Papers

Magic states are a foundational resource for universal quantum computation. To survive in a realistic noisy environment, magic states must be prepared fault-tolerantly and protected by a quantum error-correcting code. The recent discovery of highly efficient quantum low-density parity-check codes, together with efficient logic gates, lays the groundwork for low-overhead fault-tolerant quantum computation. This motivates the search for fast and parallel protocols for logical magic state preparation to enable universal quantum computation. Here, we introduce a fast code surgery procedure that performs a fault-tolerant measurement of many transversal logic gates in parallel. This is achieved by performing a generalized gauging measurement on a quantum code that supports a higher-form transversal gate. The time overhead of our procedure is constant, and the qubit overhead is linear. The procedure inherits fault-tolerance properties from the base code and the structure of the higher-form transversal gate. When applied to codes that support higher-form Clifford gates our procedure achieves fast and fault-tolerant preparation of many magic states in parallel. This motivates the search for good quantum low-density parity-check codes that support higher-form Clifford gates.

We improve on our version of the second law of thermodynamics as a deterministic theorem for quantum spin systems in two basic aspects. The first concerns the general statement of the second law: spontaneous changes in an adiabatically closed system will always be in the direction of increasing mean entropy, which rises to a maximal value. Two specific examples concern the transition from pure to mixed states in two different universality classes of dynamics in one dimension, one being the exponential model, the other the Dyson model, the dynamics of the latter exhibiting strong graphical evidence of quantum chaos, as a consequence of the results of Albert and Kiessling on the Cloitre function.

Bell conditions for local realism are critically revisited. In particular for optical experiments I criticize Bell's proposed response of detectors to signals as extremely idealized. More physical conditions are proposed, whence a realistic local model of an optical experiment is possible which violates the Clauser-Horne (Bell) inequality. The possibility rests on the existence of a coincidence-time loophole in the experiments.

We propose and investigate a scheme for the steady-state emission of quantum-correlated, telecom-band light from a single multilevel atom. By appropriately tuning the frequency of a pair of lasers, a two-photon transition is continually driven to an atomic excited state that emits photons at the desired wavelength. We show that resonantly coupling a cavity mode to the telecom transition can enhance the rate of emission while retaining the antibunched counting statistics that are characteristic of atomic light sources. We also explore coupling a second, independent cavity mode to the atom, which increases the telecom emission rate and introduces quantum correlations between the cavity modes. A model for the hyperfine structure of a single cesium atom is then described and numerically integrated to demonstrate the viability of implementing the scheme with a modern cavity QED system.

We develop a quantum theory for the scattering of squeezed coherent light by a dissipative dielectric slab. Using the Green-function quantization approach, we derive the transformation of the field quadratures and show how dispersion, absorption, and multiple reflections distort the incident squeezing. We find that the slab can selectively attenuate or amplify quadrature noise depending on the slab parameters and provide expressions for the output power spectra.

Quantum error mitigation (QEM) infers noiseless expectation values from noisy variants of a target quantum circuit. Unlike quantum error correction, QEM requires no additional hardware resources and is therefore routinely employed in experiments on contemporary quantum processors. QEM strategies based on agnostic noise amplification (ANA) are intrinsically resilient to temporal noise drift during the execution of the experiment, but their sampling cost (runtime overhead) remains a major practical bottleneck. In this work, we introduce the virtual noise scaling framework and combine it with layered mitigation to further enhance performance. While virtual noise scaling consistently reduces sampling overhead, we identify a specific noise threshold for the layered mitigation approach. When the noise level is above this threshold, layered mitigation decreases the sampling overhead; conversely, when below it, the overhead increases. Notably, this threshold is circuit-independent and depends solely on the number of layers. For strong noise, the combination of virtual noise scaling and layered mitigation yields several orders of magnitude reduction in sampling overhead compared with conventional zero-noise extrapolation post-processing. As a result, mitigation tasks that once seemed unrealistic are now challenging but achievable. The proposed approach is compatible with dynamic circuits and can be seamlessly integrated with error detection and quantum error correction schemes. In addition, it is also applicable to ANA-based mitigation of mid-circuit measurements and preparation errors. Our findings extend to any constant-step amplification factors and therefore also apply to probabilistic error amplification (PEA) QEM. We validate our post-processing approach by applying it to previously reported experimental data, where we observe a substantial improvement in mitigation efficiency and accuracy.

