Noisy Intermediate-scale Quantum Research Articles

Hybrid Quantum-Classical Multi-Agent Decision-Making Framework based on Hierarchical Bayesian Networks in the noisy intermediate-scale quantum era

Abstract Although quantum Bayesian networks provide a promising paradigm for multi-agent decision-making, their practical application faces two challenges in the noisy intermediate-scale quantum (NISQ) era. Limited qubit resources restrict direct application to large-scale inference tasks. Additionally, no quantum methods are currently available for multi-agent collaborative decision-making. To address these, we propose a hybrid quantum-classical multi-agent decision-making framework based on hierarchical Bayesian networks, comprising two novel methods. The first one is a hybrid quantum-classical inference method based on hierarchical Bayesian networks. It decomposes large-scale hierarchical Bayesian networks into modular subnetworks. The inference for each subnetwork can be performed on NISQ devices, and the intermediate results are converted into classical messages for cross-layer transmission. The second one is a multi-agent decision-making method using the variational quantum eigensolver (VQE) in the influence diagram. This method models the collaborative decision-making with the influence diagram and encodes the expected utility of diverse actions into a Hamiltonian and subsequently determines the intra-group optimal action effciently. Experimental validation on the IonQ quantum simulator demonstrates that the hierarchical method outperforms the non-hierarchical method at the functional inference level, and the VQE method can obtain the optimal strategy exactly at the collaborative decision-making level. Our research not only extends the application of quantum computing to multi-agent decision-making but also provides a practical solution for the NISQ era.

Machine learning approach toward quantum error mitigation for accurate molecular energetics.

Despite significant efforts, the realization of the hybrid quantum-classical algorithms has predominantly been confined to proof-of-principles, mainly due to the hardware noise. With fault-tolerant implementation being a long-term goal, going beyond small molecules with existing error mitigation (EM) techniques with current noisy intermediate scale quantum devices has been a challenge. That being said, statistical learning methods are promising approaches to learning the noise and its subsequent mitigation. We devise a graph neural network and regression-based machine learning (ML) architecture for practical realization of EM techniques for molecular Hamiltonian without the requirement of the exponential overhead. Given the short coherence time of the quantum hardware, the ML model is trained with either ideal or mitigated expectation values over a judiciously chosen ensemble of shallow sub-circuits adhering to the native hardware architecture. The hardware connectivity network is mapped to a directed graph, which encodes the information of the native gate noise profile to generate the features for the neural network. We demonstrate orders of magnitude improvements in predicted energy over a few molecules, which exhibit various degrees of correlation across their dissociation energy profile.

Tight-binding energy-phase calculation for topological Josephson junction nanowire architecture

The current state of Quantum computing (QC) is extremely optimistic, and we are at a point where researchers have produced highly sophisticated quantum algorithms to address far reaching problems. However, it is equally apparent that the noisy quantum environment is a larger threat than many may realize. The noisy intermediate scale quantum era can be viewed as an inflection point for the enterprise of QC where decoherence could stagnate progress if left unaddressed. One tactic for handling decoherence is to address the problem from a hardware level by implementing topological materials into the design. In this work, we model several Josephson junctions that are modified by the presence of topological superconducting nanowires in between the host superconductors. Our primary result is a numerical calculation of the energy-phase relationship for topological nanowire junctions which is a key parameter of interest for the dynamics of qubit circuits. In addition to this, we report on the qualitative physical behavior of the bound states as a function of superconducting phase. These results can be used to further develop and inform the construction of more complicated systems, and it is hopeful that these types of designs could manifest as a fault tolerant qubit.

Minimal state-preparation times for silicon spin qubits

Efficient preparation of quantum states on noisy intermediate-scale quantum processors remains a significant challenge to achieve quantum advantage. While gate-based methods have been the traditional approach, pulse-based algorithms offer promising alternatives with finer control and potentially reduced overheads. Here, we leverage the concept of minimum evolution time (MET) as a fundamental metric for evaluating and benchmarking quantum-state-preparation efficiency. Using numerical modeling, we investigate METs achievable through optimized microwave and exchange pulse sequences on silicon quantum hardware. We focus our investigations on molecular ground states and arbitrary state transitions. Our results demonstrate remarkably low METs: 2.3 ns for H2, 4.6 ns for HeH+, and 27 ns for LiH. METs consistently remain below 50 ns for arbitrary four-qubit state transitions, outperforming gate-based methods. We perform further analyses, revealing the impact of silicon device parameters on MET performance. Notably, increasing the maximal exchange amplitude from 10 MHz to 1 GHz significantly reduces METs, while higher maximal microwave drive amplitudes lead to faster state transitions. These findings surpass results reported for other quantum architectures. Our numerical analysis also demonstrates reasonable robustness of pulse-based state preparation to device imperfections and leakage. Our study contributes to developing efficient quantum-simulation techniques and provides insights into the strengths of silicon quantum hardware.

