Noisy Intermediate-scale Quantum Research Articles

Quantum-assisted rendezvous on graphs: explicit algorithms and quantum computer simulations

Abstract We study quantum advantage in one-step rendezvous games on simple graphs analytically, numerically, and using noisy intermediate-scale quantum (NISQ) processors. Our protocols realise the recently discovered (Mironowicz 2023 New J. Phys. 25 013023) optimal bounds for small cycle graphs and cubic graphs. In the case of cycle graphs, we generalise the protocols to arbitrary graph size. The NISQ processor experiments realise the expected quantum advantage with high accuracy for rendezvous on the complete graph K 3. In contrast, for the graph 2 K 4 , formed by two disconnected 4-vertex complete graphs, the performance of the NISQ hardware is sub-classical, consistent with the deeper circuit and known qubit decoherence and gate error rates.

Gate-based quantum neurons in hybrid neural networks

Abstract Quantum computing is conceived as a promising and powerful next-generation platform for information processing and it has been shown that it could bring significant accelerations to certain tasks, compared to its classical counterparts. With recent advances in noisy intermediate-scale quantum (NISQ) devices, we can process classical data from real-world problems using hybrid quantum systems. In this work, we investigate the critical problem of designing a gate-based hybrid quantum neuron under NISQ constraints to enable the construction of scalable hybrid quantum deep neural networks (HQDNNs). We explore and characterize diverse quantum circuits for hybrid quantum neurons and discuss related critical components of HQDNNs. We also utilize a new schema to infer multiple predictions from a single hybrid neuron. We further compose a highly customizable platform for simulating HQDNNs via Qiskit and test them on diverse classification problems including the iris and the wheat seed datasets. The results show that even HQDNNs with the simplest neurons could lead to superior performance on these tasks. Finally, we show that the HQDNNs are robust to certain levels of noise, making them preferred on NISQ devices. Our work provides a comprehensive investigation of building scalable near-term gate-based HQDNNs and paves the way for future studies of quantum deep learning via both simulations on classical computers and experiments on accessible NISQ devices.

Delayed-measurement one-way quantum computing on cloud quantum computer

Abstract One-way quantum computation focuses on initially generating an entangled cluster state followed by a sequence of measurements with classical communication of their individual outcomes. Recently, a delayed-measurement approach has been applied to replace classical communication of individual measurement outcomes. In this work, by considering the delayed-measurement approach, we demonstrate a modified one-way CNOT gate using the on-cloud superconducting quantum computing platform: Quafu. The modified protocol for one-way quantum computing requires only three qubits rather than the four used in the standard protocol. Since this modified cluster state decreases the number of physical qubits required to implement one-way computation, both the scalability and complexity of the computing process are improved. Compared to previous work, this modified one-way CNOT gate is superior to the standard one in both fidelity and resource requirements. We have also numerically compared the behavior of standard and modified methods in large-scale one-way quantum computing. Our results suggest that in a noisy intermediate-scale quantum (NISQ) era, the modified method shows a significant advantage for one-way quantum computation.

Quantum support vector data description for anomaly detection

Abstract Anomaly detection is a critical problem in data analysis and pattern recognition, finding applications in various domains. We introduce quantum support vector data description (QSVDD), an unsupervised learning algorithm designed for anomaly detection. QSVDD utilizes a shallow-depth quantum circuit to learn a minimum-volume hypersphere that tightly encloses normal data, tailored for the constraints of noisy intermediate-scale quantum (NISQ) computing. Simulation results on the MNIST and Fashion MNIST image datasets, as well as credit card fraud detection, demonstrate that QSVDD outperforms both quantum autoencoder and deep learning-based approaches under similar training conditions. Notably, QSVDD requires an extremely small number of model parameters, which increases logarithmically with the number of input qubits. This enables efficient learning with a simple training landscape, presenting a compact quantum machine learning model with strong performance for anomaly detection.

Overdispersion in gate tomography: Experiments and continuous, two-scale random walk model on the Bloch sphere

