Quantum Physics
Kernel Learning for Regression via Quantum Annealing Based Spectral Sampling
Yasushi Hasegawa and Masayuki Ohzeki
While
quantum annealing (QA) has been developed for combinatorial optimization, practical QA devices operate at finite temperature and under noise, and their outputs can be regarded as
stochastic samples close to a Gibbs–Boltzmann distribution. In this study, we propose a QA-in-the-loop kernel learning framework that integrates QA not merely as a substitute for Markov-chain Monte Carlo sampling but as a component that directly determines the learned kernel for regression. Based on Bochner's
theorem, a shift-invariant kernel is represented as an expectation over a spectral distribution, and random
Fourier features (RFF) approximate the kernel by sampling frequencies. We model the spectral distribution with a (multi-layer) restricted Boltzmann machine (RBM), generate discrete RBM samples using QA, and map them to continuous frequencies via a Gaussian–Bernoulli transformation. Using the resulting RFF, we construct a data-adaptive kernel and perform Nadaraya–Watson (NW) regression. Because the RFF approximation based on $\cos(\bm{\omega}^{\top}\Delta\bm{x})$ can yield small negative values and cancellation across neighbors, the Nadaraya–Watson denominator $\sum_j k_{ij}$ may become close to zero. We therefore employ nonnegative squared-kernel weights $w_{ij}=k(\bm{x}_i,\bm{x}_j)^2$, which also enhances the contrast of kernel weights. The kernel parameters are trained by minimizing the leave-one-out NW mean squared error, and we additionally evaluate local linear regression with the same squared-kernel weights at inference. Experiments on multiple
benchmark regression
datasets demonstrate a decrease in training loss, accompanied by structural changes in the kernel
matrix, and show that the learned kernel tends to improve $R^2$ and RMSE over the baseline Gaussian-kernel NW. Increasing the number of random features at inference further enhances accuracy.
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Quantum Physics · Cross-listed from hep-th
Superadditivity of Krylov Complexity for Tensor Products
Jeff Murugan and Hendrik J.R. van Zyl
We study Krylov complexity for
quantum systems whose
Hamiltonians factorise as tensor products. We prove that complexity is superadditive under tensor products, $C_{12}\ge C_1+C_2$, and identify a positive operator that quantifies the resulting excess complexity. The underlying mechanism is made transparent by introducing a Krylov graph representation in which tensor products generate a higher-dimensional
lattice whose diagonal shells encode operator growth and binomial path multiplicities. In the continuum limit, Krylov dynamics reduces to
diffusion on this graph, with superadditivity arising from
geometric broadening across shells. Explicit examples illustrate how deviations from synchronous
evolution generate bounded, oscillatory excess complexity.
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Quantum Physics
Fragility of Optimal Measurements due to Noise in Probe States for Quantum Sensing
Andrew Kolmer Forbes, Marco A. Rodríguez-García and Ivan H. Deutsch
For a given
quantum state used in sensing, the
quantum Cramér-Rao bound (QCRB) sets a fundamental limit on the precision achievable by an unbiased
estimator of an unknown parameter, determined by the inverse of the
quantum Fisher information (QFI). The QFI serves as an upper bound on the classical Fisher information (CFI), representing the maximum extractable information about the unknown parameter from measurements on a physical system. Thus, a central goal in
quantum parameter estimation is to find a measurement, described by a POVM, that saturates the QFI (achieves maximum CFI), and thereby achieves the QCRB. In the idealization that one uses pure states and
unitary encodings for sensing, discontinuities can appear in the CFI but not the QFI. In this article, we demonstrate that these discontinuities are important features, quantifying how much Fisher information is lost in the presence of noise. We refer to this as the Fisher information "fragility". We present a simple framework for understanding how discontinuities increase fragility through Jensen's inequality, and demonstrate how one can use this framework to design more robust POVMs for
quantum advantage in metrology.
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Quantum Physics · Cross-listed from hep-th
On equivalent methods for functional determinants
Matthias Carosi
Computing functional determinants of differential operators is central to any field-theoretical calculation relying on a saddle-point expansion. A variety of approaches is available for the computation that avoid having to know the eigenspectrum of the operator, and in particular the Gel'fand-Yaglom
theorem and the Green's function method. In this note, we show how both approaches can be constructed using a contour integral argument and conclude that these are completely equivalent for computing ratios of determinants of one-dimensional operators. Furthermore, we comment on the presence of vanishing as well as negative
eigenvalues and show how the Green's function method provides a natural prescription for handling them.
