Noisy Intermediate-scale Quantum Research Articles

Quafu-RL: The cloud quantum computers based quantum reinforcement learning

With the rapid advancement of quantum computing, hybrid quantum–classical machine learning has shown numerous potential applications at the current stage, with expectations of being achievable in the noisy intermediate-scale quantum (NISQ) era. Quantum reinforcement learning, as an indispensable study, has recently demonstrated its ability to solve standard benchmark environments with formally provable theoretical advantages over classical counterparts. However, despite the progress of quantum processors and the emergence of quantum computing clouds, implementing quantum reinforcement learning algorithms utilizing parameterized quantum circuits (PQCs) on NISQ devices remains infrequent. In this work, we take the first step towards executing benchmark quantum reinforcement problems on real devices equipped with at most 136 qubits on the BAQIS Quafu quantum computing cloud. The experimental results demonstrate that the policy agents can successfully accomplish objectives under modified conditions in both the training and inference phases. Moreover, we design hardware-efficient PQC architectures in the quantum model using a multi-objective evolutionary algorithm and develop a learning algorithm that is adaptable to quantum devices. We hope that the Quafu-RL can be a guiding example to show how to realize machine learning tasks by taking advantage of quantum computers on the quantum cloud platform.

Expressive quantum supervised machine learning using Kerr-nonlinear parametric oscillators

Quantum machine learning with variational quantum algorithms (VQA) has been actively investigated as a practical algorithm in the noisy intermediate-scale quantum (NISQ) era. Recent researches reveal that the data reuploading, which repeatedly encode classical data into quantum circuit, is necessary for obtaining the expressive quantum machine learning model in the conventional quantum computing architecture. However, the data reuploading tends to require a large amount of quantum resources, which motivates us to find an alternative strategy for realizing the expressive quantum machine learning efficiently. In this paper, we propose quantum machine learning with Kerr-nonlinear parametric oscillators (KPOs), as another promising quantum computing device. We use not only the ground state and first excited state but also higher excited states, which allows us to use a large Hilbert space even if we have a single KPO. Our numerical simulations show that the expressibility of our method with only one mode of the KPO is much higher than that of the conventional method with six qubits. Our results pave the way towards resource-efficient quantum machine learning, which is essential for the practical applications in the NISQ era.

Ensembles of quantum classifiers

In the current era, known as Noisy Intermediate-Scale Quantum (NISQ), encoding large amounts of data in the quantum devices is challenging and the impact of noise significantly affects the quality of the obtained results. A viable approach for the execution of quantum classification algorithms is the introduction of a well-known machine learning paradigm, namely, the ensemble methods. Indeed, the ensembles combine multiple internal classifiers, which are characterized by compact sizes due to the smaller data subsets used for training, to achieve more accurate and robust prediction performance. In this way, it is possible to reduce the qubit requirements with respect to a single larger classifier while achieving comparable or improved performance. In this work, we present an implementation and an extensive empirical evaluation of ensembles of quantum instance-based classifiers for binary classification, with the purpose of providing insights into their effectiveness, limitations, and potential for enhancing the performance of basic quantum models. In particular, three classical ensemble methods and three quantum instance-based classifiers have been taken into account here. Hence, the scheme that has been implemented (in Python) has a hybrid nature. The results (obtained on real-world datasets) have shown an accuracy advantage for the ensemble techniques with respect to the single quantum classifiers, and also an improvement in robustness. In fact, ensembles have proven effective not only in mitigating unsuitable data normalizations but also in reducing the impact of noise on quantum classifiers, enhancing their stability.