Noisy intermediate-scale quantum computers (NISQ) are computing hardware in their childhood, but they are showing high promise and growing quickly. They are based on so-called qubits, which are the quantum equivalents of bits. Any given qubit state results in a given probability of observing a value of zero or one in the readout process. One of the main concerns for NISQ machines is the inherent noisiness of qubits, i.e. the observable frequencies of zeros and ones do not correspond to the theoretically expected probability, as the qubit states are subject to random disturbances over time and with each additional algorithmic operation applied to them. Models to describe the influence of this noise exist. In this study, we conduct extensive experiments on quantum noise. Based on our data, we show that existing noise models lack important aspects. Specifically, they fail to properly capture the aggregation of noise effects over time (or over an algorithm’s runtime), and they are underdispersed. With underdispersion, we refer to the fact that observable frequencies scatter much more between repeated experiments than what the standard assumptions of the binomial distribution would allow for. Based on these shortcomings, we develop an extended noise model for the probability distribution of observable frequencies as a function of the number of gate operations. The model roots back to a known continuous random walk on the (Bloch) sphere, where the angular diffusion coefficient can be used to characterize the standard noisiness of gate operations. Here, we superimpose a second random walk at the scale of multiple readouts to account for overdispersion. Further, our model has known, explicit components for noise during state preparation and measurement (SPAM). The interaction of these two random walks predicts theoretical, runtime-dependent bounds for probabilities. Overall, it is a three-parameter distributional model that fits the data much better than the corresponding one-scale model (without overdispersion), and we demonstrate the better fit and the plausibility of the predicted bounds via Bayesian data-model analysis.

H-QNN: A Hybrid Quantum–Classical Neural Network for Improved Binary Image Classification

Image classification is an important application for deep learning. With the advent of quantum technology, quantum neural networks (QNNs) have become the focus of research. Traditional deep learning-based image classification involves using a convolutional neural network (CNN) to extract features from the image and a multi-layer perceptron (MLP) network to create the decision boundaries. However, quantum circuits with parameters can extract rich features from images and also create complex decision boundaries. This paper proposes a hybrid QNN (H-QNN) model designed for binary image classification that capitalizes on the strengths of quantum computing and classical neural networks. Our H-QNN model uses a compact, two-qubit quantum circuit integrated with a classical convolutional architecture, making it highly efficient for computation on noisy intermediate-scale quantum (NISQ) devices that are currently leading the way in practical quantum computing applications. Our H-QNN model significantly enhances classification accuracy, achieving a 90.1% accuracy rate on binary image datasets. In addition, we have extensively evaluated baseline CNN and our proposed H-QNN models for image retrieval tasks. The obtained quantitative results exhibit the generalization of our H-QNN for downstream image retrieval tasks. Furthermore, our model addresses the issue of overfitting for small datasets, making it a valuable tool for practical applications.

Flexible blind quantum computation with unnecessarily universal quantum servers

Blind quantum computation (BQC) allows clients with limited quantum capabilities to delegate their tasks to powerful quantum servers and still keep their inputs, algorithms, and outputs private. However, in the noisy intermediate-scale quantum (NISQ) era, quantum computers as servers only control limited number of qubits and are not powerful enough. In addition, each of current BQC models is usually suitable for only one type of users. Therefore, this paper offers a flexible BQC (BQCf for short) model for two types of users with different quantum capabilities where any one of two types of users can complete BQC tasks with the help of the other type of users and quantum servers. To be more specific, we propose two BQCf protocols by using the given model. In the first protocol, one user Alice only with the ability to prepare single-qubit states can realize BQC tasks by cooperating with another user Bob who is just capable of performing single-qubit measurements and a quantum server Charlie. Similarly in the second one, Bob can realize BQC tasks by cooperating with Alice and Charlie. In both protocols, the server Charlie only requires a quantum register of small size and performing CZ gates and thus it is unnecessary to be universal and may be less difficult to realize in the short run. Furthermore, both proposed protocols are verifiable, namely that the user can detect whether the server is honest. Finally, examples of the proposed protocols for implementing Deutsch’s algorithms are simulated through Qiskit framework to show their feasibility and correctness.

Impact of unreliable devices on stability of quantum computations

Noisy intermediate-scale quantum (NISQ) devices are valuable platforms for testing the tenets of quantum computing, but these devices are susceptible to errors arising from de-coherence, leakage, cross-talk and other sources of noise. This raises concerns regarding the stability of results when using NISQ devices since strategies for mitigating errors generally require well-characterized and stationary error models. Here, we quantify the reliability of NISQ devices by assessing the necessary conditions for generating stable results within a given tolerance. We use similarity metrics derived from device characterization data to derive and validate bounds on the stability of a 5-qubit implementation of the Bernstein-Vazirani algorithm. Simulation experiments conducted with noise data from IBM washington, spanning January 2022 to April 2023, revealed that the reliability metric fluctuated between 41% and 92%. This variation significantly surpasses the maximum allowable threshold of 2.2% needed for stable outcomes. Consequently, the device proved unreliable for consistently reproducing the statistical mean in the context of the Bernstein-Vazirani circuit.