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Quantum Physics · Cross-listed from physics.optics
Attosecond quantum optics
Mohamed Sennary, Javier Rivera-Dean, Yihe Wange et al. (+2 more)
Modern
quantum optics primarily operates in the quasistationary regime, isolated from the intrinsic timescales of ultrafast optical fields. Pushing these boundaries into the femtosecond and attosecond domains is a critical frontier. Here, we generate, shape, and interrogate the
quantum state of an ultrafast squeezed light field. Our optical metrology reveals a highly dynamic, time dependent squeezing distribution across individual half cycles of the electric field. Incorporating this intracycle squeezing into strong field simulations demonstrates that the temporal redistribution of
quantum uncertainty fundamentally reshapes the
quantum strong field physics of high harmonic emission. Furthermore, we achieve attosecond scale control of the squeezed state, visualized through inferred effective Wigner representations. Finally, we show that ultrafast squeezed light encodes its
quantum properties into a photoinduced tunneling current within a petahertz phototransistor with subfemtosecond resolution, demonstrating a direct optical electronic
quantum coupling. This work lays the foundation for the emerging field of ultrafast
quantum optics and unlocks new avenues for high speed
quantum communication and photonics.
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All authors Mohamed Sennary, Javier Rivera-Dean, Yihe Wange, Maciej Lewenstein, Mohammed Th. Hassan
Quantum Physics · Cross-listed from cs.AI
From Classical to Quantum Reinforcement Learning and Its Applications in Quantum Control: A Beginner's Tutorial
Abhijit Sen, Sonali Panda, Mahima Arya et al. (+3 more)
This tutorial is designed to make reinforcement learning (RL) more accessible to undergraduate students by offering clear, example-driven explanations. It focuses on bridging the gap between RL theory and practical coding applications, addressing common challenges that students face when transitioning from conceptual understanding to implementation. Through hands-on examples and approachable explanations, the tutorial aims to equip students with the foundational skills needed to confidently apply RL techniques in real-world scenarios.
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All authors Abhijit Sen, Sonali Panda, Mahima Arya, Subhajit Patra, Zizhan Zheng, Denys I. Bondar
Quantum Physics · Cross-listed from cs.IT
Quantum CSS LDPC Codes based on Dyadic Matrices for Belief Propagation-based Decoding
Alessio Baldelli, Massimo Battaglioni, Jonathan Mandelbaum et al. (+2 more)
Quantum low-density parity-check (QLDPC) codes provide a practical balance between error-correction capability and implementation complexity in
quantum error correction (QEC). In this paper, we propose an algebraic construction based on dyadic
matrices for designing both classical and
quantum LDPC codes. The method first generates classical binary quasi-dyadic LDPC codes whose Tanner graphs have girth 6. It is then extended to the Calderbank-Shor-Steane (CSS) framework, where the two component parity-check
matrices are built to satisfy the compatibility condition required by the recently introduced CAMEL-ensemble quaternary belief propagation decoder. This compatibility condition ensures that all unavoidable cycles of length 4 are assembled in a single variable node, allowing the mitigation of their detrimental effects by decimating that variable node.
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All authors Alessio Baldelli, Massimo Battaglioni, Jonathan Mandelbaum, Sisi Miao, Laurent Schmalen
Quantum Physics · Cross-listed from cond-mat.str-el
Parameterized families of 2+1d $G$-cluster states
Shuhei Ohyama and Kansei Inamura
We construct a $G$-cluster
Hamiltonian in 2+1 dimensions and analyze its properties. This model exhibits a $G\times2\mathrm{Rep}(G)$
symmetry, where the $2\mathrm{Rep}(G)$ sector realizes a non-invertible
symmetry obtained by condensing appropriate
algebra objects in $\mathrm{Rep}(G)$. Using the
symmetry interpolation method, we construct $S^1$- and $S^2$-parameterized families of short-range-entangled (SRE) states by interpolating an either invertible $0$-form or $1$-form
symmetry contained in $G\times2\mathrm{Rep}(G)$. Applying an adiabatic
evolution argument to this family, we analyze the pumped interface mode generated by this adiabatic process. We then explicitly construct the
symmetry operator acting on the interface and show that the interface mode carries a nontrivial charge under this
symmetry, thereby demonstrating the nontriviality of the parameterized family.
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Quantum Physics · Cross-listed from cond-mat.str-el
Generalized cluster states in 2+1d: non-invertible symmetries, interfaces, and parameterized families
Kansei Inamura and Shuhei Ohyama
We construct 2+1-dimensional
lattice models of
symmetry-protected topological (SPT) phases with non-invertible
symmetries and investigate their properties using tensor networks. These models, which we refer to as generalized cluster models, are constructed by gauging a subgroup
symmetry $H \subset G$ in models with a finite group 0-form
symmetry $G$. By construction, these models have a non-invertible
symmetry described by the group-theoretical fusion 2-category $\mathcal{C}(G; H)$. After identifying the tensor network representations of the
symmetry operators, we study the
symmetry acting on the interface between two generalized cluster states. In particular, we will see that the
symmetry at the interface is described by a multifusion category known as the strip 2-
algebra. By studying possible interface modes allowed by this
symmetry, we show that the interface between generalized cluster states in different SPT phases must be degenerate. This result generalizes the ordinary bulk-boundary correspondence. Furthermore, we construct parameterized families of generalized cluster states and study the topological charge pumping phenomena, known as the generalized Thouless pump. We exemplify our construction with several concrete cases, and compare them with known phases, such as SPT phases with $2\mathrm{Rep}((\mathbb{Z}_{2}^{[1]}\times\mathbb{Z}_{2}^{[1]})\rtimes\mathbb{Z}_{2}^{[0]})$
symmetry.