Noise resilience in adaptive and symmetric monitored quantum circuits

Monitored quantum circuits offer great perspectives for exploring the interplay of quantum information and complex quantum dynamics. These systems exhibit entanglement and purification phase transitions, along with various symmetry-enforced and ordered non-equilibrium phases. The central question is whether these phases can persist in real-world noisy devices. We study the fate of the symmetry-enforced absorbing state and charge-sharpening transitions in the presence of noise, and establish that noise results in coherent and incoherent symmetry-breaking effects. The coherent effects blur the distinction between phases, turning sharp transitions into crossovers, but states far from phase boundaries largely retain their essential character. We find, corrective feedback and postselected measurements can mitigate noise, stabilizing the absorbing and charge-sharp phases. Hence, if challenges like postselection are addressed, errors do not prevent the observation of symmetry-enforced phases in noisy intermediate-scale quantum (NISQ) devices. Additionally, we propose a symmetry-based method to characterize noise and gate fidelity.

Practicality of training a quantum-classical machine in the Noisy Intermediate-Scale Quantum era

Practicality of training a quantum-classical machine in the Noisy Intermediate-Scale Quantum era

Quantum Surface Topological Code for Bell State Stabilization in Superconducting Physical Qubit Systems

Stabilizing quantum states in physical qubits quantum computers has been a widely explored topic in the Noisy Intermediate-Scale Quantum era. However, much of this work has focused on simulation rather than practical implementation. In this study, an experimental advancement in Bell state stabilization is presented, which utilizes surface codes for quantum error correction across three quantum computers: ibm_fez, ibm_torino, and ibm_brisbane. Our findings indicate that error correction produces an improvement of approximately 3% in accuracy for 127-qubit systems while demonstrating a more significant enhancement of around 20% for 156-qubit systems in stabilizing the Bell state with fidelity up to 0.6 in all the experiments. This paper outlines the methodology for implementing this strategy in other applications, offering a pathway to improve results (≈20%) when experimenting with superconducting quantum computers.

Balanced ternary reversible comparator for qutrit quantum circuits

Abstract In recent years, quantum computing has emerged as a leading approach for accelerating complex computations, leveraging quantum parallelism and entanglement to surpass classical limits. Although numerous quantum circuits based on reversible gates have been proposed, optimizing circuit efficiency remains a critical challenge, particularly in the noisy intermediate-scale quantum era, where error rates and coherence times constrain performance. Ternary quantum computing, which operates on three-level quantum systems (qutrits), offers a promising alternative by reducing circuit complexity and resource overhead. In particular, balanced ternary logic presents advantages over conventional ternary logic by enhancing resource efficiency and potentially mitigating quantum gate error rates. This paper focuses on two key objectives: first, the synthesis of a reversible 1-qutrit comparator circuit using balanced ternary logic, and second, the extension to a generalized n-qutrit comparator. The proposed 1-qutrit comparator achieves notable improvements over existing unbalanced designs, demonstrating a 65% reduction in quantum cost, 50% fewer constant inputs, and a 33% decrease in garbage outputs. These results highlight the potential of balanced ternary logic to enhance the efficiency of quantum circuits, making it a valuable contribution to the development of scalable and error-resilient quantum hardware.

Quantum Time Dynamics Mediated by the Yang-Baxter Equation and Artificial Neural Networks.

