quant-ph

arXiv:2503.22641v1 Announce Type: cross Abstract: Property-based testing has been previously proposed for quantum programs in Q# with QSharpCheck; however, this implementation was limited in functionality, lacked extensibility, and was evaluated on a narrow range of programs using a single property. To address these limitations, we propose QuCheck, an enhanced property-based testing framework in Qiskit. By leveraging Qiskit and the broader Python ecosystem, QuCheck facilitates property construction, introduces flexible input generators and assertions, and supports expressive preconditions. We assessed its effectiveness through mutation analysis on five quantum programs (2-10 qubits), varying the number of properties, inputs, and measurement shots to assess their impact on fault detection and demonstrate the effectiveness of property-based testing across a range of conditions. Results show a strong positive correlation between the mutation score (a measure of fault detection) and number of properties evaluated, with a moderate negative correlation between the false positive rate and number of measurement shots. Among the most thorough test configurations, those evaluating three properties achieved a mean mutation score ranging from 0.90 to 0.92 across all five algorithms, with the false positive rate between 0 and 0.04. QuCheck identified 36.0% more faults than QSharpCheck, with execution time reduced by 81.1%, despite one false positive. These findings underscore the viability of property-based testing for verifying quantum systems.

arXiv:2503.21815v1 Announce Type: cross Abstract: Quantum Neural Networks (QNNs) offer promising capabilities for complex data tasks, but are often constrained by limited qubit resources and high entanglement, which can hinder scalability and efficiency. In this paper, we introduce Adaptive Threshold Pruning (ATP), an encoding method that reduces entanglement and optimizes data complexity for efficient computations in QNNs. ATP dynamically prunes non-essential features in the data based on adaptive thresholds, effectively reducing quantum circuit requirements while preserving high performance. Extensive experiments across multiple datasets demonstrate that ATP reduces entanglement entropy and improves adversarial robustness when combined with adversarial training methods like FGSM. Our results highlight ATPs ability to balance computational efficiency and model resilience, achieving significant performance improvements with fewer resources, which will help make QNNs more feasible in practical, resource-constrained settings.

arXiv:2305.05433v3 Announce Type: replace-cross Abstract: Quantum state tomography (QST) is the process of reconstructing the state of a quantum system (mathematically described as a density matrix) through a series of different measurements, which can be solved by learning a parameterized function to translate experimentally measured statistics into physical density matrices. However, the specific structure of quantum measurements for characterizing a quantum state has been neglected in previous work. In this paper, we explore the similarity between highly structured sentences in natural language and intrinsically structured measurements in QST. To fully leverage the intrinsic quantum characteristics involved in QST, we design a quantum-aware transformer (QAT) model to capture the complex relationship between measured frequencies and density matrices. In particular, we query quantum operators in the architecture to facilitate informative representations of quantum data and integrate the Bures distance into the loss function to evaluate quantum state fidelity, thereby enabling the reconstruction of quantum states from measured data with high fidelity. Extensive simulations and experiments (on IBM quantum computers) demonstrate the superiority of the QAT in reconstructing quantum states with favorable robustness against experimental noise.

arXiv:2503.22650v1 Announce Type: cross Abstract: Free tensors are tensors which, after a change of bases, have free support: any two distinct elements of its support differ in at least two coordinates. They play a distinguished role in the theory of bilinear complexity, in particular in Strassen's duality theory for asymptotic rank. Within the context of quantum information theory, where tensors are interpreted as multiparticle quantum states, freeness corresponds to a type of multiparticle Schmidt decomposition. In particular, if a state is free in a given basis, the reduced density matrices are diagonal. Although generic tensors in $\mathbb{C}^n \otimes \mathbb{C}^n \otimes \mathbb{C}^n$ are non-free for $n \geq 4$ by parameter counting, no explicit non-free tensors were known until now. We solve this hay in a haystack problem by constructing explicit tensors that are non-free for every $n \geq 3$. In particular, this establishes that non-free tensors exist in $\mathbb{C}^n \otimes \mathbb{C}^n \otimes \mathbb{C}^n$, where they are not generic. To establish non-freeness, we use results from geometric invariant theory and the theory of moment polytopes. In particular, we show that if a tensor $T$ is free, then there is a tensor $S$ in the GL-orbit closure of $T$, whose support is free and whose moment map image is the minimum-norm point of the moment polytope of $T$. This implies a reduction for checking non-freeness from arbitrary basis changes of $T$ to unitary basis changes of $S$. The unitary equivariance of the moment map can then be combined with the fact that tensors with free support have diagonal moment map image, in order to further restrict the set of relevant basis changes.