Classical mechanics admits multiple equivalent formulations, from Newton's equations to the variational Lagrange-Hamilton framework and the scalar Hamilton-Jacobi (HJ) theory. In the HJ formulation, classical ensembles evolve through the continuity equation for a real density $\rho = R^{2}$ coupled to Hamilton's principal function $S$. Here we develop a complementary formulation, the Hamilton-Jacobi-Schrödinger (HJS) theory, by embedding the pair $(R,S)$ into a single complex field. Starting from a completely general complex ansatz $\psi = f(R,S)\, e^{i g(R,S)},$ and imposing two minimal structural requirements, we obtain a unique map $\psi = R\, e^{iS/\kappa}\, $ together with a linear HJS equation whose $|\kappa| \to 0$ limit reproduces the HJ formulation exactly. Remarkably, when $\mathrm{Re}(\kappa)\neq 0$, essential features of quantum mechanics, superposition, operator algebra, commutators, the Heisenberg uncertainty principle, Born's rule and unitary evolution, follow naturally as structural consistency conditions. HJS thus provides a unified mathematical viewpoint in which classical and quantum dynamics appear as different limits of a single underlying structure.

Conventionally, dispersion forces mediated by quantum vacuum fluctuations are known to exhibit universal distance scalings, with retardation typically leading to a faster decay of the interaction. Here, we show that this expectation fails for intrinsically discrete systems. Using the microscopic scattering approach, we study the Casimir-Polder interaction between two atomic arrays, and uncover an unconventional distance scaling in which the force crosses over from a faster decay at short separations to a slower decay in the retarded regime. This behavior originates from the discrete lattice structure and can be consistently understood within the scattering picture. Extending our analysis to Rydberg atomic arrays, we predict an even stronger deviation from conventional scaling and propose an experimentally feasible scheme for direct measurement. Our results provide a new platform for exploring dispersion forces beyond the continuum limit.

In this work, we introduce a unified method to characterize and measure multipartite entanglement using the framework of thermodynamics. A family of the new entanglement measures is proposed: ergotropic-gap concentratable entanglement. Furthermore, we establish that ergotropic-gap concentratable entanglement constitutes a well-defined entanglement measure within a specific parameter regime, satisfying key properties including continuity, majorization monotonicity and monogamy. We demonstrate the utility of this measure by showing it effectively distinguishes between multi-qubit Greenberger-Horne-Zeilinger states and W states. It also proves effective in detecting entanglement in specific classes of four-partite star quantum network states.

Entanglement concurrence is an important bipartite entanglement measure that has found wide applications in quantum technologies. In this work, inspired by unified entropy, we introduce a two-parameter family of entanglement measures, referred to as the unified $(q,s)$-concurrence. Both the standard entanglement concurrence and the recently proposed $q$-concurrence emerge as special cases within this family. By combining the positive partial transposition and realignment criteria, we derive an analytical lower bound for this measure for arbitrary bipartite mixed states, revealing a connection to strong separability criteria. Explicit expressions are obtained for the unified $(q,s)$-concurrence in the cases of isotropic and Werner states under the constraint $q>1$ and $qs\geq 1$. Furthermore, we explore the monogamy properties of the unified $(q,s)$-concurrence for $q\geq 2$, $0\leq s\leq 1$ and $1\leq qs\leq 3$, in qubit systems. In addition, we derive an entanglement polygon inequality for the unified $(q,s)$-concurrence with $q\geq 1$ and $qs\geq 1$, which manifests the relationship among all the marginal entanglements in any multipartite qudit system.

Quantum $(r,\delta)$-locally recoverable codes ($(r,\delta)$-LRCs) are the quantum version of classical $(r,\delta)$-LRCs designed to recover multiple failures in large-scale distributed and cloud storage systems. A quantum $(r,\delta)$-LRC, $Q(C)$, can be constructed from an $(r,\delta)$-LRC, $C$, which is Euclidean or Hermitian dual-containing. This article is devoted to studying how to get quantum $(r,\delta)$-LRCs from BCH and homothetic-BCH codes. As a consequence, we give pure quantum $(r,\delta)$-LRCs which are optimal for the Singleton-like bound.