HQ-DCGAN: Hybrid quantum deep convolutional generative adversarial network approach for ECG generation

The class imbalance of electrocardiogram (ECG) data is a serious impediment to the development of diagnostic systems for heart disease. To address this issue, this paper proposes HQ-DCGAN, a hybrid quantum deep convolutional generative adversarial network, specifically designed for the generation of ECGs. The proposed algorithm employs different quantum convolutional layers for the generator and discriminator as feature extractors and utilizes parameterized quantum circuits (PQCs) to enhance computational capabilities, along with the model-feature mapping process. Moreover, this algorithm preserves the nonlinearity and scalability inherent to classical convolutional neural networks (CNNs), thereby optimizing the utilization of quantum resources, and ensuring compatibility with contemporary quantum devices. In addition, this paper proposes a novel evaluation metric, 1D Fréchet Inception Distance (1DFID), to assess the quality of the generated ECG signals. Simulation experiments show that HQ-DCGAN exhibits strong performance in ECG signal generation. Furthermore, the generated signals achieve an average classification accuracy of 82.2%, outperforming the baseline algorithms. It has been experimentally proven that HQ-DCGAN is friendly to currently noisy intermediate-scale quantum (NISQ) computers, in terms of both number of qubits and circuit depths, while improving the stability.

Prolonging a discrete time crystal by quantum-classical feedback

Nonequilibrium phases of quantum matter featuring time crystalline eigenstate order have been realized recently on noisy intermediate-scale quantum (NISQ) devices. While ideal quantum time crystals exhibit collective subharmonic oscillations and spatiotemporal long-range order persisting for infinite times, the decoherence time of current NISQ devices sets a natural limit to the survival of these phases, restricting their observation to a shallow quantum circuit. Here we propose a time-periodic scheme that leverages quantum-classical feedback protocols in subregions of the system to enhance a time crystal signal significantly exceeding the decoherence time of the device. As a case of study, we demonstrate the survival of the many-body localized discrete time crystal phase in the one-dimensional periodically kicked Ising model, accounting for decoherence of the system with an environment. Based on classical simulation of quantum circuit realizations we find that this approach is suitable for implementation on existing quantum hardware and presents a prospective path to simulate complex quantum many-body dynamics that transcend the low depth limit of current digital quantum computers. Published by the American Physical Society 2024

HQC-MCDCNN: a novel hybrid quantum–classical multi-path denoising convolutional neural network

Image denoising is a longstanding and enduring visual problem, and with the continuous rise of quantum computing in the field of machine learning, its role in image processing has become increasingly important. This paper introduces for the first time the use of multiscale variational quantum circuits in the field of image denoising, aiming to enhance the performance of classical convolutional neural networks and explore the potential advantages of combining quantum and classical approaches. In this work, we propose a novel Hybrid Quantum-Classical Multi-Path Denoising Convolutional Neural Network, abbreviated as HQC-MCDCNN. The HQC-MCDCNN is composed of a hybrid of quantum and classical elements, with the quantum part using multiscale variational quantum circuits instead of classical convolutional layers for feature extraction, and the classical part employing a newly designed multi-path denoising convolutional neural network for supervised learning. Together, these components synergistically achieve image denoising. It is worth noting that this paper aims to build readers’ intuition for quantum computing, presenting all internal details of this work with rich images and visualizations. To demonstrate the denoising capability of HQC-MCDCNN, we conducted rigorous comparative experiments. Due to the constraints of Noisy Intermediate-Scale Quantum (NISQ) devices and the limited number of quantum bits, the experiments were based on the MNIST and Fashion-MNIST datasets with varying degrees of noise (noise factors ranging from 0.3 to 0.7), employing a 6-fold stratified sampling strategy for cross-validation. The experimental results indicate that HQC-MCDCNN is promising across all evaluation metrics, particularly outperforming other models by 56.5% in the average UIQ index. This suggests that our hybrid model exhibits outstanding feature extraction capabilities and excellent denoising performance, providing a promising path for addressing image denoising challenges.

The influence of basis sets and ansatze building to quantum computing in chemistry.