arXiv:2503.22292v1 Announce Type: cross Abstract: An Entanglement Generation Switch (EGS) is a quantum network hub that provides entangled states to a set of connected nodes by enabling them to share a limited number of hub resources. As entanglement requests arrive, they join dedicated queues corresponding to the nodes from which they originate. We propose a load-balancing policy wherein the EGS queries nodes for entanglement requests by randomly sampling d of all available request queues and choosing the longest of these to service. This policy is an instance of the well-known power-of-d-choices paradigm previously introduced for classical systems such as data-centers. In contrast to previous models, however, we place queues at nodes instead of directly at the EGS, which offers some practical advantages. Additionally, we incorporate a tunable back-off mechanism into our load-balancing scheme to reduce the classical communication load in the network. To study the policy, we consider a homogeneous star network topology that has the EGS at its center, and model it as a queueing system with requests that arrive according to a Poisson process and whose service times are exponentially distributed. We provide an asymptotic analysis of the system by deriving a set of differential equations that describe the dynamics of the mean-field limit and provide expressions for the corresponding unique equilibrium state. Consistent with analogous results from randomized load-balancing for classical systems, we observe a significant decrease in the average request processing time when the number of choices d increases from one to two during the sampling process, with diminishing returns for a higher number of choices. We also observe that our mean-field model provides a good approximation to study even moderately-sized systems.

arXiv:2503.22071v1 Announce Type: cross Abstract: We propose a model for quantum computing with long chains of trapped ions and we design quantum error correction schemes for this model. The main components of a quantum error correction scheme are the quantum code and a quantum circuit called the syndrome extraction circuit, which is executed to perform error correction with this code. In this work, we design syndrome extraction circuits tailored to our ion chain model, a syndrome extraction tuning protocol to optimize these circuits, and we construct new quantum codes that outperform the state-of-the-art for chains of about $50$ qubits. To establish a baseline under the ion chain model, we simulate the performance of surface codes and bivariate bicycle (BB) codes equipped with our optimized syndrome extraction circuits. Then, we propose a new variant of BB codes defined by weight-five measurements, that we refer to as BB5 codes, and we identify BB5 codes that achieve a better minimum distance than any BB codes with the same number of logical qubits and data qubits, such as $[[30, 4, 5]]$ and $[[48, 4, 7]]$ BB5 codes. For a physical error rate of $10^{-3}$, the $[[48, 4, 7]]$ BB5 code achieves a logical error rate per logical qubit of $5 \cdot 10^{-5}$, which is four times smaller than the best BB code in our baseline family. It also achieves the same logical error rate per logical qubit as the distance-7 surface code but using four times fewer physical qubits per logical qubit.

arXiv:2503.22656v1 Announce Type: cross Abstract: Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to design protocols that are hardware-aware, making efficient use of limited available quantum resources. We focus here on promising variational methods derived from scientific machine learning: differentiable quantum circuits (DQC), addressing specifically their cost in number of circuit evaluations. Reducing the number of quantum circuit evaluations is particularly valuable in hybrid quantum/classical protocols, where the time required to interface and run quantum hardware at each cycle can impact the total wall-time much more than relatively inexpensive classical post-processing overhead. Here, we propose and test two sample-efficient protocols for solving non-linear DEs, achieving exponential savings in quantum circuit evaluations. These protocols are based on redesigning the extraction of information from DQC in a ``measure-first" approach, by introducing engineered cost operators similar to the randomized-measurement toolbox (i.e. classical shadows). In benchmark simulations on one and two-dimensional DEs, we report up to $\sim$ 100 fold reductions in circuit evaluations. Our protocols thus hold the promise to unlock larger and more challenging non-linear differential equation demonstrations with existing quantum hardware.