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Quantum Physics
Open quantum spin chains with non-reciprocity: a theoretical approach based on the time-dependent generalized Gibbs ensemble
Alice Marché, Hironobu Yoshida, Alberto Nardin et al. (+2 more)
We study an open
quantum spin chain with non-reciprocal dissipation using a theoretical approach known as time-dependent generalized Gibbs ensemble. In the regime of weak dissipation the system is fully characterized by its rapidity distribution and we derive a closed set of coupled differential equations governing their time
evolution. We check the accuracy of this theory by benchmarking the results against numerical simulations. Using this framework we are able to compute both the magnetization density and current dynamics, identifying some relations between the two. The problem of the anomalous power-law exponents identified in a previous work is discussed. Our work constitutes a theoretical approach that is able to describe the physics of non-reciprocal open
quantum spin chains beyond analyses based on non-interacting
fermions.
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All authors Alice Marché, Hironobu Yoshida, Alberto Nardin, Hosho Katsura, Leonardo Mazza
Quantum Physics
Sample Complexity of Composite Quantum Hypothesis Testing
Jacob Paul Simpson, Efstratios Palias and Sharu Theresa Jose
This paper investigates symmetric composite binary
quantum hypothesis testing (QHT), where the goal is to determine which of two uncertainty sets contains an unknown
quantum state. While asymptotic error exponents for this problem are well-studied, the finite-sample regime remains poorly understood. We bridge this gap by characterizing the sample complexity – the minimum number of state copies required to achieve a target error level. Specifically, we derive lower bounds that generalize the sample complexity of simple QHT and introduce new upper bounds for various uncertainty sets, including of both finite and infinite cardinalities. Notably, our upper and lower bounds match up to universal constants, providing a tight characterization of the sample complexity. Finally, we extend our analysis to the differentially private setting, establishing the sample complexity for
privacy-preserving composite QHT.
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Quantum Physics
Entanglement-swapping measurements for deterministic entanglement distribution
Mir Alimuddin, Jaemin Kim, Antonio Acín et al. (+1 more)
Entanglement swapping is a key primitive for distributing
entanglement over
quantum networks, but different measurement outcomes can produce end-to-end states with different
entanglement, requiring branch-dependent processing or the rejection of unfavorable outcomes. We characterize all projective swapping measurements with full-Schmidt-rank vectors such that, for every pair of pure input links, all outcomes yield the same end-to-end state up to local-
unitary corrections. Within this family, the measurements that maximize the average G-concurrence for every input pair are built from complex Hadamard operators, and every outcome individually attains the optimum. Classifying the underlying complex Hadamard operators that preserve optimal deterministic swapping gives one class for $d=2,3$, exactly $72$ classes for $d=5$, and uncountably many whenever $d=4k$. We show further that for $d=2,3$, the corrected end-to-end state in a swapping chain is independent of the swapping order, and discuss noise robustness under depolarizing noise and arbitrary convex input contamination. For pure inputs, these schemes retain every outcome while achieving optimal G-concurrence and therefore eliminate outcome-based postselection.
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All authors Mir Alimuddin, Jaemin Kim, Antonio Acín, Leonardo Zambrano
Quantum Physics
Phase-sensitive superposition of quantum states
Xiaotong Wang, Shunlong Luo and Yue Zhang
Although the principle of superposition lies at the heart of
quantum mechanics and is the root of almost all
quantum phenomena such as coherence and
entanglement, its quantification, except for that related to the resource theory of coherence and interference, remains relatively less studied. In this work, we address quantification of superposition from an information-theoretic perspective. We introduce a family of quantifiers of superposition, the phase-sensitive superposition, by taking into account the phases of amplitudes in the superposition of a fixed basis states (e.g., computational basis states). We establish a conservation relation for the phase-sensitive superposition, which is a kind of complementary relation and is reminiscent of wave-particle duality. We evaluate explicitly the second moment of phase-sensitive superposition and show that it is intrinsically related to the $l^2$-norm coherence. We characterize the dephasing channel induced by the maximally superposed states. We investigate the minimum and maximum superpositions, reveal their basic properties, and illustrate them through various examples. We further explore the dynamics of superposition in the Grover search
algorithm, and demonstrate a complementary relation between superposition and success probability of the search
algorithm. These results and quantifiers offer tools for analyzing structural features and implications of
quantum superposition.
