rate within the potential-barrier approximation. The agreement is demonstrated between analytical calculations and numerical simulations obtained by diagonalization of the Liouvillian superoperator. In the purely dissipative limit, the switching rate increases monotonically with detuning, as the two metastable states approach each other in phase space. However, the exponential contribution to the bit-flip rate exhibits a nontrivial dependence on system parameters, extending beyond the naive scaling with the average photon number. In the presence of large Kerr nonlinearity, the switching rate becomes a nonmonotonic function of the detuning and reaches a minimum at a finite detuning. This effect arises because detuning lowers the activation barrier for weak nonlinearity but increases it for large ones, ensuring a minimum of the switching-rate at nonzero detuning. These results establish key conditions for optimizing the performance of critical cat qubits and are directly relevant for the design of scalable superconducting bosonic quantum architectures.

Hardware-friendly quantum low-density parity-check (QLDPC) decoders are commonly built upon belief propagation (BP) processing. Yet, quantum degeneracy often prevents BP from achieving reliable convergence. To overcome this fundamental limitation, we propose the restart belief (RB) decoder, an iterative BP-based algorithm inspired by branch-and-bound optimization principles. From our analysis we find that the RB decoder represents both the fastest and most accurate decoding algorithm applicable to QLDPC codes to date, conceived with the explicit goal of approaching error correction up to the code distance.

Quantum error mitigation (QEM) has been proposed as a class of hardware-friendly error suppression techniques. While QEM has been primarily studied for mitigating errors in the estimation of expectation values of observables, recent works have explored its application to estimating noiseless probability distributions. In this work, we propose two protocols to improve the accuracy of QEM for probability distributions, inspired by techniques in software engineering. The first is the N-version programming method, which compares probability distributions obtained via different QEM strategies and excludes the outlier distribution, certifying the feasibility of the error-mitigated distributions. The second is a consistency-based method for selecting an appropriate extrapolation strategy. Specifically, we prepare $K$ data points at different error rates, choose $L<K$ of them for extrapolation, and evaluate error-mitigated results for all $\binom{K}{L}$ possible choices. We then select the extrapolation method that yields the smallest variance in the error-mitigated results. This procedure can also be applied bitstring-wise, enabling adaptive error mitigation for each probability in the distribution.

We present a systematic numerical construction of a universal quantum gate set for topological quantum computation based on the non-semisimple Ising anyons model. Using the elementary braiding matrices (EBMs) of this model by the Monte Carlo-enhanced Solovay-Kitaev algorithm (MC-enhanced SKA), we achieve high-fidelity approximations of standard one-qubit gates (Hadamard H-gate and phase T-gate). Remarkably, a recursion level of just three suffices to meet the fidelity requirements for fault-tolerant quantum computation. Our numerical results demonstrate that for the parameter α /in (2, 2.031], a single braiding operation can approximate the local equivalence class [CNOT] with high precision and great unitary measurement. Specifically, at α = 2.031, 2.047, and 2.063, we successfully construct a universal gate set {H-gate, T-gate, CNOT-gate} with high accuracy. This work establishes a new pathway towards universal quantum computation using non-semisimple Ising anyons.

Color codes present distinct advantages for fault-tolerant quantum computing, such as high encoding rates and the transversal implementation of Clifford gates. However, existing matching-based decoders for the color codes such as the restricted decoder (Kubica and Delfosse, 2023), suffer from limited decoding performance. Inspired by the global decoding insight of the unified decoder (Benhemou et al., 2023), this paper introduces a correlated decoder for the 4.8.8 color code, which improves upon the conventional restricted decoder by leveraging correlations between restricted lattices, and is derived by mapping the correlated matching decoder for the surface code onto the color code lattice. Analytical and numerical results show that the correlated decoder achieves higher thresholds than the restricted and unified decoders, while matching the performance of the unified decoder at very low physical error rates. Under the code capacity and phenomenological noise models, the estimated thresholds for the color code against bit-flip error are 10.38% and 3.13%, respectively. Furthermore, by applying the surface-color code mapping, the thresholds of 16.62% and 3.52% are obtained for the surface code against depolarizing noise.

Quantum computing is an emerging computational paradigm with the potential to outperform classical computers in solving a variety of problems. To achieve this, quantum programs are typically represented as quantum circuits, which must be optimized and adapted for target hardware through quantum circuit compilation. We introduce ZX-DB, a data-driven system that performs quantum circuit simplification and rewriting inside a graph database using ZX-calculus, a complete graphical formalism for quantum mechanics. ZX-DB encodes ZX-calculus rewrite rules as standard openCypher queries and executes them on an example graph database engine, Memgraph, enabling efficient, database-native transformations of large-scale quantum circuits. ZX-DB integrates correctness validation via tensor and graph equivalence checks and is evaluated against the state-of-the-art PyZX framework. Experimental results show that ZX-DB achieves up to an order-of-magnitude speedup for independent rewrites, while exposing pattern-matching bottlenecks in current graph database engines. By uniting quantum compilation and graph data management, ZX-DB opens a new systems direction toward scalable, database-supported quantum computing pipelines.

Quantum computers have steadily improved over the last decade, but developing fault-tolerant quantum computing (FTQC) techniques, required for useful, universal computation remains an ongoing effort. Key elements of FTQC such as error-correcting codes and decoding are supported by a rich bed of stabilizer simulation software such as Stim and CHP, which are essential for numerically characterizing these protocols at realistic scales. Recently, experimental groups have built nascent high-dimensional quantum hardware, known as qudits, which have a myriad of attractive properties for algorithms and FTQC. Despite this, there are no widely available qudit stabilizer simulators. We introduce the first open-source realization of such a simulator for all dimensions. We demonstrate its correctness against existing state vector simulations and benchmark its performance in evaluating and sampling quantum circuits. This simulator is the essential computational infrastructure to explore novel qudit error correction as earlier stabilizer simulators have been for qubits.

We present the Lukasiewicz logic as a viable system for an implication algebra on a system of qubits. Our results show that the three valued Lukasiewicz logic can be embedded in the stabilized space of an arbitrary quantum error correcting stabilizer code. We then fully characterize the non trivial errors that may occur up to group isomorphism. Lastly, we demonstrate by explicit algorithmic example, how any algorithm consistent with the Lukasiewicz logic can immediately run on a quantum system and utilize the indeterminate state.

Quantum computers based on cold-atom arrays offer long-lived qubits with programmable connectivity, yet their progress toward fault-tolerant operation is limited by the relatively low fidelity of site-selective local control. We introduce an artificial-intelligence (AI) framework that overcomes this limitation. Trained on atom-laser dynamics, a deep neural network autonomously designs composite pulses that improve local control fidelities tenfold while remaining compatible with existing control hardware. We further demonstrate the robustness of these pulses against optical aberrations and beam misalignment. This approach establishes AI-trained pulse compilation for high-fidelity qubit control and can be readily extended to other atom-like platforms, such as trapped ions and solid-state color centers.

Quantum error correction is essential for fault-tolerant quantum computing. However, standard methods relying on active measurements may introduce additional errors. Autonomous quantum error correction (AQEC) circumvents this by utilizing engineered dissipation and drives in bosonic systems, but identifying practical encoding remains challenging due to stringent Knill-Laflamme conditions. In this work, we utilize curriculum learning enabled deep reinforcement learning to discover Bosonic codes under approximate AQEC framework to resist both single-photon and double-photon losses. We present an analytical solution of solving the master equation under approximation conditions, which can significantly accelerate the training process of reinforcement learning. The agent first identifies an encoded subspace surpassing the breakeven point through rapid exploration within a constrained evolutionary time-frame, then strategically fine-tunes its policy to sustain this performance advantage over extended temporal horizons. We find that the two-phase trained agent can discover the optimal set of codewords, i.e., the Fock states $\ket{4}$ and $\ket{7}$ considering the effect of both single-photon and double-photon loss. We identify that the discovered code surpasses the breakeven threshold over a longer evolution time and achieve the state-of-art performance. We also analyze the robustness of the code against the phase damping and amplitude damping noise. Our work highlights the potential of curriculum learning enabled deep reinforcement learning in discovering the optimal quantum error correct code especially in early fault-tolerant quantum systems.

The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains computationally challenging for multiqubit systems due to exponential scaling. We present a machine learning framework that efficiently predicts the quantum W-distance by extracting physically meaningful features from quantum state pairs, including Pauli measurements, statistical moments, quantum fidelity, and entanglement measures. Our approach employs both classical neural networks and traditional machine learning models. On three-qubit systems, the best-performing Random Forest model achieves near-perfect accuracy ($R^2 = 0.9999$) with mean absolute errors on the order of $10^{-5}$. We further validate the framework's practical utility by successfully verifying two fundamental theoretical propositions in quantum information theory: the bound on measurement probability differences between unitary operations and the $W_1$ gate error rate bound. The results establish machine learning as a viable and scalable alternative to traditional numerical methods for W-distance computation, with particular promise for real-time quantum circuit assessment and error correction protocol design in NISQ devices.

Quantum data learning (QDL) provides a framework for extracting physical insights directly from quantum states, bypassing the need for any identification of the classical observable of the theory. A central challenge in many-body physics is that the identity of quantum phases, especially those with topological order, are often inaccessible through local observables or simple symmetry-breaking diagnostics. Here, we apply QDL techniques to the 2+1-dimensional toric-code loop-gas model in a magnetic field. Ground states are generated across multiple lattice sizes using a parametrized loop-gas circuit (PLGC) with a variational quantum-eigensolver (VQE) approach. We then train a quantum convolutional neural network (QCNN) across the full field-parameter range to perform phase classification and capture the overall phase structure. We also employ a physics-aware training protocol that excludes the near-critical region (0.2 <= x <= 0.4)) around (x_c = 0.25), the phase-transition point estimated by quantum Monte Carlo, reserving this window for testing to evaluate the ability of the model to learn the phase transition. In parallel, we implement an unsupervised quantum k-means method based on state overlaps, which partitions the dataset into two phases without prior labeling. Our supervised QDL approach recovers the phase structure and accurately locates the phase transition, in close agreement with previously reported values; the unsupervised QDL approach recovers the phase structure and locates the phase transition with a small offset as expected in finite volumes; both QDL methods outperform classical alternatives. These findings establish QDL as an effective framework for characterizing topological quantum matter, studying finite volume effects, and probing phase diagrams of higher-dimensional systems.

In previous work, we developed a method for computing two-point correlators by decomposing the mode degrees of freedom into fast and slow components. Building on this framework, we present a numerical implementation to study the evolution of primordial scalar perturbations under controlled state deformations induced by the simplest environment corrections from the Lindblad equation. Our approach generalizes to an arbitrary number of degrees of freedom and does not rely on the slow-roll approximation. The computational routine is numerically efficient and allows users to configure arbitrary sequences of decoherence events, with full control over their duration, shape, amplitude and effective wavelength range. The resulting outputs are compatible with nonlinear numerical codes, enabling studies of how decoherence effects propagate during reheating.

In this thesis, we explore the intersection of two fundamental subfields of quantum information theory: quantum coherence and contextuality. Despite their apparent differences, both areas address key issues relevant to the foundations and applications of quantum theory. By developing a novel graph-theoretic approach, extending a framework recently introduced by Galvão and Brod (Phys. Rev. A 101, 062110, 2020), we establish a formal connection between inequality-based witnesses of quantum coherence and noncontextuality inequalities. Our key contributions include: the development of a graph-theoretic framework for generating coherence and contextuality witnesses; a formal mapping between the inequalities that follows from the work by Galvão and Brod to existing noncontextuality inequalities; the conceptualization of a relational form of quantum coherence; a proof of contextual advantage for the task of quantum interrogation; and the discovery of an infinite family of coherence witnesses that also require quantum states in Hilbert spaces of specific dimensions.

As quantum simulators are scaled up to larger system sizes and lower noise rates, non-Markovian noise channels are expected to become dominant. While provably efficient protocols for Markovian models of quantum simulators, either closed system models (described by a Hamiltonian) or open system models (described by a Lindbladian), have been developed, it remains less well understood whether similar protocols for non-Markovian models exist. In this paper, we consider geometrically local lattice models with both quantum and classical non-Markovian noise and show that, under a Gaussian assumption on the noise, we can learn the noise with sample complexity scaling logarithmically with the system size. Our protocol requires preparing the simulator qubits initially in a product state, introducing a layer of single-qubit Clifford gates and measuring product observables.

Solving excited states is a challenging task for interacting systems. For one-dimensional critical systems, however, excited states can be directly accessed from the eigenvectors of the local effective Hamiltonian that is constructed from the ground state obtained by variational matrix product state (MPS) optimization. Despite its numerical success, the theoretical mechanism underlying this method has remained largely unexplored. In this work, we provide a conformal field theory (CFT) perspective that helps elucidate this connection. The key insight is that this construction effectively uses a truncated basis of ground-state Schmidt vectors to represent excited states, where the contribution of each Schmidt vector can be expressed as a CFT correlation function and shown to decay with increasing Schmidt index. The CFT analysis further predicts an entanglement-spectrum transition of excited states as the ratio of the subsystem size to the total system size is varied. Our numerical results support this picture and demonstrate a reorganization of the entanglement spectrum into distinct conformal towers as this ratio changes.

The aim of a quantum network is to enable the generation of end-to-end entangled links between end nodes of the network, so that they can execute quantum network applications. To facilitate this, it is desirable to have robust control of the network in order to be able to provide a reliable service to the end nodes. In recent work arXiv:2503.12582, we proposed a modular control architecture for a generate-when-request type network. This control architecture enables quantum network applications to be executed on end nodes running a modern operating system such as QNodeOS arXiv:2407.18306. In that work, we performed an evaluation of our architecture based on a proof-of-concept implementation. In the course of performing this evaluation, we discovered many outstanding questions and challenges. These relate not only to implementing our specific control architecture, but also to the design of any quantum network control architecture. Here, we describe some outstanding questions and challenges, discuss possible solutions, and identify where existing protocols require adaptation or new protocols must be designed.

Open quantum systems far from thermal equilibrium can exhibit remarkable physical phenomena including topological properties without a direct equilibrium counterpart. Along these lines, in periodically driven dissipative systems within the effective non-Hermitian (NH) Hamiltonian approximation spectral winding numbers have been linked to intriguing nonreciprocal transport properties. Here, going beyond an NH Hamiltonian description, we introduce and study a microscopic lattice model of a driven open quantum system described by a Markovian quantum master equation, which exhibits the mentioned spectral winding within a NH approximation. By encompassing quantum jump processes in the topological analysis, we uncover a distinct \emph{jump-induced} topological phase, which qualitatively corresponds to the richer non-reciprocal transport properties of the fully quantum model. In addition, we find that the NH skin effect, i.e.~the accumulation of a macroscopic number of eigenstates at one end of the system, is already visible in the transient dynamics even for systems with periodic boundary conditions. Our results exemplify the subtle correspondence between NH topological properties and physical manifestations of Liouvillian topological properties in open quantum systems, thus providing a theoretical framework towards understanding unidirectional transport in quantum dissipative Floquet dynamics.

Observation of the quantum Mpemba effect has spurred much interest in its enabling conditions and its relation to the classical counterpart. Here, we consider weakly open many-body quantum systems initialized in different thermal states and examine when the initially farther state relaxes to the (non-equilibrium) steady state faster. We claim that the number of conserved quantities in the unitary part plays a crucial role: the Mpemba effect is possible only when the Hamiltonian commutes with other extensive operators or is integrable. The reason lies in the dynamical evolution happening in spaces of different dimensions. When energy is the only approximately conserved quantity, dissipation pushes the dynamics within a single-parameter manifold of different thermal states. In contrast, for Hamiltonians with several conserved quantities, the dynamics drift in the multi-dimensional space of generalized Gibbs ensembles, whose distance to the steady state is less trivial. We provide numerical results for large system sizes using tensor networks and free-fermion techniques, thereby supporting our claim.

Significant developments made in quantum hardware and error correction recently have been driving quantum computing towards practical utility. However, gaps remain between abstract quantum algorithmic development and practical applications in computational sciences. In this Perspective article, we propose several properties that scalable quantum computational science methods should possess. We further discuss how block-encodings and polynomial transformations can potentially serve as a unified framework with the desired properties. We present recent advancements on these topics including construction and assembly of block-encodings, and various generalizations of quantum signal processing (QSP) algorithms to perform polynomial transformations. We also highlight the scalability of QSP methods on parallel and distributed quantum architectures. Promising applications in simulation and observable estimation in chemistry, physics, and optimization problems are presented. We hope this Perspective serves as a gentle introduction of state-of-the-art quantum algorithms to the computational science community, and inspires future development on scalable quantum computational science methodologies that bridge theory and practice.

The excellent sensitivities of quantum sensors are a double-edged sword: minuscule quantities can be observed, but any undesired signal acts as noise. This is challenging when detecting quantities that are obscured by such noise. Decoupling sequences improve coherence times and hence sensitivities, though only AC signals in narrow frequency bands are distinguishable. Alternatively, comagnetometers operate gaseous spin mixtures at high temperatures in the self-compensating regime to counteract slowly varying noise. These are applied with great success in various exotic spin-interaction searches. Here, we propose a method that decouples specific DC fields from DC and AC magnetic noise. It requires any spin cluster where the effect on each individual spin is different for the target field and local magnetic fields, which allows for a different approach compared to comagnetometers. The presented method has several key advantages, including an orders-of-magnitude increase in noise frequencies to which we are resistant. We explore electron-spin nuclear-spin pairs in nitrogen-vacancy centres in diamond, with a focus on their merit for light dark-matter searches. Other applications include gradient sensing, quantum memory, and gyroscopes.

Adiabatic reverse annealing (ARA) is an improvement to conventional quantum annealing (QA) that uses an initial guess at the desired ground state to circumvent problematic phase transitions. Despite encouraging results in the closed-system setting, Ref. [1] has suggested on the basis of numerical simulations that ARA may lose its advantage in the presence of decoherence. Here, we revisit this problem from a more analytical perspective. Using the $p$-spin model as a solvable example, together with the adiabatic master equation to describe the effects of the environment (valid at weak coupling), we show that ARA can in fact succeed in open systems but that the temperature of the environment plays a key role. We first demonstrate that, in the adiabatic limit, the system will follow the instantaneous equilibrium state as long as the protocol does not pass through any (finite-temperature) phase transitions. Given this, there are two distinct mechanisms by which ARA can break down at high temperature: either there are no paths that avoid transitions, or the equilibrium state itself is disordered. When the temperature is sufficiently low that neither of these occur, then ARA succeeds. Remarkably, there are even situations in which the environment benefits ARA: we find parameter values for which no transition-avoiding paths exist at zero temperature but such paths appear at non-zero temperature.

We study the real-time dynamics of multi-party entanglement signals in chaotic quantum many-body systems including but not necessarily restricted to holographic conformal field theories. We find that scrambling dynamics generates multiparty entanglement with rich structure including: (a) qualitatively different dynamical behaviours for different signals, likely reflecting different dynamics for different kinds of entanglement patterns, (b) discontinuities indicating dynamical phase transitions in the entanglement structure, (c) transient and non-monotonic multiparty entanglement, and (d) periods during which the extensive entanglement of some regions is entirely multipartite. Our main technical tool is the membrane theory of entanglement dynamics.