arXiv:2503.22651v1 Announce Type: cross Abstract: We study the tradeoffs between the locality and parameters of subsystem codes. We prove lower bounds on both the number and lengths of interactions in any $D$-dimensional embedding of a subsystem code. Specifically, we show that any embedding of a subsystem code with parameters $[[n,k,d]]$ into $\mathbb{R}^D$ must have at least $M^*$ interactions of length at least $\ell^*$, where \[ M^* = \Omega(\max(k,d)), \quad\text{and}\quad \ell^* = \Omega\bigg(\max\bigg(\frac{d}{n^\frac{D-1}{D}}, \bigg(\frac{kd^\frac{1}{D-1}}{n}\bigg)^\frac{D-1}{D}\bigg)\bigg). \] We also give tradeoffs between the locality and parameters of commuting projector codes in $D$-dimensions, generalizing a result of Dai and Li. We provide explicit constructions of embedded codes that show our bounds are optimal in both the interaction count and interaction length.

arXiv:2503.16678v3 Announce Type: replace-cross Abstract: Physics-informed neural networks (PINNs) have emerged as promising methods for solving partial differential equations (PDEs) by embedding physical laws into neural architectures. However, these classical approaches often require large number of parameters for solving complex problems or achieving reasonable accuracy. We investigate whether quantum-enhanced architectures can achieve comparable performance while significantly reducing model complexity. We propose a quantum-classical physics-informed neural network (QCPINN) combining quantum and classical components to solve PDEs with fewer parameters while maintaining comparable accuracy and training convergence. Our approach systematically evaluates two quantum circuit paradigms (e.g., continuous-variable (CV) and discrete-variable (DV)) implementations with four circuit topologies (e.g., alternate, cascade, cross-mesh, and layered), two embedding schemes (e.g., amplitude and angle) on five benchmark PDEs (e.g., Helmholtz, lid-driven cavity, wave, Klein-Gordon, and convection-diffusion equations). Results demonstrate that QCPINNs achieve comparable accuracy to classical PINNs while requiring approximately 10\% trainable parameters across different PDEs, and resulting in a further 40\% reduction in relative $L_2$ error for the convection-diffusion equation. DV-based circuits with angle embedding and cascade configurations consistently exhibited enhanced convergence stability across all problem types. Our finding establishes parameter efficiency as a quantifiable quantum advantage in physics-informed machine learning. By significantly reducing model complexity while maintaining solution quality, QCPINNs represent a potential direction for overcoming computational bottlenecks in scientific computing applications where traditional approaches require large parameter spaces.

arXiv:2111.09504v3 Announce Type: replace-cross Abstract: Quantum state tomography (QST) aiming at reconstructing the density matrix of a quantum state plays an important role in various emerging quantum technologies. Recognizing the challenges posed by imperfect measurement data, we develop a unified neural network(NN)-based approach for QST under constrained measurement scenarios, including limited measurement copies, incomplete measurements, and noisy measurements. Through comprehensive comparison with other estimation methods, we demonstrate that our method improves the estimation accuracy in scenarios with limited measurement resources, showcasing notable robustness in noisy measurement settings. These findings highlight the capability of NNs to enhance QST with constrained measurements.

arXiv:2503.22016v1 Announce Type: cross Abstract: We show how to construct simulation secure one-time memories, and thus one-time programs, without computational assumptions in the presence of constraints on quantum hardware. Specifically, we build one-time memories from random linear codes and quantum random access codes (QRACs) when constrained to non-adaptive, constant depth, and $D$-dimensional geometrically-local quantum circuit for some constant $D$. We place no restrictions on the adversary's classical computational power, number of qubits it can use, or the coherence time of its qubits. Notably, our construction can still be secure even in the presence of fault tolerant quantum computation as long as the input qubits are encoded in a non-fault tolerant manner (e.g. encoded as high energy states in non-ideal hardware). Unfortunately though, our construction requires decoding random linear codes and thus does not run in polynomial time. We leave open the question of whether one can construct a polynomial time information theoretically secure one-time memory from geometrically local quantum circuits. Of potentially independent interest, we develop a progress bound for information leakage via collision entropy (Renyi entropy of order $2$) along with a few key technical lemmas for a "mutual information" for collision entropies. We also develop new bounds on how much information a specific $2 \mapsto 1$ QRAC can leak about its input, which may be of independent interest as well.