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Quantum Physics
Quantum Computing – Strategic Recommendations for the Industry
Marvin Erdmann, Lukas Karch, Abhishek Awasthi et al. (+9 more)
This whitepaper surveys the current landscape and short- to mid-term prospects for
quantum-enabled optimization and machine learning use cases in industrial settings. Grounded in the QCHALLenge program, it synthesizes hardware trajectories from different
quantum architectures and providers, and assesses their maturity and potential for real-world use cases under a standardized traffic-light evaluation framework. We provide a concise summary of relevant hardware roadmaps, distinguishing superconducting and ion-trap technologies, their current states, modalities, and projected scaling trajectories. The core of the presented work are the use case evaluations in the domains of optimization problems and machine learning applications. For the conducted experiments, we apply a consistent set of evaluation criteria (model formulation, scalability, solution quality, runtime, and transferability) which are assessed in a shared system of three categories, ranging from optimistic (solutions produced by
quantum computers are competitive with classical methods and/or a clear path to a
quantum advantage is shown) to pessimistic (significant hurdles prevent practical application of
quantum solutions now and potentially in the future). The resulting verdicts illuminate where
quantum approaches currently offer promise, where hybrid classical-
quantum strategies are most viable, and where classical methods are expected to remain superior.
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All authors Marvin Erdmann, Lukas Karch, Abhishek Awasthi, Caitlin Isobel Jones, Pallavi Bhardwaj, Florian Krellner, Jonas Stein, Claudia Linnhoff-Popien, Nico Kraus, Peter Eder, Sarah Braun, Tong Liu
Quantum Physics
Asymptotically good CSS codes that realize the logical transversal Clifford group fault-tolerantly
K. Sai Mineesh Reddy and Navin Kashyap
This paper introduces a framework for constructing Calderbank-Shor-Steane (CSS) codes that support fault-tolerant logical transversal $Z$-rotations. Using this framework, we obtain asymptotically good CSS codes that fault-tolerantly realize the logical transversal Clifford group (i.e., transversal single-
qubit Clifford gates are realized within a single code block, while transversal two-
qubit Clifford gates are realized across two identical code blocks). Furthermore, investigating CSS-T codes, we: (a) demonstrate asymptotically good CSS-T codes wherein the transversal $T$ realizes the logical transversal $S^{\dagger}$; (b) show that the condition $C_2 \ast C_1 \subseteq C_1^{\perp}$ is necessary but not sufficient for CSS-T codes; and (c) revise the characterizations of CSS-T codes wherein the transversal $T$ implements the logical identity and the logical transversal $T$, respectively.
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Quantum Physics
Symmetry-Adapted State Preparation for Quantum Chemistry on Fault-Tolerant Quantum Computers
Viktor Khinevich and Wataru Mizukami
We present systematic and resource-efficient constructions of continuous
symmetry projectors, particularly $U(1)$ particle number and $SU(2)$ total
spin, tailored for fault-tolerant
quantum computations. Our approach employs a linear combination of
unitaries (LCU) as well as generalized
quantum signal processing (GQSP and GQSVT) to implement projectors. These projectors can then be coherently applied as state filters prior to
quantum phase estimation (QPE). We analyze their asymptotic gate complexities for explicit
circuit realizations. For the particle number and $S_z$
symmetries, GQSP offers favorable resource usage features owing to its low ancilla
qubit requirements and robustness to finite precision rotation gate synthesis. For the total
spin projection, the structured decomposition of $\hat{P}_{S,M_S}$ reduces the projector T gate count. Numerical simulations show that
symmetry filtering substantially increases the QPE success probability, leading to a lower overall cost compared to that of unfiltered approaches across representative molecular systems. Resource estimates further indicate that the cost of
symmetry filtering is $3$ to $4$ orders of magnitude lower than that of the subsequent phase estimation step This advantage is especially relevant in large, strongly correlated systems, such as FeMoco, a standard strongly correlated open-shell
benchmark. For FeMoco, the QPE cost is estimated at ${\sim}10^{10}$ T gates, while our
symmetry projector requires only ${\sim}10^{6}$–$10^{7}$ T gates. These results establish continuous-
symmetry projectors as practical and scalable tools for state preparation in
quantum chemistry and provide a pathway toward realizing more efficient fault-tolerant
quantum simulations.