The development of nonlinear and frequency-tunable superconducting microwave circuits for operation in large magnetic fields is of high relevance for hybrid quantum systems such as spin resonance spectrometers, microwave quantum magnonics, dark matter axion detectors or flux-mediated optomechanics. With these exciting perspectives in mind, we investigate niobium-based circuits with integrated nano-constriction quantum interferometers in magnetic in-plane fields up to several hundred mT. Our experiments reveal an unexpected and pronounced field-induced asymmetry in the bias-flux response of the circuits, which is demonstrated to originate from a field-induced Josephson-diode effect within the nano-constrictions and which considerably enhances the circuit figures of merit in a magnetic field. An intuitive macroscopic Josephson-diode model attributes the effect to inhomogeneous constriction properties and provides us with the diode current-phase relation as a function of the in-plane field. Finally, we demonstrate that in the diode-state the circuit Kerr nonlinearity is bimodal in frequency, not only eliminating alternative explanations for the bias-flux-asymmetries but also being potentially useful for quantum circuit applications. Overall, our report underlines that niobium nano-constriction circuits belong to the most promising candidates for high-field hybrid quantum systems and reveals the untapped potential of combining Josephson nano-diodes with microwave quantum circuits.

We present a machine learning framework to study the dynamics of entropy vectors and quantum resources, including entanglement and magic, focusing on violations of entropy inequalities. Using a reinforcement learning agent formulated as a Markov decision process, we identify quantum circuits that optimally navigate the entropy vector space to generate violations of Ingleton's inequality. We complement this approach with a classical optimization algorithm to produce arbitrary numbers of Ingleton-violating states, with tunable degrees of violation, and empirically determine the maximal attainable violation for Ingleton's inequality. Our analysis reveals characteristic patterns of quantum resources that accompany Ingleton violation. A comprehensive statistical analysis shows that Ingleton-violating states occupy sharply-defined, isolated regions of the Hilbert space, and are extremely rare. Together, these results establish a unified computational toolkit for studying entropy vector dynamics, tracking quantum resource evolution, and engineering circuits with controlled information-theoretic features.

We propose a momentum-space based variational quantum eigensolver (VQE) framework for simulating quasiparticle excitations in interacting quantum many-body systems on near-term quantum devices. Leveraging translational invariance and other symmetries of the Hamiltonian, we reconstruct the momentum-resolved quasiparticle excitation spectrum through targeted simulation of low-lying excited states using VQE. We construct a translationally symmetric variational ansatz designed to evolve a free-fermion particle-hole excited state with definite momentum $q$ to an excited state of the interacting system at the same momentum, employing a fermionic fast Fourier transform (FFFT) circuit coupled to a Hamiltonian Variational Ansatz (HVA) circuit. Even though the particle number is not explicitly conserved in the variational ansatz, the correct quasiparticle state is reached by energetic optimization. We benchmark the performance of the proposed VQE implementation on the XXZ Hamiltonian, which maps onto the Tomonaga-Luttinger liquid in the fermionic representation. Our numerical results show that VQE can capture the low-lying excitation spectrum of the bosonic quasiparticle/two-spinon dispersion of this model at various interaction strengths. We estimate the renormalized velocity of the quasiparticles by calculating the slope of the dispersion near zero momentum using the VQE-optimized energies at different system sizes, and demonstrate that it closely matches theoretical results obtained from Bethe ansatz. Finally, we highlight extensions of our proposed VQE implementation to simulate quasiparticles in other interacting quantum many-body systems.

We present a comprehensive and pedagogical formulation of Bayesian multiparameter quantum estimation, providing explicit conditions for achieving minimum quadratic losses. Within this framework, we analyse the role of measurement incompatibility and establish its quantitative effect on attainable precision. We achieve this by deriving upper bounds based on the pretty good measurement -- a notion originally developed for hypothesis testing -- combined with the evaluation of the Nagaoka--Hayashi lower bound. In general, we prove that, as in the many-copy regime of local estimation theory, incompatibility can at most double the minimum loss relative to the idealised scenario in which individually optimal measurements are assumed jointly implementable. This result implies that, in many practical situations, the latter may provide a sufficient and computationally efficient benchmark without solving the full optimisation problem. Our results, which we illustrate through a range of applications, including discrete quantum phase imaging, phase and dephasing estimation, and qubit sensing, provide analytical and numerical tools for assessing ultimate precision limits and the role of measurement incompatibility in Bayesian multiparameter quantum metrology. We also provide an open-source package that implements all bounds discussed here, enabling practical evaluation and comparison across quantum metrological models.

We show that operator dynamics in U(1) symmetric systems are constrained by two independent conserved charges and construct a non-Abelian operator size basis that respects both, enabling a symmetry-resolved characterization of operator growth. The non-Abelian operator size depends on the operator's nonlocal structure and is organized by an SU(2) algebra. Operators associated with large total angular momentum are relatively simple, while those with small angular momentum are more complex. Operator growth is thus characterized by a reduction in angular momentum and can be probed using out-of-time-ordered correlators. Using the charge-conserving Brownian Sachdev-Ye-Kitaev model, we derive an exact classical master equation that governs the size distribution, the distribution of an operator expanded in this basis, for arbitrary system sizes. The resulting dynamics reveal that the size distribution follows a chi-squared form, with the two conserved charges jointly determining the overall time scale and the shape of the distribution. In particular, single-particle operators retain a divergent peak at large angular momentum throughout the time evolution.

The integration of sensing and communication functionalities within a common system is one of the main innovation drivers for next-generation networks. In this paper, we introduce a quantum integrated sensing and communication (QISAC) protocol that leverages entanglement in quantum carriers of information to enable both superdense coding and quantum sensing. The proposed approach adaptively optimizes encoding and quantum measurement via variational circuit learning, while employing classical machine learning-based decoders and estimators to process the measurement outcomes. Numerical results for qudit systems demonstrate that the proposed QISAC protocol can achieve a flexible trade-off between classical communication rate and accuracy of parameter estimation.

We present a detailed analysis of slowly driven quantum thermal machines based on interacting qubits within the framework of the Lindblad master equation. By implementing a systematic expansion in the driving rate, we derive explicit expressions for the rate of work of the driving forces, the heat currents exchanged with the reservoirs, and the entropy production up to second order, ensuring full thermodynamic consistency in the linear-response regime. The formalism naturally separates geometric and dissipative contributions, identified by a Berry curvature and a metric in parameter space, respectively. Analytical results show that the geometric heat pumped per cycle is bounded by $k_B T N_q \ln 2$ for $N_q$ non-interacting qubits, in direct analogy with the Landauer limit for entropy change. This bound can be surpassed when qubit interactions and asymmetric couplings to the baths are introduced. Numerical results for the interacting two-qubit system reveal a non-trivial role of the interaction between qubits and the coupling between the qubits and the baths in the behavior of the dissipated power. The approach provides a general platform for studying dissipation, pumping, and performance optimization in driven quantum devices operating as heat engines.

High-performance numerical quantum compilers rely on classical optimization, but are limited by slow numerical evaluations and a design that makes extending them with new instructions a difficult, error-prone task for domain experts. This paper introduces OpenQudit, a compilation framework that solves these problems by allowing users to define quantum operations symbolically in the Qudit Gate Language (QGL), a mathematically natural DSL. OpenQudit's ahead-of-time compiler uses a tensor network representation and an e-graph-based pass for symbolic simplification before a runtime tensor network virtual machine (TNVM) JIT-compiles the expressions into high-performance native code. The evaluation shows that this symbolic approach is highly effective, accelerating the core instantiation task by up to $\mathtt{\sim}20\times$ on common quantum circuit synthesis problems compared to state-of-the-art tools.

Quantum chemistry and optimization are two of the most prominent applications of quantum computers. Variational quantum algorithms have been proposed for solving problems in these domains. However, the design of the quantum circuit ansatz remains a challenge. Of particular interest is developing a method to generate circuits for any given instance of a problem, not merely a circuit tailored to a specific instance of the problem. To this end, we present a reinforcement learning (RL) approach to learning a problem-dependent quantum circuit mapping, which outputs a circuit for the ground state of a Hamiltonian from a given family of parameterized Hamiltonians. For quantum chemistry, our RL framework takes as input a molecule and a discrete set of bond distances, and it outputs a bond-distance-dependent quantum circuit for arbitrary bond distances along the potential energy curve. The inherently non-greedy approach of our RL method contrasts with existing greedy approaches to adaptive, problem-tailored circuit constructions. We demonstrate its effectiveness for the four-qubit and six-qubit lithium hydride molecules, as well as an eight-qubit H$_4$ chain. Our learned circuits are interpretable in a physically meaningful manner, thus paving the way for applying RL to the development of novel quantum circuits for the ground states of large-scale molecular systems.

We show that a distribution related to Gaussian Boson Sampling (GBS) on graphs can be sampled classically in polynomial time. Graphical applications of GBS typically sample from this distribution, and thus quantum algorithms do not provide exponential speedup for these applications. We also show that another distribution related to Boson sampling can be sampled classically in polynomial time.

Two-mode squeezing is central to entangled-photon generation and nonlinear interferometry, yet standard perturbative low-gain and Gaussian treatments obscure how photon-number amplitudes interfere, especially in multi-crystal geometries and at high gain. Here, we derive the exact analytic action of the two-mode squeezing operator on arbitrary Fock states to analyze nonlinear interferometers directly in the number basis at arbitrary squeezing strength. Within this framework, we find new physical interpretations of previously known quantum interference effects, and theoretically discover a new and unusual multi-photon interference effect in an experimental four-crystal geometry that could readily be observed in laboratories. Our work provides a compact analytic toolkit and concrete design rules for engineering multi-photon interference, with applications in quantum sensing, precision metrology, and advanced quantum state generation.

Quantum asymmetry and coherence are genuinely quantum resources that are essential to realize quantum advantage in information technologies. However, all quantum processes are fundamentally constrained by quantum speed limits, which raises the question on the corresponding bounds on the rate of consumption of asymmetry and coherence. In the present work, we derive a formulation of the quantum speed limit for observables in terms of the trace-norm asymmetry of the time-dependent quantum state relative to the observable. This version of the quantum speed limit can be shown to be directly relevant in weak measurements and quantum metrology. It can be further related to quantum coherence relative to the observable, and we obtain a complementary relation for the speed of three mutually unbiased observables for a single qubit. As an application, we derive a notion of a quantum thermodynamic speed limit.

In Ref. Ansari et al., dynamical quantum phase transitions (DQPTs) -- non-analyticities in the Loschmidt return rate at critical times -- are investigated in the presence of noise for a two-band model. The authors report that DQPTs persist even after averaging over the noise and they use their results to derive dynamical phase diagrams. In this comment we rigorously prove that in any two-dimensional Hilbert space the Loschmidt echo of two density matrices can only become zero if and only if both density matrices are pure. As a consequence, the existence of DQPTs in the considered scenario is strictly ruled out for non-zero noise because the considered averaging leads to a mixed state. We also investigate alternative natural ways to average over noise realizations and show that in all of them DQPTs are smoothed out.

We explore the non-reciprocal intracell hopping mediated non-Hermitian topological phases of an extended Su-Schrieffer-Heeger model hosting second-nearest-neighbour hopping. We microscopically analyze the phase boundaries using the non-Bloch momentum while the off-critical (critical) phases are directly associated with the gapped (gapless) nature of the non-Bloch bands that we derive from the characteristic equation using the gauge freedom. The non-Bloch momentum accurately reflects the bulk boundary correspondence (BBC) explaining the winding number profile under open boundary conditions. We examine the adiabatic dynamics to promote the concept of adiabatic charge transport in a non-Hermitian scenario justifying the BBC in spatio-temporal Bott index and non-Bloch Chern number. Once the non-Bloch bands experience no (a) gap-closing during the evolution of time, quantized flow of is preserved (broken). Our study systematically unifies the concept of non-Bloch bands for both static and driven situations.

We introduce a novel analytical approach for studying free-fermion (XX) chains with smoothly varying, site-dependent hoppings and magnetic fields. Building on a discrete WKB-like approximation applied directly to the recurrence relation for the single-particle eigenfunctions, we derive a closed-form expression for the local fermion density profile as a function of the Fermi energy, which is valid for arbitrary fillings, hopping amplitudes and magnetic fields. This formula reproduces the depletion and saturation effects observed in previous studies of inhomogeneous free-fermion chains, and provides a theoretical framework to understand entanglement entropy suppression in these models. We demonstrate the accuracy of our asymptotic formula in several chains with different hopping and magnetic field profiles. Our findings are thus the first step towards an analytical treatment of entanglement in free-fermion chains beyond the reach of conventional field-theoretic techniques.

This paper proposes an optimization of Quantum Key Distribution (QKD) Networks using Graph Neural Networks (GNN) framework. Today, the development of quantum computers threatens the security systems of classical cryptography. Moreover, as QKD networks are designed for protecting secret communication, they suffer from multiple operational difficulties: adaptive to dynamic conditions, optimization for multiple parameters and effective resource utilization. In order to overcome these obstacles, we propose a GNN-based framework which can model QKD networks as dynamic graphs and extracts exploitable characteristics from these networks' structure. The graph contains not only topological information but also specific characteristics associated with quantum communication (the number of edges between nodes, etc). Experimental results demonstrate that the GNN-optimized QKD network achieves a substantial increase in total key rate (from 27.1 Kbits/s to 470 Kbits/s), a reduced average QBER (from 6.6% to 6.0%), and maintains path integrity with a slight reduction in average transmission distance (from 7.13 km to 6.42 km). Furthermore, we analyze network performance across varying scales (10 to 250 nodes), showing improved link prediction accuracy and enhanced key generation rate in medium-sized networks. This work introduces a novel operation mode for QKD networks, shifting the paradigm of network optimization through adaptive and scalable quantum communication systems that enhance security and performance.

Classical particles in random potentials typically experience a percolation phase transition, being trapped in clusters of mean size $χ$ that diverges algebraically at a percolation threshold. In contrast, quantum transport in random potentials is controlled by the Anderson localization length, which shows no distinct feature at this classical critical point. Here, we present a comprehensive theoretical analysis of the semi-classical crossover between these two regimes by studying particle propagation in a one-dimensional, red speckle potential, which hosts a percolation transition at its upper bound. As the system deviates from the classical limit, we find that the algebraic divergence of $χ$ continuously connects to a smooth yet non-analytic increase of the localization length. We characterize this behavior both numerically and theoretically using a semi-classical approach. In this crossover regime, the correlated and non-Gaussian nature of the speckle potential becomes essential, causing the standard DMPK description for uncorrelated disorder to break down. Instead, we predict the emergence of a bimodal transmission distribution, a behavior normally absent in one dimension, which we capture within our semi-classical analysis. Deep in the quantum regime, the DMPK framework is recovered and the universal features of Anderson localization reappear.

Simulated annealing provides a heuristic solution to combinatorial optimization problems. The cost function of a problem is mapped onto the energy function of a physical many-body system, and, by using thermal or quantum fluctuations, the system explores the state space to find the ground state, which corresponds to the optimal solution of the problem. Studies have highlighted both the similarities and differences between thermal and quantum fluctuations. Nevertheless, fundamental understanding of thermal and quantum annealing remains incomplete, making it unclear how quantum annealing outperforms thermal annealing in which problem instances. Here, we investigate the many-body dynamics of thermal and quantum annealing by examining all possible interaction networks of $\pm J$ Ising spin systems up to seven spins. Our comprehensive investigation reveals that differences between thermal and quantum annealing emerge for particular interaction networks, indicating that the structure of the energy landscape distinguishes the two dynamics. We identify the microscopic origin of these differences through probability fluxes in state space, finding that the two dynamics are broadly similar, but that quantum tunnelling produces qualitative differences. Our results provide insight into how thermal and quantum fluctuations navigate a system toward the ground state in simulated annealing, and are experimentally verifiable in atomic, molecular, and optical systems. Furthermore, these insights may improve mappings of optimization problems to Ising spin systems, yielding more accurate solutions in faster simulated annealing and thus benefiting real-world applications in industry. Our comprehensive survey of interaction networks and visualization of probability flux can help to understand, predict, and control quantum advantage in quantum annealing.

The $W$ state, a canonical representative of multipartite quantum entanglement, plays a crucial role in quantum information science due to its robust entanglement properties. Quantum uncertainty relations, on the other hand, are a fundamental cornerstone of quantum mechanics. This paper introduces a novel approach to Identifying tripartite $W$ states by leveraging tripartite quantum uncertainty relations. By employing a specific set of non-commuting observables, we formulate an uncertainty-based criterion for identifying $W$ states and rigorously demonstrate its generality in distinguishing them from other tripartite entangled states, such as the Greenberger-Horne-Zeilinger state. Our approach bypasses the need for complete quantum state tomography, as it requires only the verification of a set of uncertainty inequalities for efficient $W$-state identification. This work provides a new theoretical tool for identifying multipartite entangled states and underscores the significant role of quantum uncertainty relations in entanglement characterization.

Quantum interference underpins many quantum information protocols but is typically studied in lossless Hermitian systems. Here, we reveal an exceptional point induced phase transition in two photon Hong Ou Mandel interference within a lossy coupled waveguide system. In the PT symmetric phase. interference is ultrasensitive to coupling strength, yielding sharp bunching antibunching switches. In the PT broken phase. it becomes robust oscillation free and propagation independent with coincidence probability stably tunable via coupling. These regimes enable enhanced quantum sensing and reliable two photon control for robust quantum information processing.

We explore several aspects of the categorical symmetry-resolved entanglement entropy (SREE) in two-dimensional Rational Conformal Field Theories (RCFTs) and express it directly in terms of the modular data of the theory. Motivated by arXiv:2409.02806, we provide a general formula for SREE that applies to symmetric (weakly/strongly) and cloaking boundary conditions as well as for fusion rings with multiplicities without invoking any SymTFT construction, relying instead on a purely 2d RCFT analysis. We check the formula against several explicit examples. Additionally, we study symmetry resolution for both categorical and invertible symmetries in (non-)diagonal RCFTs and comment on the subtleties that arise in these cases. Finally, we extend our analysis to diagonal non-unitary RCFTs, focusing on theories with generalized Haagerup-Izumi modular data, and find full agreement with the given formula.

In this work, we investigate the emergence and control of genuine tripartite entanglement in a hybrid cavity quantum electrodynamics architecture consisting of two linearly coupled single mode resonators, one of which interacts coherently with a two level atom. An analytical framework is developed in a weak driving regime, where the system dynamically supports a delocalized hybrid excitation shared by the two photonic modes and the atomic degree of freedom. Tripartite concurrence fill has been used to characterize and identify parameter regimes of maximal multipartite quantum correlation that can be generated in this model. Additionally, we demonstrate how dissipative rates and detuning asymmetries govern the conversion of bipartite entanglement into a genuinely tripartite state, establishing a controllable transition from localized Jaynes Cummings correlations to delocalized photonic atomic entanglement networks. These findings outline a clear route to engineering steady state multipartite quantum resources in coupled cavity QED platforms, with direct relevance to quantum networking, distributed quantum information processing, and photonic state routing in scalable quantum architectures.