arXiv:2503.22147v1 Announce Type: cross Abstract: Characterizing non-Markovian quantum dynamics is essential for accurately modeling open quantum systems, particularly in near-term quantum technologies. In this work, we develop a structure-preserving approach to characterizing non-Markovian evolution using the time-convolutionless (TCL) master equation, considering both linear and nonlinear formulations. To parameterize the master equation, we explore two distinct techniques: the Karhunen-Loeve (KL) expansion, which provides an optimal basis representation of the dynamics, and neural networks, which offer a data-driven approach to learning system-environment interactions. We demonstrate our methodology using experimental data from a superconducting qubit at the Quantum Device Integration Testbed (QuDIT) at Lawrence Livermore National Laboratory (LLNL). Our results show that while neural networks can capture complex dependencies, the KL expansion yields the most accurate predictions of the qubit's non-Markovian dynamics, highlighting its effectiveness in structure-preserving quantum system characterization. These findings provide valuable insights into efficient modeling strategies for open quantum systems, with implications for quantum control and error mitigation in near-term quantum processors.

arXiv:2503.22633v1 Announce Type: new Abstract: Moment polytopes of tensors, the study of which is deeply rooted in invariant theory, representation theory and symplectic geometry, have found relevance in numerous places, from quantum information (entanglement polytopes) and algebraic complexity theory (GCT program and the complexity of matrix multiplication) to optimization (scaling algorithms). Towards an open problem in algebraic complexity theory, we prove separations between the moment polytopes of matrix multiplication tensors and unit tensors. As a consequence, we find that matrix multiplication moment polytopes are not maximal, i.e. are strictly contained in the corresponding Kronecker polytope. As another consequence, we obtain a no-go result for a natural operational characterization of moment polytope inclusion in terms of asymptotic restriction. We generalize the separation and non-maximality to moment polytopes of iterated matrix multiplication tensors. Our result implies that tensor networks where multipartite entanglement structures beyond two-party entanglement are allowed can go beyond projected entangled-pair states (PEPS) in terms of expressivity. Our proof characterizes membership of uniform points in moment polytopes of tensors, and establishes a connection to polynomial multiplication tensors via the minrank of matrix subspaces. As a result of independent interest, we extend these techniques to obtain a new proof of the optimal border subrank bound for matrix multiplication.

arXiv:2203.00110v3 Announce Type: replace Abstract: We consider the scenario of communicating on a $3\mhyphen$user classical-quantum broadcast channel. We undertake an information theoretic study and focus on the problem of characterizing an inner bound to its capacity region. We design a new coding scheme based \textit{partitioned coset codes} - an ensemble of codes possessing algebraic properties. Analyzing its information-theoretic performance, we characterize a new inner bound. We identify examples for which the derived inner bound is strictly larger than that achievable using IID random codes. Proceeding further, we incorporate Sen's technique of tilting smoothing and augmentation to perform simultaneous decoding via a simultaneous decoding POVM and thereby characterize a further enlarged achievable rate region for communicating classical bits over the $3-$user classical-quantum broadcast channel. Finally, in our last step, we characterize a new inner bound to the classical-quantum capacity region of the $3-$user classical-quantum broadcast channel that subsumes all previous known inner bounds by combining the conventional unstructured IID codes with structured coset code strategies.

arXiv:2503.10510v1 Announce Type: cross Abstract: Whole-slide image classification represents a key challenge in computational pathology and medicine. Attention-based multiple instance learning (MIL) has emerged as an effective approach for this problem. However, the effect of attention mechanism architecture on model performance is not well-documented for biomedical imagery. In this work, we compare different methods and implementations of MIL, including deep learning variants. We introduce a new method using higher-dimensional feature spaces for deep MIL. We also develop a novel algorithm for whole-slide image classification where extreme machine learning is combined with attention-based MIL to improve sensitivity and reduce training complexity. We apply our algorithms to the problem of detecting circulating rare cells (CRCs), such as erythroblasts, in peripheral blood. Our results indicate that nonlinearities play a key role in the classification, as removing them leads to a sharp decrease in stability in addition to a decrease in average area under the curve (AUC) of over 4%. We also demonstrate a considerable increase in robustness of the model with improvements of over 10% in average AUC when higher-dimensional feature spaces are leveraged. In addition, we show that extreme learning machines can offer clear improvements in terms of training efficiency by reducing the number of trained parameters by a factor of 5 whilst still maintaining the average AUC to within 1.5% of the deep MIL model. Finally, we discuss options of enriching the classical computing framework with quantum algorithms in the future. This work can thus help pave the way towards more accurate and efficient single-cell diagnostics, one of the building blocks of precision medicine.