Quantum machine learning for image classification

Image classification, a pivotal task in multiple industries, faces computational challenges due to the burgeoning volume of visual data. This research addresses these challenges by introducing two quantum machine learning models that leverage the principles of quantum mechanics for effective computations. Our first model, a hybrid quantum neural network with parallel quantum circuits, enables the execution of computations even in the noisy intermediate-scale quantum era, where circuits with a large number of qubits are currently infeasible. This model demonstrated a record-breaking classification accuracy of 99.21% on the full MNIST dataset, surpassing the performance of known quantum–classical models, while having eight times fewer parameters than its classical counterpart. Also, the results of testing this hybrid model on a Medical MNIST (classification accuracy over 99%), and on CIFAR-10 (classification accuracy over 82%), can serve as evidence of the generalizability of the model and highlights the efficiency of quantum layers in distinguishing common features of input data. Our second model introduces a hybrid quantum neural network with a Quanvolutional layer, reducing image resolution via a convolution process. The model matches the performance of its classical counterpart, having four times fewer trainable parameters, and outperforms a classical model with equal weight parameters. These models represent advancements in quantum machine learning research and illuminate the path towards more accurate image classification systems.

Observing Schrödinger’s cat with artificial intelligence: emergent classicality from information bottleneck

We train a generative language model on the randomized local measurement data collected from Schrödinger’s cat quantum state. We demonstrate that the classical reality emerges in the language model due to the information bottleneck: although our training data contains the full quantum information about Schrödinger’s cat, a weak language model can only learn to capture the classical reality of the cat from the data. We identify the quantum–classical boundary in terms of both the size of the quantum system and the information processing power of the classical intelligent agent, which indicates that a stronger agent can realize more quantum nature in the environmental noise surrounding the quantum system. Our approach opens up a new avenue for using the big data generated on noisy intermediate-scale quantum devices to train generative models for representation learning of quantum operators, which might be a step toward our ultimate goal of creating an artificial intelligence quantum physicist.

Markovian noise modelling and parameter extraction framework for quantum devices.

In recent years, Noisy Intermediate Scale Quantum (NISQ) computers have been widely used as a test bed for quantum dynamics. This work provides a new hardware-agnostic framework for modelling the Markovian noise and dynamics of quantum systems in benchmark procedures used to evaluate device performance. As an accessible example, the application and performance of this framework is demonstrated on IBM Quantum computers. This framework serves to extract multiple calibration parameters simultaneously through a simplified process which is more reliable than previously studied calibration experiments and tomographic procedures. Additionally, this method allows for real-time calibration of several hardware parameters of a quantum computer within a comprehensive procedure, providing quantitative insight into the performance of each device to be accounted for in future quantum circuits. The framework proposed here has the additional benefit of highlighting the consistency among qubit pairs when extracting parameters, which leads to a less computationally expensive calibration process than evaluating the entire device at once.

Quantum radio astronomy: Quantum linear solvers for redundant baseline calibration

The computational requirements of future large scale radio telescopes are expected to scale well beyond the capabilities of conventional digital resources. Current and planned telescopes are generally limited in their scientific potential by their ability to efficiently process the vast volumes of generated data. To mitigate this problem, we investigate the viability of emerging quantum computers for radio astronomy applications. In this a paper we demonstrate the potential use of variational quantum linear solvers in Noisy Intermediate Scale Quantum (NISQ) computers and combinatorial solvers in quantum annealers for a radio astronomy calibration pipeline. While we demonstrate that these approaches can lead to satisfying results when integrated in calibration pipelines, we show that current restrictions of quantum hardware limit their applicability and performance.

Quantum neural network with privacy protection of input data and training parameters

It takes a lot of computational resources to train a machine learning model. So does quantum machine learning. In the NISQ (Noisy Intermediate Scale Quantum) era, there is a need for users who cannot afford quantum computers to utilize quantum servers to complete quantum machine learning with protection privacy of data and model parameters. In this paper, novel homomorphic encryption methods and circuit design with hidden parameter for Rz, Rx and Ry gate are putting forward. Based on which, we further propose quantum neural network (QNN) with privacy protection of input data and training parameters, where hiding model parameters has hardly mentioned in existing literature. To verify the validity of the proposed scheme, we conducted experiments on MNIST and Iris datasets, and obtained losses and accuracy that are almost identical to the original algorithms. Experiments show that our scheme can protect privacy well in the training and have no effect on accuracy of the algorithm. By comparison, the proposed scheme is more secure than most existing literature and requires less extra complexity O(4n).

Efficient Quantum Image Classification Using Single Qubit Encoding.