The development of quantum internet demands on-chip quantum processor nodes and interconnection between the nodes. Path-encoded photonic qubits are suitable for on-chip quantum information processors, while time-bin encoded ones are good at long-distance communication. It is necessary to develop an on-chip converter between the two encodings to satisfy the needs of the quantum internet. In this work, a quantum photonic circuit is proposed to convert time-bin-encoded photonic qubits to path-encoded ones via a thin-film lithium niobate high-speed optical switch and low-loss matched optical delay lines. The performance of the encoding converter is demonstrated by the experiment of time-bin to path encoding conversion on the fabricated sample chip. The converted path qubits have an average fidelity higher than 97%. The potential of the encoding converter on applications in quantum networks is demonstrated by the experiments of entanglement distribution and quantum key distribution. The results show that the on-chip encoding converter can serve as a foundational component in the future quantum internet, bridging the gap between quantum information transmission and on-chip processing based on photons.

We study the optimal rates of emulation (also called interconversion) between quantum channels. When the source and the target channels are idempotent, we give a single-letter expression for the zero-error emulation capacity in terms of structural properties of the range of the two channels. This expression shows that channel emulation is not reversible for general idempotent channels. Furthermore, we establish a strong converse rate that matches with the zero-error emulation capacity when the source or the target channel is either an identity or a completely dephasing channel.

Optical cavities provide a powerful means to engineer light-matter hybrid states by coupling confined electromagnetic fields with matter excitations. Achieving in situ control of the coupling strength is essential for investigating how such hybridization evolves with the coupling strength. In this work, we use a symmetry-changing structural phase transition in lead halide perovskites to reversibly tune the phonon-photon coupling strength, leveraging the fact that their phonon frequencies and oscillator strengths are dictated by lattice symmetry. Terahertz time-domain spectroscopy of MAPbI3 embedded in nanoslot cavities reveals three polariton branches above the critical temperature Tc = 162.5 K, and the emergence of an additional branch below Tc, activated by a new phonon mode in the low-temperature phase. The full dispersion is accurately reproduced using a multimode Hopfield model, confirming that all normalized coupling strengths remain in the ultrastrong coupling regime. These results demonstrate symmetry-controlled tuning of ultrastrong coupling via phonon engineering in optical cavities.

Quantum batteries are quantum mechanical systems able to store and release energy in a controlled fashion. Among them, a special role is played by quantum structures defined as networks of two-level systems. In this context, it has recently been shown that the energy stored in free fermion quantum batteries is sensitive to the quantum phase diagram of the battery itself. This sensitivity is relevant for stabilizing the stored energy and designing optimal charging protocols. In this article, we explore universal charging behaviors of free fermion quantum batteries across quantum phase transitions. We first analyze a Dirac cone-like model to extract general features. Then, we verify our findings by means of two relevant lattice models, namely the Ising chain in a transverse field and the Haldane model.

Optomechanics with levitated nanoparticles is a promising way to combine very different types of quantum non-Gaussian aspects induced by continuous dynamics in a nonlinear or time-varying potential with the ones coming from discrete quantum elements in dynamics or measurement. First, it is necessary to prepare quantum non-Gaussian states using both methods. The nonlinear and time-varying potentials have been widely analyzed for this purpose. However, feasible preparation of provably quantum non-Gaussian states in a single mechanical mode using discrete photon detection has not been proposed yet for optical levitation. We explore pulsed optomechanical interactions combined with non-linear photon detection techniques to approach mechanical Fock states and confirm their quantum non-Gaussianity. We also predict the conditions under which the optomechanical interaction can induce multiple-phonon addition processes, which are relevant for $n$-phonon quantum non-Gaussianity. The practical applicability of quantum non-Gaussian states for sensing phase-randomized displacements is shown. Besides such applications, generating quantum non-Gaussian states of levitated nanoparticles can help to study fundamental questions of quantum thermodynamics, and macroscopic quantum effects.

For pure states, the quantum Berry curvature was well studied. However, the quantum curvature for mixed states has received less attention. From the concept of symmetric logarithmic derivative, we introduce a mixed-state quantum curvature and find that it plays a key role in the field of multi-parameter precision estimations. Through spectral decomposition, we derive the mixed-state Berry curvature for both the full-rank and non-full-rank density matrices. As an example, we obtain the exact expression of the Berry curvature for an arbitrary qubit state.

Quantum computing applications are an emerging field in high-energy physics. Its ambitious fusion with artificial intelligence is expected to deliver significant efficiency gains over existing methods and/or enable computation from a fundamentally different perspective. High-energy physics is a big data science that utilizes large-scale facilities, detectors, high-performance computing, and its worldwide networks. The experimental workflow consumes a significant amount of computing resources, and its annual cost will continue to grow exponentially at future colliders. In particular, pattern recognition is one of the most crucial and computationally intensive tasks. Three types of quantum computing technologies, i.e., quantum gates, quantum annealing, and quantum-inspired, are all actively investigated for high-energy physics applications, and each has its pros and cons. This article reviews the current status of quantum computing applications for pattern recognition at high-energy colliders.

Quantum neural networks (QNNs) are an analog of classical neural networks in the world of quantum computing, which are represented by a unitary matrix with trainable parameters. Inspired by the universal approximation property of classical neural networks, ensuring that every continuous function can be arbitrarily well approximated uniformly on a compact set of a Euclidean space, some recent works have established analogous results for QNNs, ranging from single-qubit to multi-qubit QNNs, and even hybrid classical-quantum models. In this paper, we study the approximation capabilities of QNNs for periodic functions with respect to the supremum norm. We use the Jackson inequality to approximate a given function by implementing its approximating trigonometric polynomial via a suitable QNN. In particular, we see that by restricting to the class of periodic functions, one can achieve a quadratic reduction of the number of parameters, producing better approximation results than in the literature. Moreover, the smoother the function, the fewer parameters are needed to construct a QNN to approximate the function.

We demonstrate channel-selective frequency up-conversion from telecom wavelengths around 1540 nm for optical fiber communication to visible wavelengths around 780 nm, based on second-order optical nonlinearity in a cavity of the converted modes. In our experiment, we selectively convert a light from any frequency mode within frequency-multiplexed telecom signals to a desired output mode, determined by the cavity resonances. Based on the experimental results of the frequency up-conversion, we derive the signal-to-noise ratio of the process at the single-photon level, and discuss its applicability to channel-selective quantum frequency conversion (CS-QFC) in the context of frequency-multiplexed quantum networks. Finally, we describe specific use cases of the CS-QFC, which show its utility as a reconfigurable switching element in frequency-multiplexed networks, particularly for selectively performing Bell-state measurements between two photons originating from different frequencies.

Noisy intermediate-scale quantum (NISQ) devices impose dual challenges on quantum circuit execution: limited qubit connectivity requires extensive SWAP-gate routing, while time-dependent decoherence progressively degrades quantum information. Existing qubit mapping algorithms optimize for hardware topology and static calibration metrics but systematically neglect transverse relaxation dynamics (T2), creating a fundamental gap between compiler decisions and evolving noise characteristics. We present TRAM (Transverse Relaxation Time-Aware Qubit Mapping), a coherence-guided compilation framework that elevates decoherence mitigation to a primary optimization objective. TRAM integrates calibration-informed community detection to construct noise-resilient qubit partitions, generates time-weighted initial mappings that anticipate coherence decay, and dynamically schedules SWAP operations to minimize cumulative error accumulation. Evaluated on Qiskit-based simulators with realistic noise models, TRAM outperforms SABRE by 3.59% in fidelity, reduces gate count by 11.49%, and shortens circuit depth by 12.28%, establishing coherence-aware optimization as essential for practical quantum compilation in the NISQ era.

Low-frequency Raman peaks, below 250 cm-1, are observed in hydrogen between 2-174 GPa and 13-300 K. The origin of these features is attributed to reorientational transitions (DeltaJ = 0; Q0-branch), which shift from the Rayleigh line as anisotropic intermolecular interactions lift the mJ degeneracy. This family of excitations closely follows the behavior of the S0-branches, sharing their dependence on pressure, temperature, and ortho-H2 concentration. Above 65 K, spectra corrected by the Bose-Einstein population factor reveal a broad continuum arising from populated higher J-states and increased ortho-para disorder. Upon entering phase III, where molecular rotation is inhibited, this continuum is quenched, giving way to well-established optical phonons. Below 25 K, equilibrated samples demonstrate a fine structure from isolated and pair excitations from impurity ortho-H2 molecules in a parahydrogen lattice, the latter a sensitive probe to anisotropic intermolecular interactions relevant to the quantum modeling of solid H2.

Recent advancements in quantum algorithms have reached a state where we can consider how to capitalize on quantum and classical computational resources to accelerate molecular resonance state identification. Here we identify molecular resonances with a method that combines quantum computing with classical high-throughput computing (HTC). This algorithm, which we term qDRIVE (the quantum deflation resonance identification variational eigensolver) exploits the complex absorbing potential formalism to distill the problem of molecular resonance identification into a network of hybrid quantum-classical variational quantum eigensolver tasks, and harnesses HTC resources to execute these interconnected but independent tasks both asynchronously and in parallel, a strategy that minimizes wall time to completion. We show qDRIVE successfully identifies resonance energies and wavefunctions in simulated quantum processors with current and planned specifications, which bodes well for qDRIVE's ultimate application in disciplines ranging from photocatalysis to quantum control and places a spotlight on the potential offered by integrated heterogenous quantum computing/HTC approaches in computational chemistry.

We study the universality of work statistics performed during a quench in gapless quantum systems. We show that the cumulants of work scale separately in the fast and slow quench regimes, following a power law analogous to the universal scaling in the Kibble-Zurek mechanism for topological defect formation in phase transition. As an example, we analyze the nonequilibrium dynamics of a quenched Heisenberg XXZ chain at its critical gapless state using the bosonization picture, resulting in a Tomonaga-Luttinger liquid. The analytical scaling is in agreement with the exact numerical calculation for the fast and slow quench regimes. In finite systems, the characteristic function display an oscillatory pattern which disappears in the thermodynamic limit. This study is particularly useful for understanding the thermodynamics of adiabatic quantum computation.

Quantum machine learning (QML) is a computational paradigm that seeks to apply quantum-mechanical resources to solve learning problems. As such, the goal of this framework is to leverage quantum processors to tackle optimization, supervised, unsupervised and reinforcement learning, and generative modeling-among other tasks-more efficiently than classical models. Here we offer a high level overview of QML, focusing on settings where the quantum device is the primary learning or data generating unit. We outline the field's tensions between practicality and guarantees, access models and speedups, and classical baselines and claimed quantum advantages-flagging where evidence is strong, where it is conditional or still lacking, and where open questions remain. By shedding light on these nuances and debates, we aim to provide a friendly map of the QML landscape so that the reader can judge when-and under what assumptions-quantum approaches may offer real benefits.

Loop quantum gravity (LQG) attempts to unify general relativity with quantum physics to offer a complete description of the universe by quantising spacetime geometry, but the numerical calculations we encounter are extraordinarily difficult. Progress has been made in the covariant formulation of LQG, but the tools do not carry over to the canonical formulation. These tools are graphical by nature, describing space with spin networks to make calculations in LQG more intuitive to the human hand. Recently, a new notation for working with spin networks has been used by arXiv:2412.20272 to offer the first accurate numerical results in canonical LQG by allowing the underlying graphs to change throughout the calculation, though they are forced to concede visual intuitiveness. In this thesis, we offer a more radical rephrasing of spin network calculations by translating them into the finite-dimensional ZX-calculus, extending previous attempts to translate into the standard (qubit) ZX-calculus (arXiv:2111.03114). Specifically, we derive the mixed-dimensional ZX-diagrams representing the generating objects of spin networks and the rules for the Penrose Spin Calculus (arXiv:2511.06012), and use these to present the ZX-form and correctness of "loop removal". We also derive the forms for several fundamental LQG objects in the finite-dimensional ZX-calculus for the first time. This gives us a high-level, intuitive graphical language that retains a flexibility to handle changing graph structures, and thus we argue positions the PSC as the new definitive language for canonical LQG. Furthermore, we investigate the possibility for a matrix-like normal form for spin networks deriving from a novel perspective of the PSC in terms of W-nodes.

Measurement incompatibility--the impossibility of jointly measuring certain quantum observables--is a fundamental resource for quantum information processing. We develop a graph-theoretic framework for quantifying this resource for large families of binary measurements, including Pauli observables on multi-qubit systems and $k$-body Majorana observables on $n$-mode fermionic systems. To each set of observables we associate an anti-commutativity graph, whose vertices represent observables and whose edges indicate pairs that anti-commute. In this representation, the incompatibility robustness--the minimal amount of classical noise required to render the set jointly measurable--becomes a graph invariant. We derive general bounds on this invariant in terms of the Lovász number, clique number, and fractional chromatic number, and show that the Lovász number yields the correct asymptotic scaling for $k$-body Majorana observables. For line graphs $L(G)$, which naturally arise in the characterisation of exactly solvable spin models, we obtain spectral bounds on the robustness expressed through the energy and skew-energy of the underlying graph $G$. These bounds become tight for highly symmetric graphs, leading to closed formulas for several graph families. Finally, we identify structural conditions under which the robustness is determined by a simple function of the graph's maximum degree and the number of vertices and edges, and show that such extremal cases occur only when combinatorial structures such as Hadamard, conference or weighing matrices exist.

We introduce a new renormalisation scheme to construct the Landau quasiparticles of Fermi fluids. The scheme relies on an energy cutoff $Λ$ which removes the quasi-resonant couplings, enabling the dressing of the particles into quasiparticles via a unitary transformation. The dynamics of the quasiparticles is then restricted to low-energy transitions and is fully determined by an effective Hamiltonian which unifies the Landau interaction function $f$ and the collision amplitude in a single amplitude $\mathcal{A}$ regularized by $Λ$. Our effective theory captures all the low-energy physics of Fermi fluids that support Landau quasiparticles, from the equation of state to the transport properties, both in the normal and in the superfluid phase. We apply it to an atomic Fermi gas with contact interaction to compute the speed of zero sound in function of the scattering length $a$. We also recover the Gork'ov-Melik Barkhudarov correction to the superfluid gap and critical temperature as a direct consequence of the dressing of particles into Landau quasiparticles.

We use the Tomonaga-Schwinger (TS) formulation of quantum field theory to determine when state-dependent additions to the local Hamiltonian density (i.e., modifications to linear Schrodinger evolution) violate relativistic covariance. We derive new operator integrability conditions required for foliation independence, including the Frechet derivative terms that arise from state-dependence. Nonlinear modifications of quantum mechanics affect operator relations at spacelike separation, leading to violation of the integrability conditions.

Spins in solids and molecules are promising for applications of quantum sensing technology. The sensitivity of the quantum sensing depends on how precisely spin observables can be determined in the measurement, and is intrinsically limited by the uncertainties of the observables. The use of a spin-squeezed state in a quantum sensor can reduce the uncertainty below the standard quantum limit when combined with an appropriate measurement procedure. Here, we discuss the simulation study of the generation of a squeezed state in an interacting spin system. We show that a spin system coupled by the magnetic dipole interaction can create a squeezed state. Model systems to realize the spin squeezing experimentally are also discussed. In addition, we find that a squeezed state is a type of entangled state. The present work paves the way to realize a squeezed state using a spin system to build a quantum sensor network with improved sensitivity, and to use it for the detection of quantum entanglement.

In this work, we present a novel method to express the stabilizer of a k-uniform complete hypergraph state as a linear combination of local operators. Quantum hypergraph states generalize graph states and exhibit properties that are not shared by their graph counterparts, most notably, their stabilizers are intrinsically nonlocal, as hyperedges can involve arbitrary subsets of vertices. Our formulation provides an explicit description of the stabilizers for k-uniform complete hypergraphs and may offer new insights for exploring these states within the stabilizer formalism. In particular, this approach could facilitate the construction of new Bell inequalities or find applications in quantum error correction.

We propose an experimental scheme to test the nonclassicality of a macroscopic ensemble of qubits, through the violation of the classical notion of macrorealism (MR) via the fundamental measurement-induced disturbance of quantum systems. An electromagnetic resonator is used to probe the parity of the qubit-ensemble. The action of sequential measurements allows the nonclassicality of whole ensemble to manifest itself, in the ideal case, irrespective of its size. This enables to probe the macroscopic limits of quantum mechanics as the qubit-ensemble is, effectively, a single large spin of many $\hbar$ units. Even as $\hbar \rightarrow 0$ in comparison to the total angular momentum of the ensemble, a constant amount of violation of MR is found in the noiseless case. However, environmental decoherence and inhomogeneity of qubit-electromagnetic field couplings precipitate the quantum-to-classical transition. This implies that Bohr's correspondence principle is not fundamental, but a consequence of practical limitations. We outline an implementation with a variety of qubits (superconducting qubits, spins in semiconductors, and Rydberg atoms) coupled to a coplanar waveguide resonator, and - via the corresponding noise analysis - find that violation of MR is detectable up to $100$ qubits via current technology.

To perform meaningful computations, Quantum Computers (QCs) must scale to macroscopic levels - i.e., to a large number of qubits - an objective pursued by most quantum companies. How to efficiently test their quantumness at these scales? We show that the violation of Macrorealism (MR), being the fact that classical systems possess definite properties that can be measured without disturbances, provide a fruitful avenue to this aim. The No Disturbance Condition (NDC) - the equality used here to test MR - can be violated by two consecutive parity measurements on $N$ qubits and found to be independent of $N$ under ideal conditions. However, realistic noisy QCs show a quantum-to-classical transition as $N$ increases, giving a foundationally-motivated scalable benchmarking metric. Two methods are formulated to implement this metric: one that involves a mid-circuit measurement, probing the irreversible collapse of the wavefunction, in contrast to the reversible entanglement generated in the other. Both methods are designed to be clumsiness-loophole free: the unwanted classical disturbances are negligible within statistical error. Violation of MR is detected on a IBM QC up to $N = 38$ qubits, increasing $N$ by one order of magnitude over best known results of MR. Two QCs are benchmarked using the proposed NDC metric, showing a three-fold improvement in their quantumness from one generation to the next.

A longstanding belief in quantum tomography is that estimating a mixed state is far harder than estimating a pure state. This is borne out in the mathematics, where mixed state algorithms have always required more sophisticated techniques to design and analyze than pure state algorithms. We present a new approach to tomography demonstrating that, contrary to this belief, state-of-the-art mixed state tomography follows easily and naturally from pure state algorithms. We analyze the following strategy: given $n$ copies of an unknown state $ρ$, convert them into copies of a purification $|ρ\rangle$; run a pure state tomography algorithm to produce an estimate of $|ρ\rangle$; and output the resulting estimate of $ρ$. The purification subroutine was recently discovered via the "acorn trick" of Tang, Wright, and Zhandry. With this strategy, we obtain the first tomography algorithm which is sample-optimal in all parameters. For a rank-$r$ $d$-dimensional state, it uses $n = O((rd + \log(1/δ))/\varepsilon)$ samples to output an estimate which is $\varepsilon$-close in fidelity with probability at least $1-δ$. This algorithm also uses poly$(n)$ gates, making it the first gate-efficient tomography algorithm which is sample-optimal even in terms of the dimension $d$ alone. Moreover, with this method we recover essentially all results on mixed state tomography, including its applications to tomography with limited entanglement, classical shadows, and quantum metrology. Our proofs are simple, closing the gap in conceptual difficulty between mixed and pure tomography. Our results also clarify the role of entangled measurement in mixed state tomography: the only step of the algorithm which requires entanglement across copies is the purification step, suggesting that, for tomography, the reason entanglement is useful is for consistent purification.