Accurate classification of multipartite entanglement in high-dimensional quantum systems is crucial for advancing quantum communication and information processing. However, conventional methods are resource-intensive, and even many machine-learning-based approaches necessitate large training datasets, creating a significant experimental bottleneck for data acquisition. To address this challenge, we propose a hybrid neural network architecture integrating Convolutional and Bidirectional Long Short-Term Memory networks (CNN-BiLSTM). This design leverages CNNs for local feature extraction and BiLSTMs for sequential dependency modeling, enabling robust feature learning from minimal training data. We investigate two fusion paradigms: Architecture 1 (flattening-based) and Architecture 2 (dimensionality-transforming). When trained on only 100 samples, Architecture 2 maintains classification accuracies exceeding 90% for both 3-qubit and 4-qubit systems, demonstrating rapid loss convergence within tens of epochs. Under full-data conditions (400 000 samples), both architectures achieve accuracies above 99.97%. Comparative benchmarks reveal that our CNN-BiLSTM models, especially Architecture 2, consistently outperform standalone CNNs, BiLSTMs, and MLPs in low-data regimes, albeit with increased training time. These results demonstrates that the tailored CNN-BiLSTM fusion significantly alleviates experimental data acquisition burden, offering a practical pathway toward scalable entanglement verification in complex quantum systems.

We analyze the self-thermalization dynamics of the $M$-site Bose-Hubbard model in ring geometry using the single-particle density matrix calculated via the pseudoclassical approach. We show that a weak inter-particle interaction, which has a negligible effect on the thermal state given by the Bose-Einstein distribution, suffices to convert the integrable system of non-interacting bosons into a chaotic system. Next we consider two systems of weakly interacting bosons (i.e., two Bose-Hubbard systems) in different thermal states which are coupled by a point contact. We demonstrate that the chaotic nature of the Bose-Hubbard model ensures irreversible relaxation of both systems to global thermal equilibrium. Finally, substituting the point contact with a lattice of length $L\ll M$, we numerically calculate the quasi-stationary current of Bose particles across the lattice and show that its magnitude is consistent with the solution of the master equation for the boundary-driven $L$-site Bose-Hubbard system.

Quantum sensing leverages quantum resources to surpass the standard quantum limit, yet many existing protocols rely on the preparation of complex entangled states and Hamiltonian engineering, posing challenges for universality and scalability. Here, we report an experimental realization of a universal protocol, known as Butterfly Metrology, proposed in [arXiv:2411.12794], demonstrating a scrambling-based approach for quantum-enhanced sensing on a superconducting quantum processor. By exploiting many-body information scrambling, we observe quantum-enhanced sensitivity to an encoded phase beyond the standard quantum limit, with a scaling consistent with a factor-of-two of the Heisenberg limit for system sizes of up to 10 qubits. Importantly, we experimentally establish a connection between the enhanced sensitivity and the dynamics of the out-of-time-order correlator (OTOC), and show that the buildup of scrambling-induced genuine multipartite entanglement underlies the observed sensitivity enhancement. Our results demonstrate a scalable and practical approach for quantum-enhanced sensing in interacting many-body quantum systems.

Native constant-depth non-Clifford gates on quantum low-density parity-check (qLDPC) codes can substantially reduce the space-time overhead of magic-state distillation. This paper investigates the underlying parity and structural conditions governing parallel non-Clifford gate implementations. By analyzing their invariance, algebraic forms, and circuit synthesis, we establish fundamental limits on code scaling: strict saturated implementations cannot achieve constant-depth realization as code distance grows due to tight distance-depth bounds. We evaluate alternative scaling routes, showing that scalable designs must either relax strict subspace requirements or manage gate congestion. Through analytical bounds and code searches, we demonstrate that reconciling parallel non-Clifford operations with linear distance requires navigating these fundamental structural trade-offs.

We explore the formation of Dicke states. A system consisting of two two-level atoms located in the right Rindler wedge, has investigated to determine the conditions under which the superradiant or subradiant state can be formed. The dynamics of N two-level atoms forming symmetric state has also been analyzed and showed that the probability to excite any one atom of a collection of N atoms is related to the probability of exciting a single atom. We derive the analytical expression for the joint excitation probability which demonstrates the the interference effect. These findings provide new insights into the behavior of quantum systems in non-inertial frames and contribute to the broader understanding of relativistic quantum information theory.