arXiv:2503.07804v2 Announce Type: replace Abstract: We undertake a Shannon theoretic study of the problem of communicating classical information over a $3-$user quantum interference channel (QIC) and focus on characterizing inner bounds. In our previous work, we had demonstrated that coding strategies based on coset codes can yield strictly larger inner bounds. Adopting the powerful technique of \textit{tilting}, \textit{smoothing} and \textit{augmentation} discovered by Sen recently, and combining with our coset code strategy we derive a new inner bound to the classical-quantum capacity region of a $3-$user QIC. The derived inner bound subsumes all current known bounds.

arXiv:2503.10302v1 Announce Type: cross Abstract: Recent demonstrations on specialized benchmarks have reignited excitement for quantum computers, yet whether they can deliver an advantage for practical real-world problems remains an open question. Here, we show that probabilistic computers (p-computers) when co-designed with hardware to implement powerful Monte Carlo algorithms surpass state-of-the-art quantum annealers [\href{https://www.nature.com/articles/s41586-023-05867-2}{King et al., Nature (2023)}] in solving hard optimization problems. We focus on two key algorithms: discrete-time simulated quantum annealing (DT-SQA) and adaptive parallel tempering (APT), both applied to 3D spin glasses. For DT-SQA, we find that increasing the number of replicas improves residual energy scaling, while parallelizing fewer replicas across independent runs also achieves comparable scaling. Both strategies align with the theoretical expectations from extreme value theory. In addition, APT outperforms DT-SQA when supported by non-local isoenergetic cluster moves. Finite-size scaling analysis suggests a universal behavior that explains the superior performance of APT over both DT-SQA and quantum annealing. We show that these algorithms are readily implementable in modern hardware thanks to the mature semiconductor technology. Unlike software simulations, replicas can be monolithically housed on a single chip and a large number of spins can be updated in parallel and asynchronously, similar to a quantum annealer. We project that custom Field Programmable Gate Arrays (FPGA) or specialized chips leveraging massive parallelism can further accelerate these algorithms by orders of magnitude, while drastically improving energy efficiency. Our results challenge the notion of a practical quantum advantage in optimization and present p-computers as scalable, energy-efficient hardware for real-world optimization problems.

arXiv:2503.09776v1 Announce Type: new Abstract: As quantum networking continues to grow in importance, its study is of interest to an ever wider community and at an increasing scale. However, the development of its physical infrastructure remains burdensome, and services providing third party access are not enough to meet demand. A variety of simulation frameworks provide a method for testing aspects of such systems on commodity hardware, but are predominantly serial and thus unable to scale to larger networks and/or workloads. One effort to address this was focused on parallelising the SeQUeNCe discrete event simulator, though it has yet to be proven to work well across system architectures or at larger scales. Therein lies the contribution of this work - to more deeply examine its scalability using ORNL Frontier. Our results provide new insight into its scalability behaviour, and we examine its strategy and how it may be able to be improved.

arXiv:2503.10469v1 Announce Type: cross Abstract: We introduce a novel machine learning based framework for discovering integrable models. Our approach first employs a synchronized ensemble of neural networks to find high-precision numerical solution to the Yang-Baxter equation within a specified class. Then, using an auxiliary system of algebraic equations, [Q_2, Q_3] = 0, and the numerical value of the Hamiltonian obtained via deep learning as a seed, we reconstruct the entire Hamiltonian family, forming an algebraic variety. We illustrate our presentation with three- and four-dimensional spin chains of difference form with local interactions. Remarkably, all discovered Hamiltonian families form rational varieties.

arXiv:2503.10492v1 Announce Type: cross Abstract: While machine learning holds great promise for quantum technologies, most current methods focus on predicting or controlling a specific quantum system. Meta-learning approaches, however, can adapt to new systems for which little data is available, by leveraging knowledge obtained from previous data associated with similar systems. In this paper, we meta-learn dynamics and characteristics of closed and open two-level systems, as well as the Heisenberg model. Based on experimental data of a Loss-DiVincenzo spin-qubit hosted in a Ge/Si core/shell nanowire for different gate voltage configurations, we predict qubit characteristics i.e. $g$-factor and Rabi frequency using meta-learning. The algorithm we introduce improves upon previous state-of-the-art meta-learning methods for physics-based systems by introducing novel techniques such as adaptive learning rates and a global optimizer for improved robustness and increased computational efficiency. We benchmark our method against other meta-learning methods, a vanilla transformer, and a multilayer perceptron, and demonstrate improved performance.