Bosonic systems, such as photons and ultracold atoms, have played a central role in demonstrating quantum-enhanced sensing. Quantum entanglement, through squeezed and GHZ states, enables sensing beyond classical limits. However, such a quantum advantage has so far been confined to two-mode bosonic systems, as analogous multi-mode squeezed states are non-trivial to prepare. Here, we develop a Monte-Carlo based optimization technique which can be used to efficiently engineer a Hamiltonian control-sequence for multi-mode bosonic systems to prepare multi-mode squeezed states. Specifically, we consider a Bose-Einstein condensate in an optical lattice, relevant for applications in gravimetry and gradiometry, and demonstrate that metrologically useful squeezed states can be generated using the Bose-Hubbard Hamiltonian which includes on-site atomic interactions, tunable via Feshbach resonances. By analyzing the distribution (density) of the quantum Fisher information (QFI) over the Hilbert space, we identify a characteristic \textit{intermediate scaling} of the QFI: $\mathcal{O}(N^2 L+L^2 N)$, which lies between the standard quantum limit (SQL) and the Heisenberg limit (HL) for $N$ atoms in $L$ modes. We show that in general, within the Hilbert space there is a finite, $\mathcal{O}(1)$ measure subset of Hilbert space with an intermediate QFI scaling. Therefore, one can find a Hamiltonian control sequence using a Monte Carlo optimization over random control sequences, that produces a state with intermediate scaling of the QFI. We assume an experimentally accessible range of the control parameters in the Hamiltonian resources and show that the intermediate scaling can be readily achieved. Our results indicate that the HL can be approached in quantum gravimetry using realistic experimental parameters for systems with $L=\mathcal{O}(1)$ and $N\gg L$.

We propose a class of periodically driven (Hermitian) modified bosonic Kitaev chains that effectively hosts rich nonHermitian Floquet topological phenomena. Two particular models are investigated in details as case studies. The first of these represents a minimal topologically nontrivial model in which nonHermitian skin effect, topological zero modes, and topological $π$ modes coexist. The other displays a more sophisticated model that supports multiple topological zero modes and topological $π$ modes in a tunable manner. By subjecting both models to perturbations such as a finite onsite bosonic frequency and spatial disorder, these features exhibit distinct responses. In particular, while generally all topological edge modes are robust against such perturbations, the nonHermitian skin effect is easily suppressed and revived by, respectively, the onsite bosonic frequency and spatial disorder in the first model, but it could be insensitive to both perturbations in the second model. Our studies thus demonstrate the prospect of a periodically driven bosonic Kitaev chain as a starting point in exploring various nonHermitian Floquet topological phases through the lens of a Hermitian system.

We study quantum advantage in the 1-step graph domination game on cycle graphs numerically, analytically and through the use of Noisy intermediate scale quantum (NISQ) processors. We find explicit strategies that realise the recently found upper bounds for small graphs and generalise them to larger cycles. We demonstrate that NISQ computers realise the predicted quantum advantages with high accuracy.

We establish a direct correspondence between Krylov and Nielsen complexity by choosing the Krylov basis to be part of the elementary gate set of Nielsen geometry and selecting a Nielsen complexity metric compatible with the Krylov metric. Up to normalization, the Krylov complexity of a Hermitian operator then equals the length squared of a straight-line trajectory on the manifold of unitaries that connects the identity operator with a precursor operator. The corresponding length provides an upper bound on Nielsen complexity that saturates whenever the straight line is a minimal geodesic. While for general systems we can only establish saturation in the limit of small precursors, we provide evidence that in the Sachdev-Ye-Kitaev (SYK) model there is a precise correspondence between Krylov complexity and (the square of) Nielsen complexity for a finite range of precursors.

We investigate the critical behavior and real-time scattering dynamics of the interacting $φ^4$ quantum field theory in $(1+1)$ dimensions using uniform matrix product states and the time-dependent variational principle. A finite-entanglement scaling analysis at $λ= 0.8$ bounds the critical mass-squared to $μ_c^2 \in [-0.3190,-0.3185]$ and provides a quantitative map of the symmetric, near-critical, weakly broken, and deeply broken regimes. Using these ground states as asymptotic vacua, we simulate two-particle collisions in a sandwich geometry and extract the elastic scattering probability $P_{11\to 11}(E)$ and Wigner time delay $Δt(E)$ following the prescription of Jha et al. [Phys. Rev. Research 7, 023266 (2025)]. We find strongly inelastic scattering in the symmetric phase ($P_{11\to 11} \simeq 0.63$, $Δt \simeq -180$ for $μ^2 = 0.2$), almost perfectly elastic collisions in the spontaneously broken phase ($P_{11\to 11} \simeq 0.998$, $Δt \simeq -270$ for $μ^2=-0.2$ and $P_{11\to 11} \simeq 1$, $Δt \simeq -177.781$ for $μ^2=-0.5$), and a breakdown of the sandwich evolution precisely at the critical coupling, which provides a dynamical signature of the quantum critical point. These results demonstrate that TDVP-based uniform matrix product states can probe nonperturbative scattering and critical dynamics in lattice $φ^4$ theory with controlled entanglement truncation.

Drawing inspiration from gradient-descent methods developed for data processing in quantum state tomography [\href{https://iopscience.iop.org/article/10.1088/2058-9565/ae0baa}{Quantum Sci.~Technol.~\textbf{10} 045055 (2025)}] and quantum process tomography [\href{https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.130.150402}{Phys.~Rev.~Lett.~\textbf{130}, 150402 (2023)}], we introduce stochastic gradient descent (SGD) algorithms for fast quantum measurement tomography (QMT), applicable to both discrete- and continuous-variable quantum systems -- thus completing the tomography trio. A measurement device or detector in a quantum experiment is characterized by a set of positive operator-valued measure (POVM) elements; the goal of QMT is to estimate these operators from experimental data. To ensure physically valid (positive and complete) POVM reconstructions, we propose two distinct parameterization schemes within the SGD framework: one leveraging optimization on a Stiefel manifold and one based on Hermitian operator normalization via eigenvalue scaling. Within the SGD-QMT framework, we further investigate two loss functions: mean squared error, equivalent to L2 or Euclidean norm, and average negative log-likelihood, inspired by maximum likelihood estimation. We benchmark performance against state-of-the-art constrained convex optimization methods. Numerical simulations demonstrate that, compared to standard methods, our SGD-QMT algorithms offer significantly lower computational cost, superior reconstruction fidelity, and enhanced robustness to noise. We make a Python implementation of the SGD-QMT algorithms publicly available at \href{https://github.com/agtomo/SGD-QMT}{github.com/agtomo/SGD-QMT}.

For the preparation of high-dimensional functions on quantum computers, we introduce tensor network algorithms that are efficient with regard to dimensionality, optimize circuits composed of hardware-native gates and take gate errors into account during the optimization. To avoid the notorious barren plateau problem of vanishing gradients in the circuit optimization, we smoothly transform the circuit from an easy-to-prepare initial function into the desired target function. We show that paradigmatic multivariate functions can be accurately prepared such as, by numerical simulations, a 17-dimensional Gaussian encoded in the state of 102 qubits and, through experiments, a 9-dimensional Gaussian realized using 54 qubits on Quantinuum's H2 quantum processor.

We establish exact scalings for the maximal group velocity of translation-invariant quantum walks in periodic electric fields. Our main result shows that the maximal group velocity decays exponentially with the period of the field in the whole parameter range, thus affirming a conjecture of arXiv:2302.01869 and at the same time augmenting it to an exact equality. We further demonstrate explicit revival relations and characterize the absolutely continuous spectrum in these models. Our results apply directly also to generalized CMV matrices.

We consider stimulated Raman adiabatic passage (STIRAP) when the final state is a superposition of two non-degenerate states. The system consists of four states coupled by two light fields. We find the relative phase of the final superposition depends on relative amplitude, width and timing of the adiabatic transfer pulses. We discuss these results in the context of experiments measuring symmetry violation in atomic and molecular systems.

Quantum computing promises transformative advances, but remains constrained by recurring misconceptions and methodological pitfalls. This paper demonstrates a fundamental incompatibility between traditional agent-based modeling (ABM) implementations and quantum optimization frameworks like Quadratic Unconstrained Binary Optimization (QUBO). Using Schelling's segregation model as a case study, we show that the standard practice of directly translating ABM state observations into QUBO formulations not only fails to deliver quantum advantage, but actively undermines computational efficiency. The fundamental issue is architectural. Traditional ABM implementations entail observing the state of the system at each iteration, systematically destroying the quantum superposition required for computational advantage. Through analysis of Schelling's segregation dynamics on lollipop networks, we demonstrate how abandoning the QUBO reduction paradigm and instead reconceptualizing the research question, from "simulate agent dynamics iteratively until convergence" to "compute minimum of agent moves required for global satisfaction", enables a faster classical solution. This structural reconceptualization yields an algorithm that exploits network symmetries obscured in traditional ABM simulations and QUBO formulations. It establishes a new lower bound which quantum approaches must outperform to achieve advantage. Our work emphasizes that progress in quantum agent-based modeling does not require forcing classical ABM implementations into quantum frameworks. Instead, it should focus on clarifying when quantum advantage is structurally possible, developing best-in-class classical baselines through problem analysis, and fundamentally reformulating research questions rather than preserving classical iterative state change observation paradigms.

We extend Gleason's theorem to the two-dimensional Hilbert space of a qubit by invoking the standard axiom that describes composite quantum systems. The tensor-product structure allows us to derive density matrices and Born's rule for $d=2$ from a simple requirement: the probabilities assigned to measurement outcomes must not depend on whether a system is considered on its own or as a subsystem of a larger one. In line with Gleason's original theorem, our approach assigns probabilities only to projection-valued measures, while other known extensions rely on considering more general classes of measurements.

Long distance entanglement generation at a high rate is a major quantum technological goal yet to be fully realized, with the promise of many interesting applications, such as secure quantum computing on remote servers and quantum cryptography. One possible implementation is using a variant of the DLCZ-scheme by combining atomic-ensemble memories and linear optics with spontaneous parametric down conversion (SPDC) sources. As we edge closer to the realization of such a technology, the complete details of the underlying components become crucial. In this paper we consider the impact of the multimode emission from the SPDC source on quantum repeaters based on the DLCZ-scheme. We consider two cases, driving the SPDC using short Gaussian pulses and continuously. For pulsed driving, we find that the use of very narrow laser pulses to drive SPDC source is crucial to obtain high fidelity end-to-end entangled states but this puts demands on the peak intensity. By introducing a maximally allowed laser intensity, we find optimal pulse widths for each swap depth. For continuous driving, we find the temporal acceptance window of clicks relative to the heralding time to be a crucial parameter, and we can similarly optimize the acceptance window for each swap depth. For both cases, we thus identify optimal parameters given experimental limitations and aims. We have thus provided helpful knowledge towards the realization of long distance entanglement generation using the DLCZ-scheme.

Task scheduling with constrained time intervals and limited resources remains a fundamental challenge across domains such as manufacturing, logistics, cloud computing, and healthcare. This study presents a novel variant of the Quantum Approximate Optimization Algorithm (QAOA) designed to address the task scheduling problem formulated as a Quadratic Unconstrained Binary Optimization (QUBO) model. The proposed method, referred to as Quantum Time Interval Scheduler (QTIS), integrates an ancilla-assisted quantum circuit to dynamically detect and penalize overlapping tasks, enhancing the enforcement of scheduling constraints. Two complementary implementations are explored for overlap detection: a quantum approach based on RY rotations and CCNOT gates, and a classical alternative relying on preprocessed interval comparisons. QTIS decomposes the problem Hamiltonian, Hp, into two components, each parameterized by a distinct angle. The first component encodes the objective function, while the second captures penalty terms associated with overlapping intervals, which are controlled by the auxiliary circuit. Subsequently, three minimization strategies are evaluated: standard QAOA, T-QAOA, and HT-QAOA, showing that employing separate parameters for the different components of the problem Hamiltonian leads to lower energy values and improved solution quality. Results confirm the efficiency of QTIS in scheduling tasks with fixed temporal windows while minimizing conflicts, demonstrating its potential to advance hybrid quantum-classical optimization in complex scheduling environments.

Quantum algorithms for combinatorial optimization typically encode constraints as soft penalties within the objective function, which can reduce efficiency and scalability compared to state-of-the-art classical methods that instead exploit constraints to guide the search toward high-quality solutions. Although solving this issue for an arbitrary problem is inherently a hard task, we address this challenge for a specific problem in the field of telecommunications, the multi-frequency antenna placement problem, by introducing a constraint-preserving quantum adiabatic algorithm (QAA). To this aim, we construct a quantum circuit that prepares an initial state comprising an equal superposition of all feasible solutions, and define a custom mixer that preserves both the one-hot encoding constraint for vertex coloring and the cardinality constraint on the number of antennas. This scheme can be extended to a broader range of applications characterized by similar constraints. We first benchmark the performance of this quantum algorithm against a basic version of QAA, demonstrating superior performance in terms of feasibility and success probability. We then apply this algorithm to large problem sizes with hundreds of variables using a constraint-aware decomposition method based on the SPLIT framework. Our results indicate competitive performance against other large-scale classical approaches, such as branch-and-bound and simulated annealing. This work supports previous claims that constraint-aware algorithms are crucial for the practical and efficient application of quantum methods in industrial settings.

As quantum networks evolve toward a full quantum Internet, reliable transmission in quantum multiple-input multiple-output (QuMIMO) settings becomes essential, yet remains difficult due to noise, crosstalk, and the mixing of quantum information across subchannels. To improve reliability in such settings, we study an adaptive diversity strategy for discrete-variable QuMIMO systems based on universal asymmetric cloning at the transmitter and probabilistic purification at the receiver. An input qubit is encoded into M approximate clones, transmitted over an N x N multi-mode quantum channel, and recovered through a purification map optimized using available channel state information (CSI). For the given cloning asymmetry parameters, we derive an eigenvalue-based expression for the decoder-optimal end-to-end fidelity in the form of a generalized Rayleigh quotient, which enables efficient tuning of the cloner without iterative optimization. As a design choice, we employ semidefinite program (SDP) to construct the purification map for only a targeted success probability p. This numerical framework is used to study fixed-noise, dimension-scaling noise, and stochastic depolarization regimes. A cloning asymmetry index is introduced to quantify the distribution of quantum information across the multiple subchannels across these operating conditions. The results show that the proposed scheme yields significant fidelity gains in crosstalk-dominated settings and automatically adapts to channel symmetry and channel conditions. This work provides design guidelines for future QuMIMO systems and establishes a robust baseline for more advanced transmission and decoding strategies.

We demonstrate that Dirac fermions in 2+1 dimensions, coupled to Abelian gauge fields in multiply-connected regions, exhibit a parity anomaly that directly manifests as Aharonov-Bohm (AB) type topological phases. Using the Fujikawa method, we show that this anomaly reproduces both the AB phase and the spin-dependent Aharonov-Casher (AC) phase. We explicitly calculate the induced topological currents, establishing that their characteristic divergence-free form provides a direct signature of this parity-anomalous topological phase.

We analyze Su-Schrieffer-Heeger (SSH) models using the doubling method for orthogonal polynomial sequences. This approach yields the analytical spectrum and exact eigenstates of the models. We demonstrate that the standard SSH model is associated with the doubling of Chebyshev polynomials. Extending this technique to the doubling of other finite sequences enables the construction of Hamiltonians for inhomogeneous SSH models which are exactly solvable. We detail the specific cases associated with Krawtchouk and $q$-Racah polynomials. This work highlights the utility of polynomial-doubling techniques in obtaining exact solutions for physical models.

Stochastic unravelings allow to efficiently simulate open system dynamics, yet their application has traditionally been restricted to master equations that preserve both Hermiticity and trace. In this work, we introduce a general framework that extends piecewise-deterministic unravelings to arbitrary trace-nonpreserving master equations, requiring only positivity and Hermiticity of the dynamics. Our approach includes, as special cases, unravelings of arbitrary dynamics in the Heisenberg picture, evolutions interpolating between fully Lindblad and non-Hermitian Hamiltonian generators, and equations employed in the derivation of full counting statistics, for which we show it can be used to obtain the moments of the associated probability distribution. The framework is suitable for both trace-decreasing and trace-increasing processes through stochastic disappearance and replication of the stochastic realizations, and it is compatible with different unraveling schemes and with reverse jumps in the non-Markovian regime. Thereby, our approach provides a powerful and versatile simulation method that significantly broadens the applicability of stochastic techniques for open system dynamics.

Although they have enabled several advances in the field of optomechanics, optomechanical disk resonators have not yet been operated in the quantum regime. We present the first experimental demonstration of an optomechanical disk resonator prepared in the quantum ground state. With a gigahertz frequency, the mechanical breathing mode of the investigated semiconductor disk reaches a level of excitation below a single phonon when cooled in a dilution refrigerator. We quantify the phonon occupancy of the mechanical mode by performing Brillouin sideband spectroscopy: a conical optical fiber is evanescently coupled to the disk optical whispering-gallery mode, and Stokes and anti-Stokes photons scattered by phonon emission and absorption are counted on a single-photon detector. We measure a suppression of the absorption process corresponding to a phonon occupancy of $0.66\pm0.20$. We experimentally investigate the mechanisms ruling laser-induced heating, which limits the lowest measurable phonon occupancy, and notably witness an extra-cavity heating effect.

Quantum Key Distribution (QKD) networks enable unconditionally secure key exchange using quantum mechanical principles. However, routing cryptographic keys across multi-hop quantum networks introduces challenges unique to quantum communication. This survey analyzes and classifies 26 routing strategies proposed between 2013 and 2024 for terrestrial, satellite, and hybrid QKD infrastructures. Dynamic, key-aware routing algorithms have been shown to reduce service rejection rates by 25-40% compared to static shortest-path methods by incorporating real-time key pool availability and link error rates. Multi-path strategies improve resilience against trusted-node compromise by distributing keys across disjoint routes, albeit with an increase in key consumption of 30-60%. SDN-based orchestration frameworks emerge as essential enablers of flexible, QoS-aware routing for hybrid networks integrating terrestrial fibers and intermittent satellite links. Critical research directions include reducing dependence on trusted nodes through quantum repeaters or post-quantum cryptography, developing standardized key management interfaces for interoperability, and adopting AI-driven predictive routing for adapting to fluctuating network states. This comprehensive synthesis of routing algorithms, performance trade-offs, and unresolved issues offers practical guidance for engineering secure, adaptable, and large-scale QKD networks capable of meeting real-world deployment demands.

We propose a topological transport platform for microwave-to-optical conversion at the single-photon level in a Rydberg atom-cavity setting. This setting leverages a hybrid dual-mode Jaynes-Cummings (JC) configuration, where a microwave resonator couples an optical cavity mediated by a Rydberg atom ensemble. Our scheme uniquely enables the formation of Fock-state lattices (FSLs), where photon hopping rates depend on photon numbers in individual sites. We identify an inherent zero-energy mode corresponding to the dark state of the dual-mode JC model. This enables to build a high-efficiency single-photon transducer, which realizes topologically protected photon transport between the microwave and optical modes. Crucially, we show analytically that the FSL features continuous variations of the winding number. Our work establishes a robust mechanism for efficient quantum transduction in synthetic dimensions and opens avenues for exploring topological physics with continuous winding numbers in the atom-cavity system.