Quantum computing shows great potential, but errors pose a significant challenge. This study explores new strategies for mitigating quantum errors using artificial neural networks (ANNs) and the Yang-Baxter equation (YBE). Unlike traditional error mitigation methods, which are computationally intensive, we investigate artificial error mitigation. We developed a novel method that combines ANNs for noise mitigation combined with the YBE to generate noisy data. This approach effectively reduces noise in quantum simulations, enhancing the accuracy of the results. The YBE rigorously preserves quantum correlations and symmetries in spin chain simulations in certain classes of integrable lattice models, enabling effective compression of quantum circuits while retaining linear scalability with the number of qubits. This compression facilitates both full and partial implementations, allowing the generation of noisy quantum data on hardware alongside noiseless simulations using classical platforms. By introducing controlled noise through the YBE, we enhance the data set for error mitigation. We train an ANN model on partial data from quantum simulations, demonstrating its effectiveness in mitigating errors in time-evolving quantum states, providing a scalable framework to enhance quantum computation fidelity, particularly in noisy intermediate-scale quantum (NISQ) systems. We demonstrate the efficacy of this approach by performing quantum time dynamics simulations using the Heisenberg XY Hamiltonian on real quantum devices.

Variational approach to photonic quantum circuits via the parameter shift rule

In the era of noisy intermediate-scale quantum computers, variational quantum algorithms are promising approaches for solving optimization tasks by training parameterized quantum circuits with the aid of classical routines informed by quantum measurements. In this context, photonic platforms based on reconfigurable integrated optics are an ideal candidate for implementing these algorithms. Among various techniques to train variational circuits, the parameter shift rule enables the exact calculation of cost function derivatives efficiently, facilitating gradient descent-based optimization. In this paper, we derive a formulation of the parameter shift rule for computing derivatives and integrals tailored to reconfigurable optical linear circuits and based on the Boson Sampling paradigm. This allows us to naturally embed common types of experimental noise, such as partial distinguishability and mixedness of the states, thus obtaining a resilient approach. Finally, we employ the developed approach to experimentally test variational algorithms with single-photon states processed in a reconfigurable six-mode universal integrated interferometer. Specifically, we apply the photonic parameter shift rules to the variational implementation, on a photonic platform, of both an eigensolver and a Universal- gate. Published by the American Physical Society 2025

LEVERAGING QUANTUM CONVOLUTIONAL LAYERS FOR ENHANCED IMAGE CLASSIFICATION: AN EXAMINATION OF QUANVOLUTIONAL NEURAL NETWORK CHARACTERISTICS

The rapid advancements in quantum computing have opened new avenues for enhancing classical machine learning paradigms, particularly in the realm of image classification. Traditional Deep Convolutional Neural Networks (DCNNs) have achieved remarkable success, yet they face challenges related to computational intensity and the need for vast datasets [4, 19, 31]. Quanvolutional Neural Networks (QNNs) emerge as a promising hybrid quantum-classical approach that integrates quantum circuits directly into the feature extraction process of convolutional layers. This article explores the fundamental characteristics and operational advantages of QNNs, focusing on how their unique quantum-enhanced feature maps contribute to improved image classification performance. We delve into the architecture of quanvolutional layers, the mechanisms of data encoding, and the potential for quantum advantage in feature learning. By synthesizing recent research, we demonstrate the theoretical underpinnings and observed benefits of QNNs in extracting richer, more discriminative features, potentially leading to higher accuracy and efficiency, especially in the Noisy Intermediate-Scale Quantum (NISQ) era [22]. Challenges such as data encoding complexity, parameter optimization, and hardware limitations are also discussed, alongside future directions for scalable and robust QNN implementations.

Classical-quantum approach to image classification: Autoencoders and quantum SVMs

In order to leverage quantum computers for machine learning tasks such as image classification, consideration is required. Noisy Intermediate-Scale Quantum (NISQ) computers have limitations that include noise, scalability, read-in and read-out times, and gate operation times. Therefore, strategies should be devised to mitigate the impact complex datasets that can have on the overall efficiency of a quantum machine learning pipeline. This may otherwise lead to excessive resource demands or noise. We apply a classical feature extraction using a ResNet10-inspired convolutional autoencoder to reduce dataset dimensionality and extract abstract, meaningful features before feeding them into a quantum layer. The chosen quantum layer is a quantum-enhanced support vector machine (QSVM), as SVMs typically do not require large sample sizes to identify patterns in data and have short-depth quantum circuits, which limits the impact of noise. The autoencoder is trained to extract meaningful features through image reconstruction, aiming to minimize the mean squared error across a training set of images. We use three datasets to illustrate the pipeline: HTRU-1, MNIST, and CIFAR-10. We include a quantum-enhanced one-class support vector machine (QOCSVM) for the highly unbalanced HTRU-1 set, with classical machine learning results for comparison. HTRU-2 is also included to serve as a benchmark for a dataset with meaningful features. The autoencoder achieved near-perfect reconstruction and high accuracy for MNIST, while CIFAR-10 showed poorer performance due to image complexity, and HTRU-1 struggled due to the imbalance in the dataset. The varying performance across datasets highlights the need to balance dimensionality reduction and prediction performance using quantum methods.