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Quantum Physics
MultiQ: Multi-Programming Neutral Atom Quantum Architectures
Francisco Romão, Daniel Vonk, Emmanuil Giortamis et al. (+2 more)
Neutral atom
Quantum Processing Units (QPUs) are emerging as a popular
quantum computing technology due to their large
qubit counts and flexible connectivity. However, performance challenges arise as large
circuits experience significant fidelity drops, while small
circuits underutilize hardware and face initialization latency issues. To tackle these problems, we propose $\textit{multi-programming on neutral atom QPUs}$, allowing the co-execution of multiple
circuits by logically partitioning the
qubit array. This approach increases resource utilization and mitigates initialization latency while maintaining result fidelity. Currently, state-of-the-art compilers for neutral atom architectures do not support multi-programming. To fill this gap, we introduce MultiQ, the first system designed for this purpose. MultiQ addresses three main challenges: (i) it compiles
circuits into a $\textit{virtual zone layout}$ to optimize spatio-temporal hardware utilization; (ii) it parallelizes the execution of co-located
circuits, allowing single hardware instructions to operate on different
circuits; and (iii) it includes an
algorithm to verify the functional independence of the bundled
circuits. MultiQ functions as a cross-layer system comprising a compiler, controller, and checker. Our compiler generates virtual zone layouts to enhance performance, while the controller efficiently maps these layouts onto the hardware and resolves any conflicts. The checker ensures the correct bundling of
circuits. Experimental results show a throughput increase from 3.8$\times$ to 12.3$\times$ when multi-programming 4 to 14
circuits, with fidelity largely maintained, ranging from a 1.3% improvement for four
circuits to only a 3.5% loss for fourteen
circuits. Overall, MultiQ facilitates concurrent execution of multiple
quantum circuits, boosting throughput and hardware utilization.
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All authors Francisco Romão, Daniel Vonk, Emmanuil Giortamis, Dennis Sprokholt, Pramod Bhatotia
Quantum Physics
Toolchain for shuttling trapped-ion qubits in segmented traps
Andreas Conta, Santiago Bogino, Frodo Köhncke et al. (+2 more)
Scalable trapped-ion
quantum computing requires fast and reliable transport of ions through complex, segmented radiofrequency trap architectures without inducing excessive motional excitation. We present a numerical toolchain for the systematic generation of time-dependent electrode voltages enabling fast, low-excitation ion shuttling in segmented radiofrequency traps. Based on a model of the trap electrode geometry, the framework combines an electrostatic field solver, efficient unconstrained optimization, waveform postprocessing, and dynamical simulations of ion motion to compute voltage waveforms that realize prescribed transport trajectories while respecting experimental constraints such as voltage limits and bandwidth. The toolchain supports arbitrary trap geometries, including junctions and multi-zone layouts, and allows for the flexible incorporation of optimization objectives. We provide a detailed assessment of the accuracy of the framework by investigating its numerical stability and by comparing measured and predicted secular frequencies. The framework is optimized for numerical performance, enabling rapid numerical prototyping of trap architectures of increasing complexity. As application examples, we apply the framework to the transport of a potential well along a linear, uniformly segmented trap, and we compute a solution for shuttling a potential well around the corner of an X-type trap junction. The presented approach provides an extensible and highly efficient numerical foundation for designing and validating transport protocols in current and next-generation trapped-ion processors.
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All authors Andreas Conta, Santiago Bogino, Frodo Köhncke, Ferdinand Schmidt-Kaler, Ulrich Poschinger
Quantum Physics
Phase-error-estimation security framework for quantum key distribution with correlated sources
Guillermo Currás-Lorenzo, Margarida Pereira, Kiyoshi Tamaki et al. (+1 more)
Practical QKD modulators introduce correlations between consecutively emitted pulses due to bandwidth limitations, violating key assumptions underlying many security proof techniques. Here, we address this problem by introducing a simple yet powerful mathematical framework to directly extend phase-error-estimation-based security proofs for imperfect but uncorrelated sources to also incorporate encoding correlations. Our framework overcomes important limitations of previous approaches in terms of generality and rigor, significantly narrowing the gap between theoretical security guarantees and real-world QKD implementations.
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All authors Guillermo Currás-Lorenzo, Margarida Pereira, Kiyoshi Tamaki, Marcos Curty
Quantum Physics
On-chip semi-device-independent quantum random number generator exploiting contextuality
Maddalena Genzini, Caterina Vigliar, Mujtaba Zahidy et al. (+6 more)
We present a semi-device-independent
quantum random number generator (QRNG) based on the violation of a contextuality inequality, implemented by the integration of two silicon photonic chips. Our system combines a heralded single-
photon source with a reconfigurable interferometric mesh to implement qutrit state preparation, transformations, and measurements suitable for testing a KCBS contextuality inequality. This architecture enables the generation of random numbers from the intrinsic randomness of single-
photon interference in a complex optical network, while simultaneously allowing a quantitative certification of their security without requiring
entanglement. We observe a contextuality violation exceeding the classical bound by more than 10{\sigma}, unambiguously confirming non-classical behavior. From this violation, we certify a conditional min-
entropy per experimental round of Hmin = 0.077 +- 0.002, derived via a tailored semidefinite-programming-based security analysis. Each measurement outcome therefore contains at least 0.077 +- 0.002 bits of extractable genuine randomness, corresponding to an asymptotic generation rate of 21.7 +- 0.5 bits/s. These results establish a viable route towards general-purpose, untrusted
quantum random number generators compatible with practical integrated photonic
quantum networks.