An important distinction in our understanding of capacities of classical versus quantum channels is marked by the following question: is there an algorithm which can compute (or even efficiently compute) the capacity? While there is overwhelming evidence suggesting that quantum channel capacities may be uncomputable, a formal proof of any such statement is elusive. We initiate the study of the hardness of computing quantum channel capacities. We show that, for a general quantum channel, it is QMA-hard to compute its quantum capacity, and that the entanglement-assisted zero-error capacity under some restrictions is uncomputable; indicative of the fact that quantum channel capacities may generally be undecidable.

In this paper, we formulate the compression of large language models (LLMs) by optimally deleting transformer blocks (“block removal”) as a constrained binary optimization (CBO) problem that can be mapped to a physical system (Ising glass), whose energies are a strong proxy for downstream model performance. This formulation enables an efficient ranking of a large number of candidate block-removal configurations yielding many high-quality, non-trivial solutions beyond those only removing consecutive regions. Our method performs strongly in the deep compression regime, such as for 50% compression of Llama-3.3-70B-Instruct, where we achieve an almost 23 percentage point increase on the MMLU benchmark compared to other state-of-the-art (SOTA) block-removal methods. For lighter compression, it performs on par with those methods across several benchmarks for Llama-3.1-8B-Instruct, Qwen3-14B (both before and after retraining), as well as Llama-3.3-70B-Instruct. The approach is computationally efficient and requires only forward and backward passes on a calibration dataset for a few active parameters. Additionally, we demonstrate that using good heuristic solvers for the CBO problem provides solutions that perform well on downstream tasks in negligible runtime when it is unfeasible to solve the problem exactly. The method can be readily applied to any architecture. We illustrate this generality on the recent NVIDIA-Nemotron-3-Nano-30B-A3B-FP8 model, which exhibits a highly inhomogeneous and challenging block structure, and where we outperform SOTA for AIME25 and GPQA when removing either 2 attention layers or 3 mixture-of-experts layers.

Genome sequencing is essential to decode genetic information, identify organisms, understand diseases and advance personalized medicine. A critical step in any genome sequencing technique is genome assembly. However, de novo genome assembly, which involves constructing an entire genome sequence from scratch without a reference genome, presents significant challenges due to its high computational complexity, affecting both time and accuracy. In this study, we propose a hybrid approach utilizing a quantum computing-based optimization algorithm integrated with classical pre-processing to expedite the genome assembly process. Specifically, we present a method to solve the Hamiltonian and Eulerian paths within the genome assembly graph using gate-based quantum computing through a Higher-Order Binary Optimization (HOBO) formulation with the Variational Quantum Eigensolver algorithm (VQE), in addition to a novel bitstring recovery mechanism to improve optimizer traversal of the solution space. A comparative analysis with classical optimization techniques was performed to assess the effectiveness of our quantum-based approach in genome assembly. The results indicate that, as quantum hardware continues to evolve and noise levels diminish, our formulation holds a significant potential to accelerate genome sequencing by offering faster and more accurate solutions to the complex challenges in genomic research.

We study the problem of learning complex-valued linear dynamical systems (CLDS) with sector-bounded spectrum. This class captures oscillatory and long-memory dynamics arising in signal processing, structured state space models, and quantum systems. We introduce a spectral filtering method based on the Slepian basis and show that learnability is governed by an effective dimension independent of the ambient state dimension. As a consequence, we obtain dimension-free regret bounds for sequence prediction in CLDS with spectrum contained in a sector of the unit disk.

These are the notes for the 4.5-hour course with the same title that I delivered in August 2025 at the Les Houches summer school “Exact Solvability and Quantum Information”. In these notes I pedagogically introduce the setting of brickwork quantum circuits and show that it provides a useful framework to study non-equilibrium quantum many-body dynamics in the presence of local interactions. I first show that brickwork quantum circuits evolve quantum correlations in a way that is fundamentally similar to local Hamiltonians, and then present examples of brickwork quantum circuits where, surprisingly, one can compute exactly several relevant dynamical and spectral properties in the presence of non-trivial interactions.