The domain of image classification has been seen to be dominated by high-performing deep-learning (DL) architectures. However, the success of this field, as seen over the past decade, has resulted in the complexity of modern methodologies scaling exponentially, commonly requiring millions of parameters. Quantum computing (QC) is an active area of research aimed toward greatly reducing problems of complexity faced in classical computing. With growing interest toward quantum machine learning (QML) for applications of image classification, many proposed algorithms require usage of numerous qubits. In the noisy intermediate-scale quantum (NISQ) era, these circuits may not always be feasible to execute effectively; therefore, we should aim to use each qubit as effectively and efficiently as possible, before adding additional qubits. This article proposes a new single-qubit-based deep quantum neural network for image classification that mimics traditional convolutional neural network (CNN) techniques, resulting in a reduced number of parameters compared with previous works. Our aim is to prove the concept of the initial proposal by demonstrating classification performance of the single-qubit-based architecture, as well as to provide a tested foundation for further development. To demonstrate this, our experiments were conducted using various datasets including MNIST, Fashion-MNIST, and ORL face datasets. To further our proposal in the context of the NISQ era, our experiments were intentionally conducted in noisy simulation environments. Initial test results appear promising, with classification accuracies of 94.6%, 89.5%, and 82.5% achieved on the subsets of MNIST, FMNIST, and ORL face datasets, respectively. In addition, proposals for further investigation and development were considered, where it is hoped that these initial results can be improved.

Efficient quantum simulation of open quantum system dynamics on noisy quantum computers

Quantum simulation represents the most promising quantum application to demonstrate quantum advantage on near-term noisy intermediate-scale quantum (NISQ) computers, yet available quantum simulation algorithms are prone to errors and thus difficult to realize with limited circuit depth on nowadays quantum devices. Herein, we propose a novel scheme to utilize intrinsic gate errors of NISQ devices to enable controllable simulation of open quantum system dynamics without ancillary qubits or explicit bath engineering, thus turning unwanted quantum noises into useful quantum resources. Specifically, we simulate the energy transfer process in a photosynthetic dimer system on IBM-Q cloud. By employing tailored decoherence-inducing gates, we show that quantum dissipative dynamics can be simulated efficiently across coherent-to-incoherent regimes with results comparable to those of the numerically exact classical method. Moreover, we demonstrate a calibration routine that enables consistent and predictive simulations of open-quantum system dynamics in the intermediate coupling regime. This work provides a new direction for quantum advantage in the NISQ era.

Quantum variational distance-based centroid classifier

Quantum machine learning is a rapidly growing field with the potential to surpass classical methods and offer novel solutions to learning problems. Supervised classification, a prominent pattern recognition task, has attracted significant attention for improving existing methods using quantum techniques. Although previous quantum algorithms for distance-based classification have shown promise, they are not compatible with current Noisy Intermediate-Scale Quantum (NISQ) devices and cannot handle multiclass problems. To address these limitations, we present the quantum Variational Distance-based Centroid Classifier (qVDCC), a hybrid approach that combines the Quantum One-Class Classifier (QOCC) and Parameterized Quantum Circuits (PQCs). This approach greatly improves the feasibility of multiclass classification on NISQ devices, as it eliminates the need for a label qubit and uses a single-qubit measurement, regardless of data size. Our simulations on seven benchmark datasets using both noisy and noise-free simulations show that qVDCC is competitive with the k-nearest neighbors algorithm, while providing exponential data compression and efficient quantum data processing.

Computing electronic correlation energies using linear depth quantum circuits

Efficient computation of molecular energies is an exciting application of quantum computing for quantum chemistry, but current noisy intermediate-scale quantum (NISQ) devices can only execute shallow circuits, limiting existing variational quantum algorithms, which require deep entangling quantum circuit ansatzes to capture correlations, to small molecules. Here we demonstrate a variational NISQ-friendly algorithm that generates a set of Hartree–Fock ansatzes using multiple shallow circuits with depth linear in the number of qubits to estimate electronic correlation energies via perturbation theory up to the second order. We tested the algorithm on several small molecules, both with classical simulations including noise models and on cloud quantum processors, showing that it not only reproduces the equilibrium molecular energies but it also captures the perturbative electronic correlation effects at longer bond distances. The number of shallow circuits required for our algorithms scales O(N5) , with N being the system size, thus enabling the study of larger molecules compared to other approaches, where circuit depth or number of qubits required become prohibitive for NISQ devices.