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All authors Maddalena Genzini, Caterina Vigliar, Mujtaba Zahidy, Hamid Tebyanian, Andrzej Gajda, Klaus Petermann, Lars Zimmermann, Davide Bacco, Francesco Da Ros
Quantum Physics
A dataflow programming framework for linear optical distributed quantum computing
Giovanni de Felice, Boldizsár Poór, Cole Comfort et al. (+4 more)
Photonic systems offer a promising platform for interconnecting
quantum processors and enabling scalable, networked architectures. Designing and verifying such architectures requires a unified formalism that integrates linear algebraic
reasoning with probabilistic and control-flow structures. In this work, we introduce a graphical framework for distributed
quantum computing that brings together linear optics, the ZX-calculus, and dataflow programming. Our
language supports the formal analysis and optimization of distributed protocols involving both
qubits and photonic modes, with explicit interfaces for classical control and feedforward, all expressed within a synchronous dataflow model with discrete-time dynamics. Within this setting, we classify entangling photonic fusion measurements, show how their induced Pauli errors can be corrected via a novel flow structure for fusion networks, and establish correctness proofs for new repeat-until-success protocols enabling arbitrary fusions. Layer by layer, we construct
qubit architectures incorporating practical optical components such as beam splitters, switches, and
photon sources, with graphical proofs that they are deterministic and support universal
quantum computation. Together, these results establish a foundation for verifiable compilation and automated optimization in networked
quantum computing.
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All authors Giovanni de Felice, Boldizsár Poór, Cole Comfort, Lia Yeh, Mateusz Kupper, William Cashman, Bob Coecke
Quantum Physics
A Methodological Analysis of Empirical Studies in Quantum Software Testing
Yuechen Li, Minqi Shao, Jianjun Zhao et al. (+1 more)
In
quantum software engineering (QSE),
quantum software testing (QST) has attracted increasing
attention as
quantum software systems grow in scale and complexity. Since QST evaluates
quantum programs through execution under designed test inputs, empirical studies are widely used to assess the effectiveness of testing approaches. However, the design and reporting of empirical studies in QST remain highly diverse, and a shared methodological understanding has yet to emerge, making it difficult to interpret results and compare findings across studies. This paper presents a methodological analysis of empirical studies in QST through a systematic examination of 59 primary studies identified from a literature pool of size 384. We organize our analysis around ten research questions that cover key methodological dimensions of QST empirical studies, including objects under test, baseline comparison, testing setup, experimental configuration, and tool and artifact support. Through cross-study analysis along these dimensions, we characterize current empirical practices in QST, identify recurring limitations and inconsistencies, and highlight open methodological challenges. Based on our findings, we derive insights and recommendations to inform the design, execution, and reporting of future empirical studies in QST.
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All authors Yuechen Li, Minqi Shao, Jianjun Zhao, Qichen Wang
Quantum Physics
Verification of continuous variable entanglement with undetected photons
Sanjukta Kundu, Balakrishnan Viswanathan, Pawel Szczypkowski et al. (+3 more)
We verify transverse spatial
entanglement of
photon-pairs generated in spontaneous parametric down conversion using a nonlinear interferometric technique without relying on any coincidence detection. We experimentally demonstrate the violation of the Einstein-Podolsky-Rosen criterion and of the Mancini-Giovannetti-Vitali-Tombesi criterion using single
photon interference of one of the
photons of the pairs. We also provide a comprehensive theoretical analysis. The experimental results that we have obtained show good agreement with the theoretical values. Our method performs well under experimental losses and can be applied to highly non-degenerate sources, where there are no suitable detectors for one of the
photons in the
quantum state and our method could also be extended to the discrete degrees of freedom to certify high-dimensional (OAM)
entanglement.
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All authors Sanjukta Kundu, Balakrishnan Viswanathan, Pawel Szczypkowski, Gabriela Barreto Lemos, Mayukh Lahiri, Radek Lapkiewicz
Quantum Physics
Criteria on quantum fluctuations of vacuum and photons influence in Spontaneous-Parametric Down-Conversion and Four-Wave-Mixing
Benoît Boulanger, Gaspar Mougin-Trichon and Véronique Boutou
This article is a theoretical and quantitative exploration of the limit regarding the pump intensity between the two regimes of spontaneous-parametric down-conversion (SPDC) as well as of four-wave-mixing (FWM) in the framework of a semi-classical model and analytical calculations. A dimensionless parameter has been defined at this limit, corresponding to the
photon-pairs flux per frequency unit: it has been found equal to 0.369. The ratio between the electric field of the generated
photons and the
quantum fluctuations of
vacuum calculated at the limit is equal to 1.718. These quantitative results confirm that below the limit, the pump
photon splitting leading to
photon-pairs can be considered as spontaneous, i.e. mainly seeded by the
quantum fluctuations of
vacuum, while it is stimulated by the generated signal and idler
photons above the limit, which corresponds to an optical parametric amplification regime. Our calculations also show that this limit can be easily reached in the case of SPDC according to the typical values of non-linearities and available
crystal dimensions. In the case of FWM, it would be only possible in kilometric optical fibers. This corpus is a useful tool box for designing further
quantum experiments performed from either side of the limit, as well as at the limit it-self where the influence of the
quantum fluctuations of
vacuum and of the generated
photons should have the same weight. Furthermore, the
quantum significance of the numerical values of the two criteria defined here remains to be established, which should motivate future theoretical
quantum studies.