Quantum computing is an exciting area, which has grown at an astonishing rate in the last decade. It is especially promising for the computational and theoretical chemistry area. One algorithm has received a lot of attention lately, the variational quantum eigensolver (VQE). It is used to solve electronic structure problems and it is suitable to the noisy intermediate-scale quantum (NISQ) hardware. VQE calculations require ansatze and one of the most known is the unitary coupled cluster (UCC). It uses the chosen basis set to generate a quantum computing circuit which will be iteratively minimized. The present work investigates the circuit depth and the number of gates as a function of basis sets and molecular size. It has been shown that for the current quantum devices, only the smallest molecules and basis sets are tractable. The H molecule with the cc-pVTZ and aug-cc-pVTZ basis sets have circuit depths in the order of 10 to 10 gates and the C H molecule with 3-21G basis set has a circuit depth of gates. At the same time the analysis demonstrates that the H molecule with STO-3G basis set, requires at least 500 shots to reduce the error and that, although error mitigation schemes can diminish the error, they were not able to completely negate it. The quantum computing and electronic structure calculations were performed using the Qiskit package from IBM and the PySCF package, respectively. The ansatze were generated using the UCCSD method as implemented in Qiskit, using the basis sets STO-3G, 3-21G, 6-311G(d,p), def2-TZVP, cc-pVDZ, aug-cc-pVDZ, cc-pVTZ, and aug-cc-pVTZ. The operators and the Hamiltonian were mapped using the Jordan-Wigner scheme. The classical optimizer chosen was the simultaneous perturbation stochastic approximation (SPSA). The quantum computers used were the Nairobi and Osaka, with 7 and 127 qubits respectively.

Variational Gibbs state preparation on noisy intermediate-scale quantum devices

Variational Gibbs state preparation on noisy intermediate-scale quantum devices

Error Mitigation in the NISQ Era: Applying Measurement Error Mitigation Techniques to Enhance Quantum Circuit Performance

In quantum computing, noisy intermediate-scale quantum (NISQ) devices offer unprecedented computational capabilities but are vulnerable to errors, notably measurement inaccuracies that impact computation accuracy. This study explores the efficacy of error mitigation techniques in improving quantum circuit performance on NISQ devices. Techniques such as dynamic decoupling (DD), twirled readout error extraction (T-REx) and zero-noise extrapolation (ZNE) are examined through extensive experimentation on an ideal simulator, IBM Kyoto, and IBM Osaka quantum computers. Results reveal significant performance discrepancies across scenarios, with error mitigation techniques notably enhancing both estimator result and variance values, aligning more closely with ideal simulator outcomes. The comparison results with ideal simulator (having expected result value 0.8284) shows that T-Rex has improved results on IBM Kyoto and enhanced average expected result value from 0.09 to 0.35. Similarly, DD has improved average expected result values from 0.2492 to 0.3788 on IBM Osaka. These findings underscore the critical role of error mitigation in bolstering quantum computation reliability. The results suggest that selection of mitigation technique depends upon quantum circuit and its depth, type of hardware and operations to be performed.

Near-term quantum algorithm for solving the MaxCut problem with fewer quantum resources

MaxCut is an NP-hard combinatorial optimization problem in graph theory. The quantum approximate optimization algorithms (QAOAs) offer new methods for solving such problems, which are potentially better than classical schemes. However, the requirement of N qubits for solving graphs with N-vertex in QAOA, coupled with the large-N trainability issue due to barren plateaus, poses a substantial challenge for noisy intermediate-scale quantum (NISQ) devices. Recently, a hybrid quantum–classical algorithm has been proposed for solving semidefinite programs (SDPs), named NISQ SDP Solver (NSS). In this paper, we study the performance of the NSS for solving MaxCut problem via the introduction of a near-term quantum algorithm and execution of experimental simulations. Since the MaxCut problem admits a relaxation into an SDP formulation, the SDP can be solved using NSS, with a subsequent classical post-processing step converting the hybrid density matrix into a MaxCut solution. After performing these steps, the near-term quantum algorithm will also inherit the advantages of NSS. We analyze the algorithm as compared to QAOAs and find that the depth of the quantum circuit is independent of the number of edges on the graph. Our algorithm requires logN qubits and has O(1) circuit depth. This implies that it uses exponentially fewer qubits compared to QAOAs while also requiring a significantly reduced circuit depth to solve the MaxCut problem. To demonstrate the effectiveness of the NSS, we focused on 3-regular graphs, 9-regular graphs, and ER graphs. Numerical results indicate that the quantum algorithm achieves a comparable approximation ratio with classical methods by solving the original high dimensional problem within a lower dimensional ansatz space. Analysis under various initial states shows that the algorithm exhibits a remarkably stable performance.

Ising meson spectroscopy on a noisy digital quantum simulator

Quantum simulation has the potential to be an indispensable technique for the investigation of non-perturbative phenomena in strongly-interacting quantum field theories (QFTs). In the modern quantum era, with Noisy Intermediate Scale Quantum (NISQ) simulators widely available and larger-scale quantum machines on the horizon, it is natural to ask: what non-perturbative QFT problems can be solved with the existing quantum hardware? We show that existing noisy quantum machines can be used to analyze the energy spectrum of several strongly-interacting 1+1D QFTs, which exhibit non-perturbative effects like ‘quark confinement’ and ‘false vacuum decay’. We perform quench experiments on IBM’s quantum simulators to compute the energy spectrum of 1+1D quantum Ising model with a longitudinal field. Our results demonstrate that digital quantum simulation in the NISQ era has the potential to be a viable alternative to numerical techniques such as density matrix renormalization group or the truncated conformal space methods for analyzing QFTs.