Entanglement is a central resource in quantum technologies, and the realization of photonic entanglement necessarily relies on interaction with matter. Resonance fluorescence (RF), originating from the coherent interaction between a driving field and a two-level system, plays a pivotal role in quantum optics. Here, we demonstrate a novel route to entanglement generation based on RF from a single quantum dot. Rather than relying on generation of multiphoton states, our approach directly exploits vacuum-one-photon number superposition states created under resonant excitation. By delocalizing this superposition via a beam splitter, we realize time-bin entanglement and observe a clear violation of the Clauser-Horn-Shimony-Holt Bell inequality using Franson-type interferometry. Our scheme removes the need for multiphoton generation, simplifies the experimental requirements, and establishes a scalable pathway toward solid-state entangled photon sources.

We axiomatise the dagger category of complex Hilbert spaces and bounded linear maps, using exclusively purely categorical conditions. Our axioms are chosen with the aim of an easy interpretability: two of them describe the composition of objecs, two further ones deal with the decomposition of objects, and a final axiom expresses a symmetry property. The categorical reconstruction of complex Hilbert spaces addresses foundational issues in quantum physics. We present a simplified alternative to recent characterisations.

Quantum neural networks (QNNs) are an important model for implementing quantum machine learning (QML), while they demonstrate a high degree of vulnerability to backdoor attacks similar to classical networks. To address this issue, a quantum backdoor attack detection framework called QSentry is proposed, in which a quantum Measurement Clustering method is introduced to detect backdoors by identifying statistical anomalies in measurement outputs. It is demonstrated that QSentry can effectively detect anomalous distributions induced by backdoor samples with extensive experiments. It achieves a 75.8% F1 score even under a 1% poisoning rate, and further improves to 85.7% and 93.2% as the poisoning rate increases to 5% and 10%, respectively. The integration of silhouette coefficients and relative cluster size enable QSentry to precisely isolate backdoor samples, yielding estimates that closely match actual poisoning ratios. Evaluations under various quantum attack scenarios demonstrate that QSentry delivers superior robustness and accuracy compared with three state-of-the-art detection methods. This work establishes a practical and effective framework for mitigating backdoor threats in QML.

Efficiently encoding classical visual data into quantum states is essential for realizing practical quantum neural networks (QNNs). However, existing encoding schemes often discard spatial and semantic information when adapting high-dimensional images to the limited qubits of Noisy Intermediate-Scale Quantum (NISQ) devices. We propose a Fidelity-Preserving Quantum Encoding (FPQE) framework that performs near lossless data compression and quantum encoding. FPQE employs a convolutional encoder-decoder to learn compact multi-channel representations capable of reconstructing the original data with high fidelity, which are then mapped into quantum states through amplitude encoding. Experimental results show that FPQE performs comparably to conventional methods on simple datasets such as MNIST, while achieving clear improvements on more complex ones, outperforming PCA and pruning based encodings by up to 10.2\% accuracy on Cifar-10. The performance gain grows with data complexity, demonstrating FPQE's ability to preserve high-level structural information across diverse visual domains. By maintaining fidelity during classical to quantum transformation, FPQE establishes a scalable and hardware efficient foundation for high-quality quantum representation learning.

We introduce a new mechanism that produces a Hall-like response in time-reversal-invariant materials, driven entirely by geometric effects. Specifically, we demonstrate that a tilted potential interface causes electron wave packets to undergo a refraction-like deflection upon transmission through the barrier, leading to a finite transverse current and a corresponding Hall conductance. Our analytical framework captures the essential features of this refraction Hall effect, and the resulting Hall conductivity profile is corroborated by numerical simulations across different lattice models and device geometries. We further visualize our predicted effect through real-time wave packet dynamics, which reveals its purely geometric origin and the robustness of the transverse response. These findings establish a fundamentally distinct class of Hall-like transport phenomena in mesoscopic systems that preserve time-reversal symmetry.

Although known for negatively impacting the operation of superconducting qubits, thermal baths are shown to exert qubit control in a positive way, provided they are properly engineered. We demonstrate an experimental method to engineer the transduction of microwave driving into heat flow through a leaky resonator. Given the precise conversion, a qubit receiving the heat flow obtains a quasi-thermal equilibrium with arbitrary target temperature in hundreds of nanoseconds. We show that the dynamics of the quantum transducing process is described by thermalizing channel states, generated from the double dressings of the resonator by the semi-classical driving and the qubit-resonator coupling. Their spectrum, coupling, and driving strength determine the channel rate of energy flow, along with the relaxation rates of photon leakage into the bath. The analytical prediction is shown to match well with the experimental measurements on an Xmon qubit circuit.

In this paper, we address the calibration of the quantum efficiency of single-photon cameras using radioluminescent light sources. The proposed methods are subsequently compared with absolute calibration techniques based on the detection of correlated photon pairs. Furthermore, we propose a method for transferring absolute calibration using the aforementioned radioluminescent emitters.

Understanding the quantum evolution of light in nonlinear media is central to the development of next-generation quantum technologies. Yet modeling these processes remains computationally demanding, as the required resources grow rapidly with photon number and phase-space resolution. Here we introduce a tensor-network approach that efficiently captures the dynamics of nonlinear optical systems in a continuous-variable representation. Using the matrix product state (MPS) formalism, both quantum states and operators are encoded in a highly compressed form, enabling direct numerical integration of the Schrödinger equation. We demonstrate the method by simulating degenerate spontaneous parametric down-conversion (SPDC) and show that it accurately reproduces established theoretical benchmarks - energy conservation, pump depletion, and quadrature squeezing - even in regimes where conventional Fock-basis simulations become infeasible. For high-intensity pump fields ($α= 100$), the MPS representation achieves compression ratios above $3\cdot 10^3$ while preserving physical fidelity. This framework opens a scalable route to modeling multimode quantum light and nonlinear optical phenomena beyond the reach of traditional methods.

The vehicle routing problem (VRP) is a fundamental NP-hard task in intelligent transportation systems with broad applications in logistics and distribution. Deep reinforcement learning (DRL) with Graph Neural Networks (GNNs) has shown promise, yet classical models rely on large multi-layer perceptrons (MLPs) that are parameter-heavy and memory-bound. We propose a Quantum Graph Attention Network (Q-GAT) within a DRL framework, where parameterized quantum circuits (PQCs) replace conventional MLPs at critical readout stages. The hybrid model maintains the expressive capacity of graph attention encoders while reducing trainable parameters by more than 50%. Using proximal policy optimization (PPO) with greedy and stochastic decoding, experiments on VRP benchmarks show that Q-GAT achieves faster convergence and reduces routing cost by about 5% compared with classical GAT baselines. These results demonstrate the potential of PQC-enhanced GNNs as compact and effective solvers for large-scale routing and logistics optimization.

Single-photon emitters (SPEs) based on nitrogen-vacancy centers in nanodiamonds (neutral NV0 (wavelength 575 nm) and negative NV- (wavelength 637 nm)) represent promising platforms for quantum nanophotonics applications, yet their emission efficiencies remain constrained by weak light-matter interactions. Multi-layer metasurfaces (MLM) offer unprecedented degrees of freedom for efficient light manipulation beyond conventional single-material metasurfaces, enabling dual-resonance cavities that can simultaneously enhance pump excitation and SPE collection. However, traditional trial-and-error and forward optimization methods face significant challenges in designing these complex structures due to the vast parameter space and computational demands. Here, we present NanoPhotoNet-Inverse, an artificial intelligence-driven inverse design framework based on a hybrid deep neural network architecture. This model efficiently performs inverse design of two dual-resonance MLM cavities to amplify pump and SPE emissions of different vacancies in nanodiamond and improve SPE collection. Our approach achieves inverse design prediction efficiency exceeding 98.7%, demonstrating three orders of magnitude amplification in SPE count rate and 50 picosecond lifetime, significantly surpassing conventional cavity designs. These remarkable enhancements in emission rates and collection efficiency position our platform as a transformative technology for advancing quantum communication networks, quantum computing architectures, quantum sensing applications, and quantum cryptography systems. Therefore, it opens new pathways for intelligent photonic device engineering in quantum technologies.

Quantum spin liquids (QSL) are phases of matter which are distinguished not by the symmetries they break, but rather by the patterns of entanglement within them. Although these entanglement properties have been widely discussed for ground states, the way in which QSL form at finite temperature remains an open question. Here we introduce a method of characterizing both the depth and spatial structure of entanglement, and use this to explore how patterns of entanglement form as temperature is reduced in two widely studied models of QSL, the Kitaev honeycomb model, and the spin-1/2 Heisenberg antiferromagnet on a Kagome lattice. These results enable us to evaluate both the temperature at which spins within the high-temperature paramagnet first become entangled, and the temperature at which the system first develops the structured, multipartite entanglement characteristic of its QSL ground state.

The second law of thermodynamics sets a lower bound on the work required to drive a system between thermal equilibrium states, with equality attained in the quasistatic limit. For finite-time processes, part of the extractable work is inevitably dissipated, motivating the search for driving protocols that minimize the work. While classical stochastic systems have been extensively explored, quantum analyses remain limited and often rely on Markovian master equations valid only in the weak-coupling regime. Here, we study minimal work protocols for representative two-level systems coupled to a harmonic-oscillator bath using a numerically exact method. Inspired by known optimal solutions for Brownian oscillators, we introduce an impulse ansatz that incorporates possible boundary impulses and test it across a wide range of bath parameters. We find that impulse-like features remain nearly optimal in the quantum, non-Markovian regime, at short times. We also identify cases in which the widely used Markovian master equation fails even at weak coupling, underscoring the need for fully quantum approaches to finite-time thermodynamic optimization.

We report generation of 10.1\pm0.2-dB squeezed light from a broadband periodically poled lithium niobate (PPLN) waveguide optical parametric amplifier (OPA). Based on our previous report where a similar PPLN waveguide shows 8.3-dB squeezing [T. Kashiwazaki et al., Appl. Phys. Lett. 122, 234003 (2023)], we reduce phase fluctuations and overall optical losses in the measurement system. In particular, we introduce a novel phase detection technique that does not require tapping a part of the squeezed light to get a phase locking signal. We use a phase-detection OPA seeded by a tapped probe and pump light before a squeezer OPA. This configuration breaks the conventional trade-off between generating a phase-locking signal with high-signal-to-noise ratio and suppressing degradation of squeezing level caused by optical tapping. With all these improvements, the phase fluctuation angle is reduced from 14 mrad to 9 mrad, and the total optical loss from 12\% to 8\%. Achieving more than 10 dB of squeezing by the broadband waveguide OPA is a significant step towards realization of fault-tolerant ultra-fast universal optical quantum computation.

Interacting Rydberg atoms constitute a versatile platform for the realization of non-equilibrium states of matter. Close to phase transitions, they respond collectively to external perturbations, which can be harnessed for technological applications in the domain of quantum metrology and sensing. Owing to the controllable complexity and straightforward interpretability of Rydberg atoms, we can observe and tune the emergent collective nonlinearity. Here, we investigate the application of an interacting Rydberg vapour for the purpose of time series prediction. The vapour is driven by a laser field whose Rabi frequency is modulated in order to input the time series. We find that close to a non-equilibrium phase transition, where collective effects are amplified, the capability of the system to learn the input becomes enhanced. This is reflected in an increase of the accuracy with which future values of the time series can be predicted. Using the Lorenz time series and temperature data as examples, our work demonstrates how emergent phenomena enhance the capability of noisy many-body quantum systems for data processing and forecasting.

Optimal measurements for quantum multiparameter estimation are complicated by the uncertainty principle. Generally, there is a trade-off between the precision with which different parameters can be simultaneously estimated. The task of determining the minimum achievable estimation error is a central task of multiparameter quantum metrology. For estimating parameters encoded in pure quantum states, the ultimate limit is known, but is given by the solution of a non-trivial minimisation problem. We present a new expression for the achievable bound for two-parameter estimation with pure states that is considerably simpler. We also determine the optimal measurements, completing the problem of two-parameter estimation with pure state probes. To demonstrate the utility of our result, we determine the precision limit for estimating displacements using grid states.

Quantum Rabi model (QRM) is a fundamental model for light-matter interactions, the finite-component quantum phase transition (QPT) in the QRM has established a paradigmatic application for critical quantum metrology (CQM). However, such a paradigmatic application is restricted to a local regime of the QPT which has only a single critical point. In this work we propose a globalized CQM in the QRM by introducing an auxiliary nonlinear term which is realizable and can extend the critical point to a continuous critical regime. As a consequence, a high measurement precision is globally available over the entire coupling regime from the original critical point of the QRM down to the weak-coupling limit, as demonstrated by the globally accessible diverging quantum Fisher information in dynamics. We illustrate a measurement scheme by quadrature dynamics, with globally criticality-enhanced inverted variance as well as the scaling relation with respect to finite frequencies. In particular, we find that the globally high measurement precisions still survive in the presence of decoherence. Our proposal paves a way to break the local limitation of QPT of the QRM in CQM and enables a broader application, with implications of applicability in realistic situation.

If classical algorithms have been successful in reproducing the estimation of expectation values of observables of some quantum circuits using off-the-shelf computing resources, matching the performance of the most advanced quantum devices on sampling problems usually requires extreme cost in terms of memory and computing operations, making them accessible to only a handful of supercomputers around the world. In this work, we demonstrate for the first time a classical simulation outperforming Gaussian boson sampling experiments of one hundred modes on established benchmark tests using a single CPU or GPU. Being embarrassingly parallelizable, a small number of CPUs or GPUs allows us to match previous sampling rates that required more than one hundred GPUs. We believe algorithmic and implementation improvements will generalize our tools to photo-counting, single-photon inputs, and pseudo-photon-number-resolving scenarios beyond one thousand modes. Finally, most of the innovations in our tools remain valid for generic probability distributions over binary variables, rendering it potentially applicable to the simulation of qubit-based sampling problems and creating classical surrogates for classical-quantum algorithms.

Preserving spin symmetry in variational quantum algorithms is essential for producing physically meaningful electronic wavefunctions. Implementing spin-adapted transformations on quantum hardware, however, is challenging because the corresponding fermionic generators translate into noncommuting Pauli operators. In this work, we introduce an exact and computationally efficient factorization of spin-adapted unitaries derived from fermionic double excitation and deexcitation rotations. These unitaries are expressed as ordered products of exponentials of Pauli operators. Our method exploits the fact that the elementary operators in these generators form small Lie algebras. By working in the adjoint representation of these algebras, we reformulate the factorization problem as a low-dimensional nonlinear optimization over matrix exponentials. This approach enables precise numerical reparametrization of the unitaries without relying on symbolic manipulations. The proposed factorization provides a practical strategy for constructing symmetry-conserving quantum circuits within variational algorithms. It preserves spin symmetry by design, reduces implementation cost, and ensures the accurate representation of electronic states in quantum simulations of molecular systems.

Quantum many-body scars (QMBS) represent a mechanism for weak ergodicity breaking, characterized by the coexistence of atypical non-thermal eigenstates within an otherwise thermalizing many-body spectrum. In this work, we revisit the spin-$1$ $XY$ model on a periodic chain and construct several new families of exact scar eigenstates embedded within its extensively degenerate manifolds that owe their origins to an interplay of $U(1)$ magnetization conservation and chiral symmetries. We go beyond previously studied towers of states and first identify a novel set of interference-protected eigenstates resembling Fock space cage states, where destructive interference confines the wave function to sparse subgraphs of the Fock space. These states exhibit subextensive entanglement entropy, and when subjected to a transverse magnetic field, form equally spaced ladders whose coherent superpositions display long-lived fidelity oscillations. We further reveal a simpler organizing principle behind these nonthermal states by using the commutant algebra framework, in particular by showing that they are simultaneous eigenstates of non-commuting local operators. Moreover, in doing so, we uncover two more novel families of exact scars: a tower of volume-entangled states, and a set of mirror-dimer states with some free local degrees of freedom. Our results illustrate the power and interplay of interference-based and algebraic mechanisms of non-ergodicity, offering systematic routes to identifying and classifying QMBS in generic many-body quantum systems.

We theoretically investigate the nonequilibrium relaxation of a spatial density modulation in a one-dimensional, weakly interacting Bose gas, and its connection to the equilibrium scattering rate $\smash{γ_k\propto k^{3/2}}$ of the system's phononic excitations. We show that the relaxation is generally governed by a nonequilibrium scattering rate $γ_{k,t}$ coupled to quantum fluctuations, which approaches its equilibrium value $γ_k$ only at long times. Numerical simulations of quantum kinetic equations reveal an algebraic convergence, $\smash{γ_{k,t} - γ_k \sim t^{-2/3}}$, confirmed by analytical predictions. More broadly, our results establish a theoretical framework for experimentally probing phonon dynamics through the temporal evolution of local perturbations in quantum gases.

We investigate the fundamental time complexity, as constrained by Lieb-Robinson bounds, for preparing entangled states useful in quantum metrology. We relate the minimum time to the Quantum Fisher Information ($F_Q$) for a system of $N$ quantum spins on a $d$-dimensional lattice with $1/r^α$ interactions with $r$ being the distance between two interacting spins. We focus on states with $F_Q \sim N^{1+γ}$ where $γ\in (0,1]$, i.e., scaling from the standard quantum limit to the Heisenberg limit. For short-range interactions ($α> 2d+1$), we prove the minimum time $t$ scales as $t \gtrsim L^γ$, where $L \sim N^{1/d}$. For long-range interactions, we find a hierarchy of possible speedups: $t \gtrsim L^{γ(α-2d)}$ for $2d < α< 2d+1$, $t \gtrsim \log L$ for $(2-γ)d < α< 2d$, and $t$ may even vanish algebraically in $1/L$ for $α< (2-γ)d$. These bounds extend to the minimum circuit depth required for state preparation, assuming two-qubit gate speeds scale as $1/r^α$. We further show that these bounds are saturable, up to sub-polynomial corrections, for all $α$ at the Heisenberg limit ($γ=1$) and for $α> (2-γ)d$ when $γ<1$. Our results establish a benchmark for the time-optimality of protocols that prepare metrologically useful quantum states.

The quantum Mpemba effect (QME) is a phenomenon observed in many-body systems where initial systems configurations farther from equilibrium can be observed to equilibrate faster than configurations that are closer to it. By considering noise induced error in the initial system state preparation, we analyse the robustness of various models exhibiting the QME. We demonstrate that exponentially accelerated thermalisation in open system dynamics modelled by a Gorini-Kossakowski-Sudarshan-Lindblad master equation is highly sensitive to noise induced deviations in the initial state, making this approach to accelerated thermalisation difficult to achieve. In contrast, we demonstrate that accelerated restoration of symmetry in $U(1)$ symmetric random unitary circuits via increased initial symmetry breaking is robust in the presence of state preparation error. When large errors are present in the state preparation, we show that this can in fact induce a higher rate of symmetry restoration and a stronger QME.