Verifying whether two quantum circuits are equivalent is a central challenge in the compilation and optimization of quantum programs. We introduce Manjushri, a new automated framework for scalable quantum-circuit equivalence checking. Manjushri uses local projections as discriminative circuit fingerprints, implemented with weighted binary decision diagrams (WBDDs), yielding a compact and efficient symbolic representation of quantum behavior. We present an extensive experimental evaluation that, for random 1D Clifford+$T$ circuits, explores the trade-off between Manjushri and ECMC, a tool for equivalence checking based on a much different approach. Manjushri is much faster up to depth 30 (with the crossover point varying from 39–49, depending on the number of qubits and whether the input circuits are equivalent or inequivalent): when inputs are equivalent, Manjushri is about 10$\times$ faster (or more); when inputs are inequivalent, Manjushri is about 8$\times$ faster (or more). For both kinds of equivalence-checking outcomes, ECMC's success rate out to depth 50 is impressive on 32- and 64-qubit circuits: on such circuits, ECMC is almost uniformly successful. However, ECMC struggled on 128-qubit circuits for some depths. Manjushri is almost uniformly successful out to about depth 38, before tailing off to about 75% at depth 50 (falling to 0% at depth 48 for 128-qubit circuits that are equivalent). These results establish that Manjushri is a practical and scalable solution for large-scale quantum-circuit verification, and would be the preferred choice unless clients need to check equivalence of circuits of depth $>$38.

Product constructions constitute a powerful method for generating quantum CSS codes, yielding celebrated examples such as toric codes and asymptotically good low-density parity check (LDPC) codes. Since a CSS code is fully described by a chain complex, existing product formalisms are predominantly homological, defined via the tensor product of the underlying chain complexes of input codes, thereby establishing a natural connection between quantum codes and topology. In this Letter, we introduce the quantum bootstrap product (QBP), an approach that extends beyond this standard homological paradigm. Specifically, a QBP code is determined by solving a consistency condition termed the “bootstrap equation”. We find that the QBP paradigm unifies a wide range of important codes, including general hypergraph product (HGP) codes of arbitrary dimensions and fracton codes typically represented by the X-cube code. Crucially, the solutions to the bootstrap equation yield chain complexes where the chain groups and associated boundary maps consist of multiple components. We term such structures fork complexes. This structure elucidates the underlying topological structures of fracton codes, akin to foliated fracton order theories. Beyond conceptual insights, we demonstrate that the QBP paradigm can generate self-correcting quantum codes from input codes with constant energy barriers and surpass the code-rate upper bounds inherent to HGP codes. Our work thus substantially extends the scope of quantum product codes and provides a versatile framework for designing fault-tolerant quantum memories.

Modern supply chains must balance high-speed logistics with environmental impact and security constraints, prompting a surge of interest in AI-enabled Internet of Things (AIoT) solutions for global commerce. However, conventional supply chain optimization models often overlook crucial sustainability goals and cyber vulnerabilities, leaving systems susceptible to both ecological harm and malicious attacks. To tackle these challenges simultaneously, this work integrates a quantum-inspired reinforcement learning framework that unifies carbon footprint reduction, inventory management, and cryptographic-like security measures. We design a quantum-inspired reinforcement learning framework that couples a controllable spin-chain analogy with real-time AIoT signals and optimizes a multi-objective reward unifying fidelity, security, and carbon costs. The approach learns robust policies with stabilized training via value-based and ensemble updates, supported by window-normalized reward components to ensure commensurate scaling. In simulation, the method exhibits smooth convergence, strong late-episode performance, and graceful degradation under representative noise channels, outperforming standard learned and model-based references, highlighting its robust handling of real-time sustainability and risk demands. These findings reinforce the potential for quantum-inspired AIoT frameworks to drive secure, eco-conscious supply chain operations at scale, laying the groundwork for globally connected infrastructures that responsibly meet both consumer and environmental needs.