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Quantum Physics · Cross-listed from cond-mat.stat-mech
Eigenstate thermalization in thermal first-order phase transitions
Maksym Serbyn, Alexander Avdoshkin, Oriana K. Diessel et al. (+1 more)
The eigenstate thermalization hypothesis (ETH) posits how isolated
quantum many-body systems thermalize, assuming that individual eigenstates at the same energy density have identical expectation values of local observables in the limit of large systems. While the ETH apparently holds across a wide range of interacting
quantum systems, in this work we show that it requires generalization in the presence of thermal first-order phase transitions. We introduce a class of all-to-all
spin models, featuring first-order thermal phase transitions that stem from two distinct mean-field solutions (two “branches”) that exchange dominance in the many-body density of states as the energy is varied. We argue that for energies in the vicinity of the thermal phase transition, eigenstate expectation values do not need to converge to the same thermal value. The system has a regime with coexistence of two classes of eigenstates corresponding to the two branches with distinct expectation values at the same energy density, and another regime with Schrodinger-cat-like eigenstates that are inter-branch superpositions; these two regimes are separated by an eigenstate phase transition. We support our results by semiclassical calculations and an exact diagonalization study of a microscopic
spin model, and argue that the structure of eigenstates in the vicinity of thermal first-order phase transitions can be experimentally probed via non-
equilibrium dynamics.
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All authors Maksym Serbyn, Alexander Avdoshkin, Oriana K. Diessel, David A. Huse
Quantum Physics · Cross-listed from cond-mat.dis-nn
Critical quantum states and hierarchical spectral statistics in a Cantor potential
F. Iwase
We study the spectral statistics and wave-function properties of a one-dimensional
quantum system subject to a Cantor-type fractal potential. By analyzing the nearest-neighbor level spacings, inverse participation ratio (IPR), and the scaling behavior of the integrated density of states (IDS), we demonstrate how the self-similar geometry of the potential is imprinted on the
quantum spectrum. The energy-resolved level spacings form a hierarchical, filamentary structure, in sharp contrast to those of periodic and random systems. The normalized level-spacing distribution exhibits a bimodal structure, reflecting the deterministic recurrence of spectral gaps. A multifractal analysis of eigenstates reveals critical behavior: the generalized fractal dimensions $D_q$ lie strictly between the limits of extended and localized states, exhibiting a distinct $q$-dependence. Consistently, the IPR indicates the coexistence of quasi-extended and localized features, characteristic of critical wave functions. The IDS shows anomalous power-law scaling at low energies, with an exponent close to the Hausdorff dimension of the underlying Cantor set, indicating that the
geometric fractality governs the spectral dimensionality. At higher energies, this scaling crosses over to the semiclassical Weyl law. Our results establish a direct connection between deterministic fractal geometry, hierarchical spectral statistics, and
quantum criticality.
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Quantum Physics
Extending Qubit Coherence Time via Hybrid Dynamical Decoupling
Qi Yao, Jun Zhang, Wenxian Zhang et al. (+1 more)
Dynamical decoupling (DD) and bath engineering are two parallel techniques employed to mitigate
qubit decoherence resulting from their unavoidable coupling to the environment. Here, we present a hybrid DD approach that integrates pulsed DD with bath
spin polarization to enhance
qubit coherence within the central
spin model. This model, which can be realized using GaAs
semiconductor quantum dots or analogous
quantum simulators, demonstrates a significant extension of the central
spin's coherence time by approximately 2 to 3 orders of magnitude that compared with the free-induced decay time, where the dominant contribution from DD and a moderate improvement from
spin-bath polarization. This study, which integrates uniaxial dynamical decoupling and auxiliary bath-
spin engineering, paves the way for prolonging coherence times in various practical
quantum systems, including GaAs/AlGaAs, silicon and Si/SiGe. And this advancement holds substantial promise for applications in
quantum information processing.