Critical exponents characterize the divergent scaling of thermodynamic quantities near phase transitions and allow for the classification of physical systems into universality classes. While quantum gases thermalizing by interparticle interactions fall into the XY model universality class, the ideal Bose gas has been predicted to form a distinct universality class whose signatures have not yet been revealed experimentally. Here, we report the observation of critical scaling in a two-dimensional quantum gas of essentially noninteracting photons, which thermalize by radiative contact to a reservoir of molecules inside a microcavity. By measuring the spatial correlations near the condensation transition, we determine the critical exponent for the correlation length to be $ν= 0.52(3)$. Our results constitute a first experimental test of the long-standing scaling predictions for the Bose gas universality class.

We present a gradient-based method to construct memory-efficient, high-fidelity, single-qubit gates for fluxonium qubits. These gates are constructed using a sequence of single-flux quantum (SFQ) pulses that are sent to the qubit through either capacitive or inductive coupling. The schedule of SFQ pulses is constructed with an on-ramp and an off-ramp applied prior to and after a pulse train, where the pulses are spaced at intervals equal to the qubit period. We reduce the optimization problem to the scheduling of a fixed number of SFQ pulses in the on-ramp and solve it by relaxing the discretization constraint of the SFQ clock as an intermediate step, allowing the use of the Broyden-Fletcher-Goldfarb-Shanno optimizer. Using this approach, gate fidelities of 99.99 % can be achieved for inductive coupling and 99.9 % for capacitive coupling, with leakage being the main source of coherent errors for both approaches.

Accurate quantum many-body calculations often depend on reliable reference states or good human-designed ansätze, yet these sources of knowledge can become unreliable in hard problems like strongly correlated systems. We introduce the Trimmed Configuration Interaction (TrimCI) method, a prior-knowledge-free algorithm that builds accurate ground states directly from random Slater determinants. TrimCI iteratively expands the variational space and trims away unimportant states, allowing a random initial core to self-refine into an accurate approximation of exact ground state. Across challenging benchmarks, TrimCI achieves state-of-the-art accuracy with strikingly efficiency gains of several orders of magnitude. For [4Fe-4S] cluster, it matches recent quantum computing results with $10^6$-fold fewer determinants and CPU-hours. For the nitrogenase P-cluster, it matches selected-CI accuracy using $10^5$-fold fewer determinants. For $8\times8$ Hubbard model, it recovers over $99\%$ of the ground-state energy using only $10^{-28}$ of the Hilbert space. In some regimes, TrimCI attains orders-of-magnitude higher accuracy than AFQMC method. These results demonstrate that high-accuracy many-body ground states can be discovered directly from random determinants, establishing TrimCI as a prior-knowledge-free, accurate and highly efficient framework for quantum many-body systems. The compact explicit wavefunctions it produces further enable direct and rapid evaluation of observables.

We introduce a method called resolution refinement that allows one to bootstrap eigenstate preparation on a quantum computer. We first prepare an eigenstate of a low-resolution Hamiltonian using any method of choice. The eigenstate is then lifted to higher resolution and adiabatically evolved to produce the corresponding eigenstate of a higher-fidelity Hamiltonian. We give examples of resolution refinement applied to both single-particle basis states as well as a spatial lattice grid. For basis refinement, we compute few-body ground states of the Busch model for interacting particles in a harmonic trap in one dimension. For lattice refinement, we compute Hartree-Fock nuclear states for a central Woods-Saxon potential in three dimensions, and we compute bound states and continuum states in a multi-species Hubbard model of fermions in one dimension. In all cases, the method is efficient and requires an adiabatic evolution time comparable to the inverse of the energy gap in the physical spectrum.

Today's most sensitive experiments for detecting CP-violating permanent electric dipole moments (EDM) rely on molecular spectroscopy. The high sensitivity arises from large internal electric fields that interact with the constituents of the molecule. For molecular ions it has long been assumed that experiments with static polarization from dc electric fields are infeasible, as the ion's charge would either shift it to a field free region or eject it from the trap. This constraint appears to make single ion quantum-logic clocks, among the most precise measurement devices available, incompatible with EDM measurements. Here, we demonstrate that, under typical trapping conditions, heavy molecular ions with small $Ω/Λ$-doubling can be polarized by a static electric field while remaining confined in the Paul trap. This effect arises from a cancellation between the electrostatic force and the trap's ponderomotive force, resulting in an equilibrium position where the ion experiences a dc electric field component. Dynamic decoupling allows to implement co-magnetometry schemes in a single molecule and provides long interrogation times. This will allow the operation of a quantum-logic molecular radio-frequency clock in static electric fields, providing sensitivity to EDMs. Working with only a few ions and non-destructive detection techniques opens the door to the use of highly sensitive, rare, and radioactive molecular species as well as quantum-enhanced metrology schemes to achieve unprecedented levels of accuracy and precision.

We consider spin chains with a finite range Hamiltonian. For reasons of simplicity, the chain is taken to be infinitely long. A ground state is said to be a unique gapped ground state if its GNS Hamiltonian has a unique ground state, separated by a gap from the rest of the spectrum. By combining some powerful techniques developed in the last years, we prove that each unique gapped ground state is short-range entangled: It can be mapped into a product state by a finite time evolution map generated by a Hamiltonian with exponentially quasi-local interaction terms. This claim makes precise the common belief that one-dimensional gapped systems are topologically trivial in the bulk.

As is intrinsic to the fundamental goal of quantum computing, classical simulation of quantum algorithms is notoriously demanding in resource requirements. Nonetheless, simulation is critical to the success of the field and a requirement for algorithm development and validation, as well as hardware design. GPU-acceleration has become standard practice for simulation, and due to the exponential scaling inherent in classical methods, multi-GPU simulation can be required to achieve representative system sizes. In this case, inter-GPU communications can bottleneck performance. In this work, we present the introduction of MPI into the QED-C Application-Oriented Benchmarks to facilitate benchmarking on HPC systems. We review the advances in interconnect technology and the APIs for multi-GPU communication. We benchmark using a variety of interconnect paths, including the recent NVIDIA Grace Blackwell NVL72 architecture that represents the first product to expand high-bandwidth GPU-specialized interconnects across multiple nodes. We show that while improvements to GPU architecture have led to speedups of over 4.5X across the last few generations of GPUs, advances in interconnect performance have had a larger impact with over 16X performance improvements in time to solution for multi-GPU simulations.

Quantum information theory is a rapidly growing area of math and physics that combines two independent theories, quantum mechanics and information theory. Quantum entanglement is a concept that was first proposed in the EPR paradox. In quantum mechanics, particles can be in superposition, meaning they are in multiple different states at once. It is not until the particle is measured that it is forced into a single state. However, it is possible that particles can be tied to other particles, meaning that the measurement of one particle will determine the measurement of the other particle. Entanglement is at the very core of quantum information theory. It is one of the core pieces that allows for the massive increase in computing power. For this paper, we decided to focus on demonstrating the mathematical method (the Schmidt decomposition) for determining if a system is entangled, and a demonstration of quantum entanglement's use (quantum teleportation) as well as a quick look at how to extend the uses of the Schmidt decomposition.

This paper introduces the DIRSH algorithm for the Qubit Routing Problem (QRP), using a heuristic-guided randomized divide-and-conquer strategy. The method splits the circuit into chunks and optimizes each one with a stochastic selection of gates and swaps. It balances global search, via restarts and adaptive tuning of bandit parameters with depth-sensitive local pruning. Tested on RevLib benchmarks mapped to the 20-qubit IBMQ Tokyo topology, DIRSH outperformed three LightSABRE variants across different time budgets, achieving shorter depths and fewer swaps. These results confirm that combining chunk-based decomposition with bandit-driven heuristics is effective for routing quantum circuits on NISQ devices.

We give noise-robust, Probably Approximately Correct (PAC) guarantees of global $\varepsilon$-optimality for the Variational Quantum Eigensolver under explicit geometric conditions. For periodic ansatzes with bounded generators -- yielding a globally Lipschitz cost landscape on a toroidal parameter space -- we assume that the low-energy region containing the global minimum is a Morse--Bott submanifold whose normal Hessian has rank $r = O(\log p)$ for $p$ parameters, and which satisfies polynomial fiber regularity with respect to coordinate-aligned, embedded flats. This low-curvature-dimensional structure serves as a model for regimes in which only a small number of directions control energy variation, and is consistent with mechanisms such as strong parameter tying together with locality in specific multiscale and tied shallow architectures. Under this assumption, the sample complexity required to find an $\varepsilon$-optimal region with confidence $1-δ$ scales with the curvature dimension $r$ rather than the ambient dimension $p$. With probability at least $1-δ$, the algorithm outputs a region in which all points are $\varepsilon$-optimal, and at least one lies within a bounded neighborhood of the global minimum. The resulting complexity is quasi-polynomial in $p$ and $\varepsilon^{-1}$ and logarithmic in $δ^{-1}$. This identifies a geometric regime in which high-probability global optimization remains feasible despite shot noise.

We develop an analytic framework to extract circuit parameters and loss tangent from superconducting transmission-line resonators terminated by reactive loads, extending analysis beyond the perturbative regime. The formulation yields closed-form relations between resonant frequency, participation ratio, and internal quality factor, removing the need for full-wave simulations. We validate the framework through circuit simulations, finite-element modeling, and experimental measurements of van der Waals parallel-plate capacitors, using it to extract the dielectric constant and loss tangent of hexagonal boron nitride. Statistical analysis across multiple reference resonators, together with multimode self-calibration, demonstrates consistent and reproducible extraction of both capacitance and loss tangent in close agreement with literature values. In addition to parameter extraction, the analytic relations provide practical design guidelines for maximizing energy participation ratio in the load and improving the precision of resonator-based material metrology.

Density functional theory (DFT) is an indispensable ab initio method in both quantum chemistry and condensed matter physics. Based on recent advancements in reduced density matrix functional theory (RDMFT), a variant of DFT that is believed to be better suited for strongly correlated systems, we construct a mathematical framework generalizing all ground state functional theories, which in particular applies to fermionic, bosonic, and spin systems. We show that within the special class of such functional theories where the space of external potentials forms the Lie algebra of a compact Lie group, the $N$-representability problem is readily solved by applying techniques from the study of momentum maps in symplectic geometry, an approach complementary to Klyachko's famous solution to the quantum marginal problem. The ``boundary force'', a diverging repulsive force from the boundary of the functional's domain observed in previous works but only qualitatively understood in isolated systems, is studied quantitatively and extensively in our work. Specifically, we present a formula capturing the exact behavior of the functional close to the boundary. In the case where the Lie algebra is abelian, a completely rigorous proof of the boundary force formula based on Levy-Lieb constrained search is given. Our formula is a first step towards developing more accurate functional approximations, with the potential of improving current RDMFT approximate functionals such as the Piris natural orbital functionals (NOFs). All key concepts and ideas of our work are demonstrated in translation invariant bosonic lattice systems.

Quantum computers promise to redefine the boundaries of computational science, offering the potential for exponential speedups in solving complex problems across chemistry, optimization, and materials science. Yet, their practical utility remains constrained by unpredictable performance degradation under real-world noise conditions. A key question is how problem structure itself influences algorithmic resilience. In this work, we present a comprehensive, hardware-aware benchmarking study of the Bernstein-Vazirani algorithm across 11 diverse test patterns on multiple superconducting quantum processors, revealing that algorithmic performance is exquisitely sensitive to problem structure. Our results reveal average success rates of 100.0\% (ideal simulation), 85.2\% (noisy emulation), and 26.4\% (real hardware), representing a dramatic 58.8\% average performance gap between noisy emulation and real hardware execution. With quantum state tomography confirming corresponding average state fidelities of 0.993, 0.760, and a 0.234 fidelity drop to hardware. Performance degrades dramatically from 75.7\% success for sparse patterns to complete failure for high-density 10-qubit patterns. Most strikingly, quantum state tomography reveals a near-perfect correlation between pattern density and state fidelity degradation, providing the fundamental explanation for observed performance patterns. The catastrophic fidelity collapse observed in real hardware measurements -- dropping to 0.111 compared to the predicted 0.763 -- underscores severe limitations in current noise models for capturing structure-dependent error mechanisms. Our work establishes pattern-dependent performance as a critical consideration for quantum algorithm deployment and provides a quantitative framework for predicting algorithm feasibility in practical applications.

We present a technique for performing quantum detector tomography (QDT) of phase insensitive quantum detectors using gradient descent-based optimization to learn the positive operator-valued measure (POVM) that best describes the data collected using the detector under study. We numerically benchmark our method against constrained convex optimization (CCO) and show that it reaches higher or comparable reconstruction fidelity in much less time even in the presence of noise and limited probe state resources. We also present a possible extension of our approach to the phase sensitive case via a parametrization of POVMs on the complex Stiefel manifold which enables gradient based optimization restricted to this manifold.

Variational quantum algorithms (VQAs) combine the advantages of classical optimization and quantum computation, making them one of the most promising approaches in the Noisy Intermediate-Scale Quantum (NISQ) era. However, when optimized using gradient descent, VQAs often suffer from the vanishing gradient problem, commonly known as the barren plateau. Various methods have been proposed to mitigate this issue. In this work, we propose a hybrid approach that integrates a classical proportional-integral-derivative (PID) controller with a neural network to update the parameters of variational quantum circuits. We refer to this method as NPID, which aims to mitigate the barren plateau. The proposed algorithm is tested on randomly generated quantum input states and random quantum circuits with parametric noise to evaluate its universality, and additional simulations are conducted under different noise rates to examine its robustness. The effectiveness of the proposed method is evaluated based on its convergence speed toward the target cost value. Simulation results show that NPID achieves a convergence efficiency 2-9 times higher than NEQP and QV, with performance fluctuations averaging only 4.45% across different noise levels. These results highlight the potential of integrating classical control theory into quantum optimization, providing a new perspective for improving the trainability and stability of variational quantum algorithms.

Coherence is an inherently quantum property that deeply affects microscopic processes, including thermalization phenomena. A striking example is the quantum Mpemba effect (QME), in which a system can exhibit anomalous relaxation, thermalizing faster from a state initially farther from equilibrium than from one closer. Here, we experimentally investigate the genuine QME and observe how the dynamics of a spin-1/2 system interacting with a heat sink can be sped-up to equilibrium. Furthermore, we apply the QME in a quantum Otto refrigerator, thereby increasing its cooling power. This proof-of-concept experiment unveils new practical paths for improving quantum thermal tasks.

Quantum computing holds immense potential for transforming financial analysis and decision-making. Realising this potential necessitates the efficient encoding and processing of financial data on quantum computers. In this study, we propose using the GASP (Genetic Algorithm for State Preparation) framework to optimise the encoding of stock price data into quantum states and show it can enhance both the fidelity and efficiency of the encoding process. We demonstrate the efficacy of our approach by encoding stock price data onto both a simulated and real quantum computer to calculate the Singular Value Decomposition (SVD) entropy. Our results show improvements in fidelity and the potential for more precise financial analysis. This research provides insights into the applicability of GASP for the efficient encoding of real-world data, specifically stock price data, which is crucial for quantum advantage on noisy intermediate-scale quantum (NISQ) era quantum computers.

We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable. As a consequence, the effective dimension depends on the physical state of the system. Interestingly, systems of this form exhibit enhanced symmetries compared to their fixed-dimensional counterparts. As an explicit example, we analyze a harmonic oscillator for which the spatial dimension is represented by a quantum operator. By evaluating the corresponding partition function, we uncover a temperature-dependent effective dimension. Our framework opens a new avenue for constructing physical systems, from gravity to condensed matter, where the very notion of dimensionality becomes quantum.

We introduce a perturbative formulation for a nonlinear extension of the J-matrix method of scattering in two dimensions. That is, we obtain the scattering matrix for the time-independent nonlinear Schrödinger equation in two dimensions with circular symmetry. The formulation relies on the linearization of products of orthogonal polynomials and on the utilization of the tools of the J-matrix method. Gauss quadrature integral approximation is instrumental in the numerical implementation of the approach. We present the theory for a general ψ^{2n + 1} nonlinearity, where n is a natural number, and obtain results for the cubic and quintic nonlinearities, ψ^3 and ψ^5. At certain value(s) of the energy, we observe the occurrence of bifurcation with two stable solutions. This curious and interesting phenomenon is a clear signature and manifestation of the underlying nonlinearity.

Reconstructing protein-protein interaction networks is a central challenge in network medicine, often addressed using link prediction algorithms. Recent studies suggest that quantum walk-based approaches hold promise for this task. In this paper, we build on these algorithms by introducing chirality through the addition of random phases in the Hamiltonian generators. The resulting additional degrees of freedom enable a more diverse exploration of the network, which we exploit by employing a swarm of chiral quantum walks. Thus, we enhance the predictive power of quantum walks on complex networks. Indeed, compared to a non-chiral algorithm, the chiral version exhibits greater robustness, making its performance less dependent on the optimal evolution time--a critical hyperparameter of the non-chiral model. This improvement arises from complementary dynamics introduced by chirality within the swarm. By analyzing multiple phase-sampling strategies, we identify configurations that achieve a practical trade-off: retaining the high predictive accuracy of the non-chiral algorithm at its optimal time while gaining the robustness typical of chirality. Our findings highlight the versatility of chiral quantum walks and their potential to outperform both classical and non-chiral quantum methods in realistic scenarios, including comparisons between successive versions of evolving databases.

The Variational Quantum Eigensolver (VQE) is one of the most promising algorithms for current quantum devices. It employs a classical optimizer to iteratively update the parameters of a variational quantum circuit in order to search for the ground state of a given Hamiltonian. The efficacy of VQEs largely depends on the optimizer employed. Recent studies suggest that Quantum Natural Gradient Descent (QNG) can achieve faster convergence than vanilla gradient descent (VG), but at the cost of additional quantum resources to estimate Fubini-Study metric tensor in each optimization step. The Fubini-Study metric tensor used in QNG is related to the entire quantum state space and does not incorporate information about the target Hamiltonian. To take advantage of the structure of the Hamiltonian and address the limitation of additional computational cost in QNG, we propose Hamiltonian-aware Quantum Natural Gradient Descent (H-QNG). In H-QNG, we propose to use the Riemannian pullback metric induced from the lower-dimensional subspace spanned by the Hamiltonian terms onto the parameter space. We show that H-QNG inherits the desirable features of both approaches: the low quantum computational cost of VG and the reparameterization-invariance of QNG. We also validate its performance through numerical experiments on molecular Hamiltonians, showing that H-QNG achieves faster convergence to chemical accuracy while requiring fewer quantum computational resources.

Electron matter waves coherently diffract when passing through a periodic structure of light formed by two interfering light waves. In this so-called Kapitza-Dirac effect, the electron momentum changes due to absorption and emission of photons via stimulated Compton scattering. Until now, the effect has only been observed with low energy electrons due to the small momentum of a visible photon compared to the momentum of high energy electron leading to diffraction angles of 10^(-4) rad or smaller. We report on the observation of the Kapitza-Dirac effect in a scanning electron microscope using high energy (20 keV and 30 keV) electrons with de-Broglie wavelengths of 9 pm and 7 pm, respectively. The photon sidebands in the electron transverse momentum spectrum are detected in the convergent beam diffraction geometry using spatial filtering. As the coupling strength between the electrons and the light field increases, the sideband populations exhibit coherent, reversible oscillations among diffraction orders. The effect can serve as a coherent electron beam-splitter or a phase-plate in various types of electron microscopes.