Variational Quantum Algorithm for Solving Second-Order Linear Differential Equations

Abstract Variational quantum algorithms (VQAs) have attracted attention as quantum algorithms employing on noisy intermediate-scale quantum devices. VQAs for solving the Poisson equation were recently proposed, as this method transforms the linear equation with a symmetric positive definite matrix obtained by discretizing the Poisson equation into a minimization problem. In this study, we propose a VQA for second-order linear differential equations including the Poisson equation on the basis of the referenced study, where the coefficient matrix obtained through discretization is a non-symmetric matrix. Furthermore, in our VQAs, we succeeded in decomposing the coefficient matrices arising from the periodic and the Dirichlet boundary condition into linear combinations of measurement operators and unitary matrices.

Quantum computing and digital hardware: Revolutionizing computational power

Quantum computing stands poised to revolutionize digital hardware by offering computational capabilities that fundamentally transcend classical computing limitations. The global quantum computing market demonstrates substantial growth fueled by investments from major technology corporations as they race toward achieving practical quantum advantages. Despite formidable technical challenges—including the need for extremely low operating temperatures and error correction—significant advancements have been made in reducing error rates and increasing qubit counts. Novel architectures like Amazon's "Ocelot" cat qubits, Microsoft's topological quantum computing and Nvidia's accelerated quantum supercomputing that integrates quantum hardware with AI supercomputers address persistent challenges in error rates and qubit coherence. These developments open new frontiers in previously intractable problems across multiple domains, from cryptography to materials science and artificial intelligence. As the field progresses from the Noisy Intermediate-Scale Quantum era toward fault-tolerant quantum computing, it faces four critical challenges: scalability, error correction, quantum-classical integration, and algorithm development. Addressing these challenges will enable quantum computing to fulfill its transformative potential across industries, fundamentally reshaping computational technology.

Bayesian phase difference estimation based on single-photon projective measurement

Abstract The estimation of quantum phase differences plays an important role in quantum simulation and quantum computation, yet existing quantum phase estimation algorithms face critical limitations in noisy intermediate-scale quantum (NISQ) devices due to their excessive depth and circuit complexity. We demonstrate a highprecision phase difference estimation protocol based on the Bayesian phase difference estimation algorithm and single-photon projective measurement. The iterative framework of the algorithm, combined with the independence from controlled unitary operations, inherently mitigates circuit depth and complexity limitations. Through an experiment realization on the photonic system, we demonstrate high-precision estimation of diverse phase differences, showing root-mean-square errors (RMSE) below the standard quantum limit O(1/√N ) and reaching the Heisenberg scaling O(1/N) after a certain number of iterations. Our scheme provides a critical advantage in quantum resource-constrained scenarios, and advances practical implementations of quantum information tasks under realistic hardware constraints.

Trainable embedding quantum physics informed neural networks for solving nonlinear PDEs

This paper proposes a novel approach for solving nonlinear partial differential equations (PDEs) with a quantum computer, the trainable embedding quantum physics informed neural network (TE-QPINN). We combine quantum machine learning (QML) with physics informed neural networks (PINNs) in a hybrid approach. By leveraging the advantages of classical and quantum computers, we can create algorithms that have a potential to be run on noisy intermediate-scale quantum devices (NISQ). We use feedforward neural networks (FNN) as problem-agnostic embedding functions, giving the used quantum circuit greater expressibility than previously introduced embedding. This expressibility allows us to solve a wide range of problems without using a problem specific ansatz. Additionally, we introduce a hybrid backpropagation algorithm that allows efficient updates of the used weights and biases in the FNN embedding functions. In this paper we showcase the capabilities of TE-QPINNs of a wide range of problems, including the two-dimensional Poisson, Burgers and Navier-Stokes equations. In direct comparison with classical PINNs, this approach showed an ability to achieve superior results while using the same number of parameters, highlighting their potential for more efficient optimization in high-dimensional parameter spaces, which could be transformative for future applications.