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All authors Qi Yao, Jun Zhang, Wenxian Zhang, Chaohong Lee
Quantum Physics
A Preparation Nonstationarity Loophole in Superconducting-Qubit Bell Tests
Prosanta Pal, Shubhanshu Karoliya, Gargee Sharma et al. (+1 more)
Bell or Clauser-Horne-Shimony-Holt (CHSH) tests on superconducting
quantum processors are commonly interpreted under the assumption that repeated
circuit executions sample a single, stationary preparation ensemble. Here we show that this assumption can be violated on contemporary hardware, with direct implications for the interpretation of observed Bell violations. We introduce an ensemble-divergence framework in which slow temporal drift of the preparation process induces context-dependent effective ensembles, even when measurement independence and locality are preserved. This leads to a relaxed Bell bound $|S| \le 2 + 6\delta_{\mathrm{ens}}$, where $\delta_{\mathrm{ens}}$ quantifies preparation nonstationarity. Because $\delta_{\mathrm{ens}}$ is not directly observable, we develop an operational witness $\delta_{\mathrm{op}}$ based on bin-resolved outcome statistics for fixed measurement channels. Using Pauli-axis measurements on IBM superconducting processors, we observe statistically significant operational drift that persists after full two-
qubit readout mitigation, ruling out measurement artifacts. In contrast, drift extracted from CHSH-optimal measurements is eliminated by mitigation, demonstrating that such settings are unsuitable for diagnosing preparation nonstationarity. We further show that the observed Bell violations imply only modest ensemble divergences, comparable in scale to those required in
Hall-type measurement-dependence models, but arising here solely from preparation drift combined with experimental scheduling. Our results identify a preparation-dependent loophole relevant to Bell tests on noisy intermediate-scale
quantum devices and highlight the necessity of drift-aware protocols for reliable
quantum certification.
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All authors Prosanta Pal, Shubhanshu Karoliya, Gargee Sharma, Ramakrishna Podila
Quantum Physics
Efficient and broadband quantum frequency comb generation in a monolithic AlGaAs-on-insulator microresonator
Xiaodong Zheng, Xu Jing, Chenbo Liu et al. (+9 more)
The exploration of photonic systems for
quantum information processing has generated widespread interest in multiple cutting-edge research fields. Photonic frequency encoding stands out as an especially viable approach, given its natural
alignment with established optical communication technologies, including fiber networks and wavelength-division multiplexing systems. Substantial reductions in hardware resources and improvements in
quantum performance can be expected by utilizing multiple frequency modes. The integration of nonlinear photonics with microresonators provides a compelling way for generating frequency-correlated
photon pairs across discrete spectral modes. Here, by leveraging the high material nonlinearity and low nonlinear loss, we demonstrate an efficient chip-scale multi-wavelength
quantum light source based on AlGaAs-on-
insulator, featuring a free spectral range of approximately 200 GHz at telecom wavelengths. The optimized submicron waveguide geometry provides both high effective nonlinearity (~550 m$^{-1}$W$^{-1}$) and broad generation bandwidth, producing eleven distinct wavelength pairs across a 35.2 nm bandwidth with an average spectral brightness of 2.64 GHz mW$^{-2}$nm$^{-1}$. The generation of energy-time
entanglement for each pair of frequency modes is verified through Franson interferometry, yielding an average net visibility of 93.1%. With its exceptional optical gain and lasing capabilities, the AlGaAs-on-
insulator platform developed here shows outstanding potential for realizing fully integrated, ready-to-deploy
quantum photonic systems on chip.
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All authors Xiaodong Zheng, Xu Jing, Chenbo Liu, Yufu Li, Runqiu He, Lina Xia, Fei Wang, Yuechan Kong, Tangsheng Chen, Liangliang Lu, Jiayun Dai, Bin Niu
Quantum Physics
Reference-frame-independent Quantum secure direct communication
Jia-Wei Ying, Shi-Pu Gu, Xing-Fu Wang et al. (+7 more)
Current
quantum secure direct communication (QSDC) protocols guarantee communication security by estimating the error rates of
photons in the X and Z bases. This take the reference frame calibration between communicating parties as a necessary prerequisite. However, in mobile communications scenarios, achieving continuous and accurate reference frame calibration poses significant challenges. To address this issue, this paper proposes a reference-frame-independent (RFI) QSDC protocol. This protocol only requires ensuring the calibration accuracy of one direction of the reference frame, while allowing a misalignment angle $\beta$ in the other two directions. To improve the protocol's robustness against reference frame fluctuations, we introduce a $\beta$-independent parameter C into the security analysis framework and rederive the protocol's security bounds. Additionally, we construct a system model and optimize the pulse intensity of the signal states, enabling the protocol to achieve optimal performance under each level of channel attenuation. At an attenuation of 10 dB (corresponding to a communication distance of 25 km), the secrecy message capacities for $\beta= 0^{ \circ} $ and $45^{ \circ} $ are $8.765 \times10^{-6}$ bit/pulse and $4.150 \times10^{-6}$ bit/pulse, respectively. Compared with the single-
photon-based QSDC, the communication distance of the protocol proposed in this paper is significantly extended. When $\beta= 0^{ \circ} $ and $45^{ \circ} $, the maximum transmission distances of the RFI QSDC protocol are 27.875 km and 26.750 km, which is about 155.9 % and 149.7 % of that of the single-
photon-based QSDC protocol.
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All authors Jia-Wei Ying, Shi-Pu Gu, Xing-Fu Wang, Wei Zhong, Ming-Ming Du, Xi-Yun Li, Shu-Ting Shen, An-Lei Zhang, Lan Zhou, Yu-Bo Sheng