Realization of higher-order topological lattices on a quantum computer

Programmable quantum simulators may one day outperform classical computers at certain tasks. But at present, the range of viable applications with noisy intermediate-scale quantum (NISQ) devices remains limited by gate errors and the number of high-quality qubits. Here, we develop an approach that places digital NISQ hardware as a versatile platform for simulating multi-dimensional condensed matter systems. Our method encodes a high-dimensional lattice in terms of many-body interactions on a reduced-dimension model, thereby taking full advantage of the exponentially large Hilbert space of the host quantum system. With circuit optimization and error mitigation techniques, we measured on IBM superconducting quantum processors the topological state dynamics and protected mid-gap spectra of higher-order topological lattices, in up to four dimensions, with high accuracy. Our projected resource requirements scale favorably with system size and lattice dimensionality compared to classical computation, suggesting a possible route to useful quantum advantage in the longer term.

A meta-trained generator for quantum architecture search

Variational Quantum Algorithms (VQAs) have made great success in the Noisy Intermediate-Scale Quantum (NISQ) era due to their relative resilience to noise and high flexibility relative to quantum resources. Quantum Architecture Search (QAS) aims to enhance the performance of VQAs by refining the structure of the adopted Parameterized Quantum Circuit (PQC). QAS is garnering increased attention owing to its automation, reduced reliance on expert experience, and its ability to achieve better performance while requiring fewer quantum gates than manually designed circuits. However, existing QAS algorithms optimize the structure from scratch for each VQA without using any prior experience, rendering the process inefficient and time-consuming. Moreover, determining the number of quantum gates, a crucial hyper-parameter in these algorithms is a challenging and time-consuming task. To mitigate these challenges, we accelerate the QAS algorithm via a meta-trained generator. The proposed algorithm directly generates high-performance circuits for a new VQA by utilizing a meta-trained Variational AutoEncoder (VAE). The number of quantum gates required in the designed circuit is automatically determined based on meta-knowledge learned from a variety of training tasks. Furthermore, we have developed a meta-predictor to filter out circuits with suboptimal performance, thereby accelerating the algorithm. Simulation results on variational quantum compiling and Quantum Approximation Optimization Algorithm (QAOA) demonstrate the superior performance of our method over a state-of-the-art algorithm, namely Differentiable Quantum Architecture Search (DQAS).

Enhancing the expressivity of quantum neural networks with residual connections

In noisy intermediate-scale quantum era, the research on the combination of artificial intelligence and quantum computing has been greatly developed. Here we propose a quantum circuit-based algorithm to implement quantum residual neural networks, where the residual connection channels are constructed by introducing auxiliary qubits to data-encoding and trainable blocks in quantum neural networks. We prove that when this particular network architecture is applied to a l-layer data-encoding, the number of frequency generation forms extends from one, namely the difference of the sum of generator eigenvalues, to O(l2)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{{{{{{\\mathcal{O}}}}}}}}({l}^{2})$$\\end{document}, and the flexibility in adjusting Fourier coefficients can also be improved. It indicates that residual encoding can achieve better spectral richness and enhance the expressivity of various parameterized quantum circuits. Extensive numerical demonstrations in regression tasks and image classification are offered. Our work lays foundation for the complete quantum implementation of classical residual neural networks and offers a quantum feature map strategy for quantum machine learning.

Fighting Noise with Noise: A Stochastic Projective Quantum Eigensolver.

In the current noisy intermediate scale quantum era of quantum computation, available hardware is severely limited by both qubit count and noise levels, precluding the application of many current hybrid quantum-classical algorithms to nontrivial quantum chemistry problems. In this paper we propose applying some of the fundamental ideas of conventional Quantum Monte Carlo algorithms─stochastic sampling of both the wave function and the Hamiltonian─to quantum algorithms in order to significantly decrease quantum resource costs. In the context of an imaginary-time propagation based projective quantum eigensolver, we present a novel approach to estimating physical observables which can lead to an order of magnitude reduction in the required sampling of the quantum state to converge the ground state energy of a system relative to current state-of-the-art eigensolvers. The method can be equally applied to excited-state calculations and, combined with stochastic approximations of the system Hamiltonian, provides a promising near-term approach to Hamiltonian simulation for general chemistry on quantum devices.