Greedy gradient-free adaptive variational quantum algorithms on a noisy intermediate scale quantum computer

Hybrid quantum-classical adaptive Variational Quantum Eigensolvers (VQE) hold the potential to outperform classical computing for simulating many-body quantum systems. However, practical implementations on current quantum processing units (QPUs) are challenging due to the noisy evaluation of a polynomially scaling number of observables, undertaken for operator selection and high-dimensional cost function optimization. We introduce an adaptive algorithm using analytic, gradient-free optimization, called Greedy Gradient-free Adaptive VQE (GGA-VQE). In addition to demonstrating the algorithm’s improved resilience to statistical sampling noise in the computation of simple molecular ground states, we execute GGA-VQE on a 25-qubit error-mitigated QPU by computing the ground state of a 25-body Ising model. Although hardware noise on the QPU produces inaccurate energies, our implementation outputs a parameterized quantum circuit yielding a favorable ground-state approximation. We demonstrate this by retrieving the parameterized operators calculated on the QPU and evaluating the resulting ansatz wave-function via noiseless emulation (i.e., hybrid observable measurement).

A quantum reservoir computing approach to computer-aided music composition

This paper presents an approach to developing computer-aided music composition (CAMC) systems with quantum computing. CAMC systems are aimed at supporting musicians in creating music rather than generating complete pieces of music autonomously. For instance, they may generate ideas or prompts to be further developed during the creative process. We developed a CAMC system using a machine learning method called Quantum Reservoir Computing (QRC) that learns to create tunes in the style of given examples. The system proved to run satisfactorily on the Noisy Intermediate-Scale Quantum (NISQ) machines available today. It does not require large amounts of qubits to outperform equivalent classical Deep Learning methods. Furthermore, it can serve the purposes of a CAMC system without the need for big data for training. This paper provides a general introduction to reservoir computing fundamentals and explains how quantum mechanics can harness its performance. Then, it walks the reader through the development of our system and presents demonstrations. A comparative experiment against a classic Recurrent Neural Network (RNN) model is also discussed.

Reducing the resources required by ADAPT-VQE using coupled exchange operators and improved subroutines

Adaptive variational quantum algorithms arguably offer the best prospects for quantum advantage in the Noisy Intermediate-Scale Quantum era. Since the inception of the first such algorithm, the Adaptive Derivative-Assembled Problem-Tailored Variational Quantum Eigensolver (ADAPT-VQE), many improvements have appeared in the literature. We combine the key improvements along with a novel operator pool—which we term Coupled Exchange Operator (CEO) pool—to assess the cost of running state-of-the-art ADAPT-VQE on hardware in terms of measurement counts and circuit depth. We show a dramatic reduction of these quantum computational resources compared to the early versions of the algorithm: CNOT count, CNOT depth and measurement costs are reduced by up to 88%, 96% and 99.6%, respectively, for molecules represented by 12 to 14 qubits (LiH, H6 and BeH2). We also find that our state-of-the-art CEO-ADAPT-VQE outperforms the Unitary Coupled Cluster Singles and Doubles ansatz, the most widely used static VQE ansatz, in all relevant metrics, and offers a five order of magnitude decrease in measurement costs as compared to other static ansätze with competitive CNOT counts.

Quantum data generation in a denoising model with multiscale entanglement renormalization network

Abstract Quantum technology has entered the era of noisy intermediate-scale quantum (NISQ) information processing. The technological revolution of machine learning represented by generative models heralds a great prospect of artificial intelligence, and the huge amount of data processes poses a big challenge to existing computers. The generation of large quantities of quantum data will be a challenge for quantum artificial intelligence. In this work, we present an efficient noise-resistant quantum data generation method that can be applied to various types of NISQ quantum processors, where the target quantum data belongs to a certain class and our proposal enables the generation of various quantum data belonging to the target class. Specifically, we propose a quantum denoising probability model (QDM) based on a multiscale entanglement renormalization network (MERA) for the generation of quantum data. To show the feasibility and practicality of our scheme, we demonstrate the generations of the classes of GHZ-like states and W-like states with a success rate above 99%. Our MREA QDM can also be used to denoise multiple types of quantum data simultaneously. We show the success rate of denoising both GHZ-like and W-like states with single qubit noise environment of noise level within 1/4 can approximate to be 100%, and with two other types of noise environment with noise level within 1/4 can be above 90%. Our quantum data generation scheme provides new ideas and prospects for quantum generative models in the NISQ era.