A finite sequence of numbers is perfect if it has zero periodic autocorrelation after a nontrivial cyclic shift. In this work, we study quaternionic perfect sequences having a one-to-one correspondence with the binary sequences arising in Williamson's construction of quaternion-type Hadamard matrices. Using this correspondence, we devise an enumeration algorithm that is significantly faster than previously used algorithms and does not require the sequences to be symmetric. We implement our algorithm and use it to enumerate all circulant and possibly non-symmetric Williamson-type matrices of orders up to 21; previously, the largest order exhaustively enumerated was 13. We prove that when the blocks of a quaternion-type Hadamard matrix are circulant, the blocks are necessarily pairwise amicable. This dramatically improves the filtering power of our algorithm: in order 20, the number of block pairs needing consideration is reduced by a factor of over 25,000. We use our results to construct quaternionic Hadamard matrices of interest in quantum communication and prove they are not equivalent to those constructed by other means. We also study the properties of quaternionic Hadamard matrices analytically, and demonstrate the feasibility of characterizing quaternionic Hadamard matrices with a fixed pattern of entries. These results indicate a richer set of properties and suggest an abundance of quaternionic Hadamard matrices for sufficiently large orders.

We study the photon-graviton pair production induced by the propagation of a classical electromagnetic (EM) wave in a Minkowskian spacetime. In our model, the gravitational field is described in terms of the quantized graviton field, whereas the electromagnetic field is split into a classical drive (a linearly or circularly polarized electromagnetic wave) and a quantum fluctuation field. We analyze the time evolution of the quantum state showing that, among other outcomes, the propagation of the EM wave can generate Bell states in the photon-graviton polarization basis. We finally discuss the possibility to observe entangled photons in artificial and natural scenarios.

We address the problem of measuring nonclassicality in continuous-variable bosonic systems without having access to a known reference signal. To this end, we construct broader classes of criteria for nonclassicality which allow us to investigate quantum phenomena regardless of the quantumness of selected subsystems. Such witnesses are based on the notion of partial normal ordering. This approach is applied to balanced homodyne detection using arbitrary, potentially nonclassical local oscillator states, yet only revealing the probed signal's quantumness. Our framework is compared to standard techniques, and the robustness and advanced sensitivity of our approach is shown. Therefore, a widely applicable framework, well-suited for applications in quantum metrology and quantum information, is derived to assess the quantum features of a photonic system when a well-defined coherent laser as a reference state is not available in the physical domain under study.

Characterizing errors in quantum circuits is essential for device calibration, yet detecting rare error events requires a large number of samples. This challenge is particularly severe in calibrating fault-tolerant, error-corrected circuits, where logical error probabilities are suppressed to higher order relative to physical noise and are therefore difficult to calibrate through direct logical measurements. Recently, Wagner et al. [PRL 130, 200601 (2023)] showed that, for phenomenological Pauli noise models, the logical channel can instead be inferred from syndrome measurement data generated during error correction. Here, we extend this framework to realistic circuit-level noise models. From a unified code-theoretic perspective and spacetime code formalism, we derive necessary and sufficient conditions for learning the logical channel from syndrome data alone and explicitly characterize the learnable degrees of freedom of circuit-level Pauli faults. Using Fourier analysis and compressed sensing, we develop efficient estimators with provable guarantees on sample complexity and computational cost. We further present an end-to-end protocol and demonstrate its performance on several syndrome-extraction circuits, achieving orders-of-magnitude sample-complexity savings over direct logical benchmarking. Our results establish syndrome-based learning as a practical approach to characterizing the logical channel in fault-tolerant quantum devices.

We propose a protocol to measure impulses beyond the standard quantum limit. The protocol reduces noise in all three spatial dimensions and consists of squeezing a mechanical system's state via a series of jumps in the frequency of the harmonic potential. We quantify how decoherence in a realistic system of an optically levitated, dielectric nanoparticle limits the ultimate sensitivity. We predict that $\sim$10 dB of squeezing is achievable with current technology, enabling quantum-enhanced detection of weak impulses.

In the paper our aim was to study the properties of a new version of coherent states whose argument is a linear combination of two special singular square 2 x 2 matrix, having a single nonzero element, equal to 1, and two labeling complex variables as developing coefficients. We have shown that this new version of coherent states satisfies all the conditions imposed on coherent states, both of pure, as well as the mixed (thermal) states characterized by the density operator. As applications, we examined the connection between these coherent states and the notions of qubits and von Neuman entropy.