We develop a hybrid qubit-qumode framework for simulating quantum electrodynamics in 2+1 dimensions. In this approach, fermionic matter fields are represented by qubits, while U(1) gauge fields are encoded in continuous-variable bosonic modes whose canonical quadratures capture the electric and vector-potential components of the theory. To reconcile the non-compact phase space of the qumodes with the compact U(1) gauge symmetry, we introduce and compare two complementary constraint-enforcement strategies: (i) a squeezing-based projection that confines qumode states to the unit circle through an effective modification of the inner product, and (ii) a method that dynamically enforces compactness via a penalty Hamiltonian term. We construct the corresponding hybrid Hamiltonian, derive its decomposition into experimentally accessible qubit-qumode gates, and analyze its spectrum in the analytically tractable single-plaquette limit. The hybrid formulation reproduces the correct gauge-invariant dynamics and provides a scalable route toward simulating Abelian lattice gauge theories coupled to fermionic matter on near-term hybrid quantum architectures. Ground-state preparation and convergence are demonstrated using a continuous-variable extension of the Quantum Imaginary Time Evolution (QITE) algorithm, establishing a general framework for hybrid discrete-continuous quantum simulations of lattice gauge theories.

The Dirac delta function potential is considered within the real Hilbert space approach for complex wave functions, as well as quaternionic wave functions. As has been previously determined, the real Hilbert space approach enables the possibility of self-interacting physical systems. The self-interaction precludes confining states, and also imposes non-stationary quantum states, both of them representing novel situations that cannot be observed in terms of quantum wave functions. These results remark the differences between quaternionic quantum mechanics ($\mathbbm H$QM) and complex quantum mechanics ($\mathbbm C$QM), and also establish a method of solving the wave equation that may be applied to a variety of different cases.

Partial differential equation (PDE)-constrained optimization, where an optimization problem is subject to PDE constraints, arises in various applications such as design, control, and inference. Solving such problems is computationally demanding because it requires repeatedly solving a PDE and using its solution within an optimization process. In this paper, we first propose a fully coherent quantum algorithm for solving PDE-constrained optimization problems. The proposed method combines a quantum PDE solver that prepares the solution vector as a quantum state, and a quantum optimizer that assumes oracle access to a quantized objective function. The central idea is the explicit construction of the oracle in a form of block-encoding for the objective function, which coherently uses the output of a quantum PDE solver. This enables us to avoid classical access to the full solution that requires quantum state tomography canceling out the potential quantum speedups. We also derive the overall computational complexity of the proposed method with respect to parameters for optimization and PDE simulation, where quantum speedup is inherited from the underlying quantum PDE solver. We numerically demonstrate the validity of the proposed method by applications, including a parameter calibration problem in the Black-Scholes equation and a material parameter design problem in the wave equation. This work presents the concept of composing quantum subroutines so that the weakness of one (i.e., prohibitive readout overhead) is neutralized by the strength of another (i.e., coherent oracle access), toward a bottleneck-free quantum algorithm.

Information scrambling, the process by which quantum information spreads and becomes effectively inaccessible, is central to modern quantum statistical physics and quantum chaos. These lecture notes provide an introduction to information scrambling from both static and dynamical perspectives. The spectral properties of reduced density matrices arising from Haar-random states are developed through the geometry of the unitary group and the universal results of random matrix theory. This geometric framework yields universal, model-independent predictions for entanglement and spectral statistics, capturing generic features of quantum chaos without reference to microscopic details. Dynamical diagnostics such as the spectral form factor and out-of-time-ordered correlators further reveal the onset of chaos in time-dependent evolution. The notes are aimed at advanced undergraduate and graduate students in physics, mathematics, and computer science who are interested in the connections between quantum chaos, information dynamics, and quantum computing. Concepts such as entanglement growth, Haar randomness, random-matrix statistics, and unitary t-designs are introduced through their realization in random quantum circuits and circuit complexity. The same mathematical framework also underpins modern quantum-device benchmarking, where approximate unitary designs and random circuits translate geometric ideas into quantitative tools for assessing fidelity, noise, and scrambling efficiency in real quantum processors.

We study quantum algorithms for approximating Lasserre's hierarchy values for polynomial optimization. Let $f,g_1,\ldots,g_m$ be real polynomials in $n$ variables and $f^\star$ the infimum of $f$ over the semialgebraic set $S(g)=\{x: g_i(x)\ge 0\}$. Let $λ_k$ be the value of the order-$k$ Lasserre relaxation. Assume either (i) $f^\star=λ_k$ and the optimum is attained in the $\ell_1$-ball of radius $1/2$, or (ii) $S(g)$ lies in the simplex $\{x\ge 0: \sum_j x_j\le 1/2\}$, and the constraints define this simplex. After an appropriate coefficient rescaling, we give a quantum algorithm based on matrix multiplicative weights that approximates $λ_k$ to accuracy $\varepsilon>0$ with runtime, for fixed $k$, \[ O(n^k\varepsilon^{-4}+n^{k/2}\varepsilon^{-5}),\qquad O\!\left(s_g\!\left[n^k\varepsilon^{-4}+\!\left(n^{k}+\!\sum_{i=1}^m n^{k-d_i}\right)^{1/2}\!\varepsilon^{-5}\right]\right), \] where $s_g$ bounds the sparsity of the coefficient-matching matrices associated with the constraints. Classical matrix multiplicative-weights methods scale as $O(n^{3k}\mathrm{poly}(1/\varepsilon))$ even in the unconstrained case. As an example, we obtain an $O(n\varepsilon^{-4}+\sqrt{n}\varepsilon^{-5})$ quantum algorithm for portfolio optimization, improving over the classical $O(n^{ω+1}\log(1/\varepsilon))$ bound with $ω\approx2.373$. Our approach builds on and sharpens the analysis of Apeldoorn and Gilyén for the SDPs arising in polynomial optimization. We also show how to implement the required block encodings without QRAM. Under the stated assumptions, our method achieves a super-quadratic speedup in the problem dimension for computing Lasserre relaxations.

We demonstrate a method for generating entanglement between trapped atomic ions based on adiabatically ramped state-dependent forces. By ramping both the amplitude of the state-dependent force and the motional mode frequencies, we realize an entangling operation that is robust to motional mode occupation and drifts in the mode frequencies. We measure Bell state fidelities above 0.99 across a broad range of ramp parameters and with motional occupations up to 10 phonons. This technique enables high-fidelity entangling operations without ground-state cooling, has a reduced calibration overhead, and is well suited for both quantum logic spectroscopy applications and scalable quantum computing architectures.

Many living organisms can exploit quantum mechanical effects to gain distinct biological advantages. In plants, photosynthesis uses quantum coherence to achieve near 100% efficiency in energy transfer. With advances in experimental techniques, two-dimensional electronic spectroscopy can reveal dynamic processes such as coherence and coupling within a system, and it plays an important role in studying energy transfer in photosynthesis. On the theory side, methods such as the generalized Bloch-Redfield theory and the hierarchical equations of motion are used to model photosynthetic systems. Quantum simulation, as a high-efficiency and low-complexity approach, has also made progress across various platforms in the study of photosynthesis. In recent years, a series of studies has introduced quantum coherence into artificial systems to enhance energy transfer efficiency, laying the groundwork for the design of coherent devices with efficient energy transport. Birds can use the weak geomagnetic field and spin-dependent chemical reactions to detect direction. Theoretical frameworks for animal navigation include magnetite-based mechanisms, magnetoreceptor genes, and the radical-pair mechanism. Quantum simulations of navigation have also advanced on multiple platforms. Inspired by animal navigation, diverse quantum effects have been applied to improve sensing and to support navigation tasks. This paper presents a comprehensive review of progress on quantum coherence in photosynthesis and avian navigation, along with related theoretical methods, quantum simulation approaches, and research on quantum coherent devices.

We extend a four-qubit quantum circuit model of black hole evaporation that enforces semi-causality, a condition that allows information to enter a black hole but strictly forbids any information from escaping from the interior to outside through the horizon. In this work, we introduce a controlled violation of this principle by inserting a parametric controlled-unitary gate that enables a tunable leakage of quantum information from the black hole interior to the exterior, while preserving global unitarity. By varying the deformation parameter, we study the evolution of entanglement entropy, mutual information, and entanglement negativity throughout the evaporation process. While the semi-causal case yields a Page-like entropy curve with vanishing late-time correlations, we find that even small violations of semi-causality produce a non-zero residual entropy and persistent negativity across the horizon. These features mimic quantum-gravity-induced effects such as remnant formation and horizon permeability, suggesting that minimal deviations from classical causality can leave long-lived imprints on black hole information dynamics.

Advances in quantum algorithms as well as in control hardware designs are continuously being made. These quantum algorithms, expressed as quantum circuits, need to be translated to a set of instructions from a defined quantum instruction-set architecture (ISA), which are executed by the control hardware. These translations can be done by a compiler, targeting different qubit technologies. Specifically for diamond NV centers, no compiler exists to perform this translation. Therefore, in this paper we present a compiler designed for quantum computers utilizing diamond NV center specific instructions, such as direct carbon control and partial swaps, to reduce execution times and gate count. Additionally, our compiler adds on top of general compilers by allowing classical instructions to perform state tomography and measurement-based operations. The output of the compiler is tested in a diamond NV center specific simulator. Comparing a general compiler output with the diamond NV center specific output of our compiler while applying decoherence and depolarization noise showed reduced noise effects due to diamond specific decomposition. The compiler was also tested to perform state tomography and measurement-based operations, which showed to be functional. Our results show that we have successfully created a compiler with integrated classical and quantum instructions support, which can improve circuit execution fidelity by utilizing diamond specific optimizations.

We introduce the Constraint-Enhanced Quantum Approximate Optimization Algorithm (CE-QAOA), a shallow, constraint-aware ansatz that operates inside the one-hot product space of size [n]^m, where m is the number of blocks and each block is initialized with an n-qubit W_n state. We give an ancilla-free, depth-optimal encoder that prepares a W_n state using n-1 two-qubit rotations per block, and a two-local XY mixer restricted to the same block of n qubits with a constant spectral gap. Algorithmically, we wrap constant-depth sampling with a deterministic classical checker to obtain a polynomial-time hybrid quantum-classical solver (PHQC) that returns the best observed feasible solution in O(S n^2) time, where S is the number of shots. We obtain two advantages. First, when CE-QAOA fixes r >= 1 locations different from the start city, we achieve a Theta(n^r) reduction in shot complexity even against a classical sampler that draws uniformly from the feasible set. Second, against a classical baseline restricted to raw bitstring sampling, we show an exp(Theta(n^2)) separation in the minimax sense. In noiseless circuit simulations of TSP instances ranging from 4 to 10 locations from the QOPTLib benchmark library, we recover the global optimum at depth p = 1 using polynomial shot budgets and coarse parameter grids defined by the problem sizes.

Strongly correlated multi-photon states are indispensable resources for advanced quantum technologies, yet their deterministic generation remains challenging due to the inherent weak nonlinearity in most optical systems. Here, we propose a scalable architecture for producing correlated few-photon entangled states via cascaded inelastic scattering in a nonlinear waveguide. When a single photon scatters off a far detuned excited two-level emitter, it coherently converts into a propagating doublon, a bound photon pair with anomalous dispersion. This doublon can subsequently scatter off a downstream excited emitter to further convert into a triplon, and so on, thereby establishing a photon-number amplification cascade $|\cdot \rangle \!\! \rightarrow \!\! |\!\!: \rangle \!\! \rightarrow \! \! |\!\!\therefore \rangle \!\! \to \!\! ...$ Central to this process is the concept of a pseudo-giant atom, which we introduce here to capture the non-local scattering potential emergent from the wave functions of bound states. By implementing this scheme using a real giant atom with multiple engineered coupling points, we achieve unidirectional and full controllable photon conversion without backscattering. The resulting output state forms a programmable superposition of spatially and temporally isolated photon-number components, automatically sorted by their distinct group velocities. This work opens a new paradigm in quantum state engineering, enabling on-demand generation of complex multi-photon resources for quantum simulation, metrology, and scalable quantum networks.

We look into the task of differentiating between any two quantum channels and reconstructing them from the obtained measurement statistics with possibly limited information about the experimental set-up. We employ the communication matrix formalism where the measurement statistics of a prepare-and-measure scenario is represented as a stochastic communication matrix. In order to differentiate between any two quantum channels, the informational completeness of the set-up is both necessary and sufficient. On the other hand, if we want to uniquely characterize any quantum channel, in addition we also need to have a complete description of the set-up. We show that in many important cases we can deduce this information directly from the communication matrix of the set-up before applying the channel. Given that we trust the dimension of the system, we show that we can deduce the information completeness of the set-up directly from the rank of the communication matrix. Furthermore, we show that another quantity of the communication matrix, called the information storability, can be used to self-test the set-up (up to unitary or antiunitary freedom) for an important class of states and measurements. This provides us a semi-device-independent way to identify quantum channels from the prepare-and-measure statistics. Lastly, we consider scenarios where we might have some additional information about the channels or additional resources at our disposal which could help us relax some of the assumptions of the proposed scenario.

Magnetic topology is central to modern quantum magnet, where spin chirality governs exotic spin winding, real-space Berry phase, and topological Hall effect. A key unresolved challenge is how to electrically switch topological spin chirality and its associated gauge flux, an essential requirement for manipulating its topological quantum properties. In this work, we propose and experimentally demonstrate the concept of current-switching spin chirality. We identify the new vdW antiferromagnet Co1/3TaS2 as an ideal platform, hosting a topological 3Q state with a minimum chirality cell, an ultrahigh skyrmion density, a non-centrosymmetric geometry, and a strong Berry curvature. Using a Co1/3TaS2/Pt heterostructure, we achieve the nonvolatile and reversible switching by current via current-driven spin-orbit torque based on Pts spin Hall effect. Beyond this conventional route, we further discover intrinsic self-torque-induced chirality switching within Co1/3TaS2, driven purely by current, without a magnetic field, and with high energy efficiency. These complementary pathways establish a unified framework for electrically creating and controlling spin chirality. Our results demonstrate a practical route toward chiral spintronics. They can be naturally generalised to other skyrmion systems, offering new opportunities in symmetry control, topological manipulation, and spin-chirality-based quantum functionalities.

Entropic uncertainty relations quantify the limits on the predictability of quantum measurements. When the measured system is correlated with a quantum memory, these limits are described by the memory-assisted entropic uncertainty relation (MA-EUR). We examine the behavior of MA-EUR when the memory qubit undergoes noisy dynamics implemented via high-order controlled processes, namely, the quantum switch and the quantum time-flip. We consider a setting in which the control qubit is the very system on which the measurements are performed, while the target qubit serves as a noisy quantum memory. Focusing on Pauli channels, we show that feeding them into the quantum switch and the quantum time-flip can significantly reduce the total entropic uncertainty as compared to their direct application. Our results reveal that indefinite causal order and input-output direction can serve as resources to mitigate the effects of noise in the context of MA-EUR and its applications.

Spectrotemporal encoding of optical quantum information is emerging as a powerful tool in quantum information technology. Processing of spectrotemporal information has recently been demonstrated in multi-mode quantum memories, based on extensions to memory protocols. We simulate one such process, the fractional Fourier transform, in a system based on a dual quantum memory composed of successive gradient echo memory and electromagnetically-induced transparency operations. We demonstrate the potential of electromagnetically-induced transparency systems for spectrotemporal processing.

We formulate a canonical quantization of Equilibrium Thermodynamics by applying Dirac's theory of constrained systems. Thermodynamic variables are treated as conjugate pairs of coordinates and momenta, allowing extensive and intensive quantities to be promoted to operators in a Hilbert space. The formalism is applied to the ideal gas, the van der Waals gas, and the photon gas, illustrating both first- and second-class quantization procedures. For the ideal gas, a Schrödinger-like equation emerges in which entropy plays the role of time, and the wave function acquires a phase determined by the internal energy. A pseudo-Hermitian framework restores Hermiticity of the temperature operator and establishes the equivalence among constraint realizations. The approach naturally leads to thermodynamic uncertainty relations and suggests extensions to quantum and topological phase transitions, as well as black-hole and non-equilibrium thermodynamics.

We study the entanglement asymmetry for the space-inversion symmetry of free fermions on a two-dimensional honeycomb lattice with an on-site energy imbalance between the two sublattices. We show that the entanglement asymmetry of a local subsystem exhibits nonanalytic dependence on the energy imbalance, due to the presence of Dirac points in the Brillouin zone. We also study the quench dynamics from the ground state into the inversion-symmetric point at which the energy imbalance vanishes. Under certain conditions on the subsystem geometry, the entanglement asymmetry relaxes to a finite value after the quench, revealing that the inversion-symmetry breaking in the initial ground state can persist even under the symmetric dynamics. We attribute the absence of symmetry restoration to the presence of a flat energy dispersion (flat band) in a specific direction.

The present study systematically investigates the modulation mechanism of post-selected weak measurement (WM) on the non-classical properties of entangled coherent states (ECSs). The primary goal is achieving controllable enhancement of quantum resources such as entanglement and squeezing, while minimising disturbance to the quantum state. We theoretically analyze the post-selected weak measurement process, and its effectiveness in amplifying the non-classical features of ECSs. The von Neumann measurement model is employed to analytically describe the weak-value amplification of the pointer state. It is demonstrated that a significant enhancement of squeezing can be achieved by tuning the measurement coupling strength. The joint Wigner function analysis in phase space further reveals that, as the coupling strength increases, the coherent structure of the state evolves from symmetric double peaks to multi-branch quantum interference fringes. The entanglement, quantified by the Hillery-Zubairy criterion, exhibits a pronounced increase with stronger coupling, while the quantum Fisher information indicates a systematic improvement in phase estimation precision. The results obtained establish a tunable weak measurement framework for precise manipulation of continuous-variable entangled states. This provides a feasible theoretical pathway for enhancing quantum metrology and measurement-based state engineering.

Postselection is a non-deterministic mechanism to entangle subsystems, often used in weakly-excited systems. We here show how highly-excited ensembles of two-level emitters can be entangled by photon detection. A collective spin is formed, characterized by a squeezing parameter detected by far-field measurements. While decoherence is detrimental to this conditional entanglement, successive photon detections act as a purification process and restores the spin squeezing. Our work opens up new avenues for the generation of postselected entanglement in open quantum systems.

We examine a quantum routing mechanism utilizing a giant-atom-like array coupled to two one-dimensional waveguides. The giant-atom-like array is formed by a one-dimensional array of three-level-systems. In the regime of strong atom-waveguide coupling and weak inter-atomic interactions, this system functions as an efficient and directionally controllable single-photon router. Our analysis shows that the routing behavior is influenced by effective phase accumulation and interference effects, which can be adjusted by varying the number of coupling sites $N$, the photon energy $E$, and the inter-atomic coupling strength $J$. Importantly, we identify configurations that enable perfect photon transfer ($100 \%$ efficiency) over a wide range of energies and that provide dynamic control over the output channel. In addition, we investigate how the system responds to changes in its internal parameters, demonstrating the robustness and scalability of routing performance. These findings underscore the potential of this setup for implementation in reconfigurable and integrated quantum photonic networks.

We study a single electron confined in a uniform-torsion medium, a continuum model of a screw dislocation density, in a perpendicular magnetic field, and in the presence of an Aharonov--Bohm flux. Torsion alone produces radial confinement without any \textit{ad hoc} potential, while the Aharonov--Bohm phase breaks the usual $m\leftrightarrow -m$ symmetry. From the exact spectrum and wave functions, we find: (i) a torsion-controlled optical transition whose energy blue-shifts from $\sim 6.8$ to $\sim 15.5$~meV and whose saturation intensity varies by an order of magnitude, enabling geometry-programmable optical switching; (ii) an Aharonov--Bohm-tunable ``angular pseudospin'' formed by the $m=\pm1$ states, with flux-controlled level splitting and asymmetric oscillator strengths that allow selective optical addressability; and (iii) an approximately linear torsion dependence of the transition energy that enables nanoscale torsion metrology with an estimated resolution of $\sim 10^{5}~\mathrm{m}^{-1}$. In this context, ``torsion'' refers to the experimentally relevant continuum limit of a uniform density of parallel screw dislocations, i.e., a crystal with finite torsion but vanishing curvature, which can, in practice, be engineered and probed in twisted nanowires and strained semiconductor heterostructures. We also show how torsion provides \textit{in situ} control of emitter--cavity detuning and light--matter coupling in cavity QED, in direct analogy with strain tuning of semiconductor quantum dots in nanocavities, but here arising from a purely geometric/topological parameter.

Quantum computing has traditionally centered around the discrete variable paradigm. A new direction is the inclusion of continuous variable modes and the consideration of a hybrid continuous-discrete approach to quantum computing. In this paper, we discuss some of the advantages of this modality, and lay out a number of potential applications that can make use of it; these include applications from physics, chemistry, and computer science. We also briefly overview some of the algorithmic and software considerations for this new paradigm.

We introduce the correlation-efficient time-evolution (CETE) algorithm for simulating quantum many-body dynamics. CETE recasts each step of time evolution as a time-independent correlation problem: the ansatz begins from a mean-field single Slater determinant and is then correlated to capture the true time-evolved state. We derive this exact ansatz from a contraction of the time-dependent Schrödinger equation onto the space of two electrons. Unlike conventional evolution by sequential short-time propagators, which must both correlate and decorrelate the state as the degree of correlation fluctuates in time, CETE correlates only once. This substantially reduces circuit depth, extending accessible simulation times on near-term quantum devices. We demonstrate the approach by simulating the time evolution of the hydrogen molecule's electronic wavefunction, highlighting the potential for the CETE algorithm to simulate strongly correlated systems on near-term devices.

This study examines the quantitative relationship between linguistic regularities and computational search complexity through a hybrid classical-quantum framework applied to Renaissance Italian texts. Using four representative works from the fifteenth and sixteenth centuries-Il Principe (Machiavelli), Il Cortegiano (Castiglione), I Ricordi (Guicciardini), and Orlando Furioso (Ariosto)-we construct character-based n-gram models under both a historically grounded 25-letter orthography and the full modern Italian alphabet. These models provide corpus-derived probabilistic baselines for evaluating substitution-cipher search processes. Combining classical hill climbing and simulated annealing with Grover-style quantum-inspired estimates and a QUBO annealing formulation, we quantify how the probability that a key produces a linguistically plausible decryption (pgood) relates to expected computational effort. Across cipher lengths from 200 to 1000 characters, empirical results confirm the predicted dependence of Grover oracle calls on 1/sqrt(pgood) and show that longer texts yield sharper score distributions and smaller feasible key regions. Overall, the findings establish a link between linguistic redundancy and search-space contraction, providing an empirical framework for comparing classical, quantum-inspired, and idealized quantum search dynamics under unified corpus-driven constraints.

Quantum simulation is a promising application for quantum computing. Quantum simulation algorithms may require the ability to control the time evolution unitary. Naive techniques to control a unitary can substantially increase the required computational resources. A standard approach to controlling Trotterized time evolution doubles the number of single-qubit arbitrary rotations. Here, we describe a compilation scheme that does not increase the number of arbitrary rotations for symmetric Trotterizations, which applies to second-order and higher Suzuki-Trotter decompositions. This halves the number of arbitrary rotations required to implement controlled, Trotterized time evolution compared to the standard approach. Arbitrary rotations contribute significantly to resource estimates in a fault-tolerant architecture due to the number of required magic states. Therefore, arbitrary rotations dominate the $T$-cost of fault-tolerant implementations of quantum simulation. This construction reduces the number of arbitrary rotations for controlled Trotter evolution to that of uncontrolled Trotter evolution, thereby reducing the cost of fault-tolerant quantum simulation.

Quantum generative learning is a promising application of quantum computers, but faces several trainability challenges, including the difficulty in experimental gradient estimations. For certain structured quantum generative models, however, expectation values of local observables can be efficiently computed on a classical computer, enabling fully classical training without quantum gradient evaluations. Although training is classically efficient, sampling from these circuits is still believed to be classically hard, so inference must be carried out on a quantum device, potentially yielding a computational advantage. In this work, we introduce Fermionic Born Machines as an example of such classically trainable quantum generative models. The model employs parameterized magic states and fermionic linear optical (FLO) transformations with learnable parameters. The training exploits a decomposition of the magic states into Gaussian operators, which permits efficient estimation of expectation values. Furthermore, the specific structure of the ansatz induces a loss landscape that exhibits favorable characteristics for optimization. The FLO circuits can be implemented, via fermion-to-qubit mappings, on qubit architectures to sample from the learned distribution during inference. Numerical experiments on systems up to 160 qubits demonstrate the effectiveness of our model and training framework.

Nonstabiliserness is a fundamental resource for quantum advantage, capturing how much a quantum state breaks the symmetries that would make it classically simulable. Can nonstabiliserness be generated from stabiliser states simply by coupling them to a heat bath? We explore the thermodynamic limits of nonstabiliserness under minimal assumptions and derive a necessary and sufficient condition for when such a process can create it from an initial stabiliser state. This provides an analytic characterisation of the nonstabiliser states that are reachable in this way, together with quantitative bounds on their degree of nonstabiliserness. Our framework also identifies optimal regimes, specifying Hamiltonians that maximise nonstabiliserness generation and the critical temperatures at which it emerges.

Defects associated with non-invertible symmetries have attracted significant attention in recent years. Among them, Kramers-Wannier (KW) duality defects have been investigated in both classical statistical systems and quantum Hamiltonian models. Aasen et al. analyzed duality defects in the 2D Ising model and in statistical models built from fusion categories, while Koide et al. later constructed a duality defect in 4D lattice gauge theory. In this work, we extend these developments by providing a systematic construction of KW duality defects/KW defects for a broad class of models formulated within the chain complex framework. Our construction employs the strange correlator, an overlap between a topologically ordered state and a product state, to realize these KW defects.

Multiscale synergy -- the interplay of a system's distinct characteristic length, time, and energy scales -- is becoming a unifying thread across many contemporary branches of science. Ranging from moiré and super-moiré materials and cold atoms to DNA-templated superlattices and nested photonic networks, multiscale synergy produces behaviors not obtainable at any single scale alone. Yet a general framework that programs cross-scale interplay to steer spectra, transport, and topology has been missing. Here, we elevate multiscale synergy from a byproduct to a general design principle for emergent phenomena. Specifically, we introduce a scale-programmable framework for hierarchically nested lattices (HNLs) that can host quantum metamorphosis (QuMorph) -- a continuous evolution between system-dependent features governed by a dimensionless tunable parameter $α$ (the relative hopping). To exemplify, we show an HNL, in which as $α$ changes, the spectrum metamorphoses from integer quantum Hall-like to anomalous quantum Hall-like, passing through a cocoon regime with proliferating mini-gaps. This multiscale mixing yields multiple novel phenomena, including hybrid edge-bulk states, scale-dependent topology, topologically embedded flat bands, and isolated edge bands. We propose a feasible photonic implementation using commercially available coupled-resonator arrays, outline spatial-spectral signatures to map QuMorph, and explore applications for multi-timescale nonlinear optics. Our work establishes a scalable and programmable paradigm for engineering multiscale emergent phenomena.

We present a single-quench protocol that generates unitary $k$-designs with minimal control. A system first evolves under a random Hamiltonian $H_1$; at a switch time $t_s \geq t_{\mathrm{Th}}$ (the Thouless time), it is quenched to an independently drawn $H_2$ from the same ensemble and then evolves under $H_2$. This single quench breaks residual spectral correlations that prevent strictly time-independent chaotic dynamics from forming higher-order designs. The resulting ensemble approaches a unitary $k$-design using only a single control operation -- far simpler than Brownian schemes with continuously randomized couplings or protocols that apply random quenches at short time intervals. Beyond offering a direct route to Haar-like randomness, the protocol yields an operational, measurement-friendly definition of $t_{\mathrm{Th}}$ and provides a quantitative diagnostic of chaoticity. It further enables symmetry-resolved and open-system extensions, circuit-level single-quench analogs, and immediate applications to randomized measurements, benchmarking, and tomography.

We propose a hybrid quantum-classical algorithm for approximating the ground state of two-dimensional quantum systems using an isometric tensor network ansatz, which maps naturally to quantum circuits. Inspired by the density matrix renormalization group, we optimize tensors sequentially by diagonalizing a series of effective Hamiltonians. These are constructed using a tomography-inspired method on a qubit subset whose size depends only on the bond dimension. Our approach leverages quantum computers to enable accurate solutions without relying on approximate contractions, circumventing the exponential complexity faced by classical techniques. We demonstrate our method on the two-dimensional (2D) transverse-field Ising model, achieving ground-state optimization on up to 25 qubits with modest quantum overhead -- significantly less than standard solutions based on variational quantum eigensolvers. Overall, our results offer a path towards scalable variational quantum algorithms in both noisy and fault-tolerant regimes.

We construct parametrized isometric tensor network states -- referred to as skeletons -- that allow us to explore phases of abelian topological order and can be efficiently implemented on quantum processors. We obtain stable finite correlation length deformations of string-net fixed points, which are constructed both by conserving virtual symmetries of the tensor and by imposing local isometry constraints. They connect distinct topological phases via a shared critical point, thereby providing analytically tractable examples of phase transitions beyond anyon condensation. By mapping such classes of 2D tensor networks to 1D stochastic automata with local update rules, we show that expectation values of generalized Pauli strings of arbitrary weight can be efficiently computed using classical methods. Therefore these skeletons not only serve as an organizing principle for abelian topological order but also provide a non-trivial testbed for quantum processors.

We present a method to detect entanglement partitions of multipartite quantum systems, by exploiting their inherent symmetries. Structures like genuinely multipartite entanglement, $m$-separability and entanglement depth are detected as very special cases. This formulation enables us to characterize all the entanglement partitions of all three- and four- partite states and witnesses with unitary and permutation symmetry. In particular, we find and parametrize a complete set of bound entangled states therein. For larger systems, we provide a large family of analytical witnesses detecting many-body states of arbitrary size where none of the parties is separable from the rest. This method relies on weak Schur sampling with projective measurements, and thus can be implemented in a quantum computer. Beyond physics, our results extend to the mathematical literature: we establish new inequalities between matrix immanants, and characterize the set of such inequalities for matrices of size three and four.

We construct two quantum error correction codes for pure SU(2) lattice gauge theory in the electric basis truncated at the electric flux $j_{\rm max}=1/2$, which are applicable on quasi-1D plaquette chains, 2D honeycomb and 3D triamond and hyperhoneycomb lattices. The first code converts Gauss's law at each vertex into a stabilizer while the second only uses half vertices and is locally the carbon code. Both codes are able to correct single-qubit errors. The electric and magnetic terms in the SU(2) Hamiltonian are expressed in terms of logical gates in both codes. The logical-gate Hamiltonian in the first code exactly matches the spin Hamiltonian for gauge singlet states found in previous work.

Realizing distributed architectures for quantum computing is crucial to scaling up computational power. A key component of such architectures is a scheduler that coordinates operations over a short-range quantum network required to enable the necessary non-local entangling gates between quantum processing units (QPUs). It is desirable to determine schedules of minimum make span, which in the case of networks with constrained resources hinges on their efficient usage. Here we compare and contrast two approaches to solving the make span minimization problem, an approach based on the resource constrained project scheduling (RCPSP) framework, and another based on a greedy heuristic algorithm. The workflow considered is as follows. Firstly, the computational circuit is partitioned and assigned to different QPUs such that the number of nonlocal entangling gates acting across partitions is minimized while the qubit load is nearly uniform on the individual QPUs, which can be accomplished using, e.g., the METIS solver. Secondly, the nonlocal entangling gate requirements with respect to the partitions are identified, and mapped to network operation sequences that deliver the necessary entanglement between the QPUs. Finally, the network operations are scheduled such that the make span is minimized. As illustrative examples, we analyze the implementation of a small instance of the Quantum Fourier Transform algorithm over instances of a simple hub and spoke (star) network architecture comprised of a quantum switch as the hub and QPUs as spokes, each with a finite qubit resource budget. In one instance, our results show the RCPSP approach outperforming the greedy heuristic. In another instance, we find the two performing equally well. Our results thus illustrate the effectiveness of the RCPSP framework, while also underlining the relevance and usefulness of greedy heuristics.

We study the task of learning mixed unitary channels using Fisher information, under different quantum resource assumptions including ancilla and concatenation. Our result shows that the asymptotic sample complexity scales as $\frac{r}{d\varepsilon^2}$, where $r$ is the rank of the channel (i.e.\ the number of different unitaries), $d$ is the dimension of the system, and $\varepsilon^2$ is the mean-square error. Thus the critical resource is the ancilla, which mirrors the result in~\cite{chen2022quantum} but in a more precise form, as we point out that $r$ is also important. Additionally, we demonstrate the practical potential of mixed unitary channels by showing that random mixed unitary channels are easy to learn.

We introduce a three-stroke quantum isochoric cycle that functions as a heat engine operating between two thermal reservoirs. Implemented for a particle confined in a one-dimensional infinite potential well, the cycle's performance is benchmarked against the classical three-stroke triangular and isochoric engines. We find that the quantum isochoric cycle achieves a higher efficiency than both classical counterparts and also surpasses the efficiency of the recently proposed three-stroke quantum isoenergetic cycle. Owing to its reduced number of strokes, the design substantially lowers control complexity in nanoscale thermodynamic devices, offering a more feasible route to experimental realization compared to conventional four-stroke architectures. We further evaluate the cycle in graphene-based systems under an external magnetic field, including monolayer graphene (MLG), AB-stacked bilayer graphene (BLG), and twisted bilayer graphene (TBG) at both magic and non-magic twist angles. Among these platforms, magic-angle twisted bilayer graphene (MATBG) attains the highest efficiency at fixed work output, highlighting its promise for quantum thermodynamic applications.

The random nature of spontaneous emission leads to unavoidable fluctuations in a laser's output. This is often included through random Langevin forces in laser rate equations, but this approach falls short for nanolasers. In this paper, we show that the laser quantum noise can be quantitatively computed for a very broad class of lasers by starting from simple and intuitive rate equations and merely assuming that the number of photons and excited electrons only takes discrete values. The success of the model is explained by showing that it constitutes a Markov chain, which can be derived from the full master equations. We show that in the many-photon limit, the model simplifies to Langevin equations. We perform an extensive comparison of different approaches for computing quantum noise in lasers, identifying the best approach for different system sizes, ranging from nanolasers to macroscopic lasers, and different levels of excitation, i.e., cavity photon number. In particular, we find that the numerical solution to the Langevin equations is inaccurate below the laser threshold, while the laser Markov chain model, on the other hand, is accurate for all pump values and laser sizes when collective emitter effects are excluded.

Frequency combs are multimode photonic systems that underlie countless precision sensing and metrology applications. Since their invention over two decades ago, numerous efforts have pushed frequency combs to broader bandwidths and more stable operation. More recently, quantum squeezing and entanglement have been explored in single frequency comb systems for quantum advantages in sensing and signal multiplexing. However, the production of quantum light across multiple frequency combs remains unexplored. In this work, we theoretically explore a mechanism that generates a series of nonlinearly coupled frequency combs through cascaded three-wave upconversion and downconversion processes mediated by a single idler comb. We show how this system generates inter- and intracomb two-mode squeezing and entanglement spanning a very large spectral range, from ultraviolet to mid-IR frequencies. Finally, we show how this system can be engineered to produce on-demand multimode quantum light through covariance matrix optimization. Our findings could enable tunable broadband ghost spectroscopy protocols, squeezing-enhanced pump-probe measurements, and broadband entanglement between spectrally-multiplexed quanta of information.

We apply the methodology of our recent paper 'The Dynamics of the Hubbard Model through Stochastic Calculus and Girsanov Transformation' [1] to thermodynamic correlation functions in the Fermi-Hubbard model. They can be obtained from a stochastic differential equation (SDE) system. To this SDE system, a Girsanov transformation can be applied. This has the effect that the usual determinant or pfaffian which shows up in a pfaffian quantum Monte Carlo (PfQMC) representation [2] basically gets absorbed into the new integration variables and information from that pfaffian moves into the drift part of the transformed SDE system. While the PfQMC representation depends heavily on the choice of how the quartic interaction has been factorized into quadratic quantities in the beginning, the Girsanov transformed formula has the very remarkable property that it is nearly independent of that choice, the drift part of the transformed SDE system as well as a remaining exponential which has the obvious meaning of energy are always the same and do not depend on the Hubbard-Stratonovich details. The resulting formula may serve as a starting point for further theoretical or numerical investigations. Here we consider the spin-spin correlation at half-filling on a bipartite lattice and obtain an analytical proof that the signs of these correlations have to be of antiferromagnetic type, at arbitrary temperatures. Also, by checking against available benchmark data [3], we find that approximate ground state energies can be obtained from an ODE system. This may even hold for exact ground state energies, but future work would be required to prove or disprove this. As in [1], the methodology is generic and can be applied to arbitrary quantum many body or quantum field theoretical models.

We develop an analytic approach to evaluating the density $ρ({\cal E},Γ)$ of complex resonance poles with real energies $\mathcal{E}$ and widths $Γ$ in the pure reflection problem from a one-dimensional disordered sample with white-noise random potential. We start with establishing a general link between the density of resonances and the distribution of the reflection coefficient $r=|R(E,L)|^2$, where $R(E,L)$ is the reflection amplitude, at {\it complex} energies $E = {\cal E} +iη$, identifying the parameter $η>0$ with the uniform rate of absorption within the disordered medium. We show that leveraging this link allows for a detailed analysis of the resonance density in the weak disorder limit. In particular, for a (semi)infinite sample, it yields an explicit formula for $ρ({\cal E},Γ)$, describing the crossover from narrow to broad resonances in a unified way. Similarly, our approach yields a limiting formula for $ρ({\cal E},Γ)$ in the opposite case of a short disordered sample, with size much smaller than the localization length. This regime seems to have not been systematically addressed in the literature before, with the corresponding analysis requiring an accurate and rather non-trivial implementation of WKB-like asymptotics in the scattering problem. Finally, we study the resonance statistics numerically for the one-dimensional Anderson tight-binding model and compare the results with our analytic expressions.