On the effects of biased quantum random numbers on the initialization of artificial neural networks

Recent advances in practical quantum computing have led to a variety of cloud-based quantum computing platforms that allow researchers to evaluate their algorithms on noisy intermediate-scale quantum devices. A common property of quantum computers is that they can exhibit instances of true randomness as opposed to pseudo-randomness obtained from classical systems. Investigating the effects of such true quantum randomness in the context of machine learning is appealing, and recent results vaguely suggest that benefits can indeed be achieved from the use of quantum random numbers. To shed some more light on this topic, we empirically study the effects of hardware-biased quantum random numbers on the initialization of artificial neural network weights in numerical experiments. We find no statistically significant difference in comparison with unbiased quantum random numbers as well as biased and unbiased random numbers from a classical pseudo-random number generator. The quantum random numbers for our experiments are obtained from real quantum hardware.

QFaaS: A Serverless Function-as-a-Service framework for Quantum computing

Quantum computing is rapidly reaching a point in which its application design and engineering aspects must be seriously considered. However, quantum software engineering is still in its infancy, with numerous challenges, especially in dealing with the diversity of quantum programming languages and noisy intermediate-scale quantum (NISQ) systems. To alleviate these challenges, we propose QFaaS, a holistic Quantum Function-as-a-Service framework, which leverages the advantages of the serverless model, DevOps lifecycle, and the state-of-the-art software techniques to advance practical quantum computing for next-generation application development in the NISQ era. Our framework provides essential elements of a serverless quantum system to streamline service-oriented quantum application development in cloud environments, such as combining hybrid quantum–classical computation, automating the backend selection, cold start mitigation, and adapting DevOps techniques. QFaaS offers a full-stack and unified quantum serverless platform by integrating multiple well-known quantum software development kits (Qiskit, Q#, Cirq, and Braket), quantum simulators, and cloud providers (IBM Quantum and Amazon Braket). This paper proposes the concept of quantum function-as-a-service, system design, operation workflows, implementation of QFaaS, and lessons learned on the benefits and limitations of quantum serverless computing. We also present practical use cases with various quantum applications on today’s quantum computers and simulators to demonstrate our framework capability to facilitate the ongoing quantum software transition.

Systematic study on the dependence of the warm-start quantum approximate optimization algorithm on approximate solutions

Quantum approximate optimization algorithm (QAOA) is a promising hybrid quantum-classical algorithm to solve combinatorial optimization problems in the era of noisy intermediate-scale quantum computers. Recently it has been revealed that warm-start approaches can improve the performance of QAOA, where approximate solutions are obtained by classical algorithms in advance and incorporated into the initial state and/or unitary ansatz. In this work, we study in detail how the accuracy of approximate solutions affects the performance of the warm-start QAOA (WS-QAOA). We numerically find that in typical MAX-CUT problems, WS-QAOA achieves higher fidelity (probability that exact solutions are observed) and approximation ratio than QAOA as the Hamming distance of approximate solutions to the exact ones becomes smaller. We reveal that this could be quantitatively attributed to the initial state of the ansatz. We also solve MAX-CUT problems by WS-QAOA with approximate solutions obtained via QAOA, having higher fidelity and approximation ratio than QAOA especially when the circuit is relatively shallow. We believe that our study may deepen understanding of the performance of WS-QAOA and also provide a guide as to the necessary quality of approximate solutions.

SimuQ: A Framework for Programming Quantum Hamiltonian Simulation with Analog Compilation

Quantum Hamiltonian simulation, which simulates the evolution of quantum systems and probes quantum phenomena, is one of the most promising applications of quantum computing. Recent experimental results suggest that Hamiltonian-oriented analog quantum simulation would be advantageous over circuit-oriented digital quantum simulation in the Noisy Intermediate-Scale Quantum (NISQ) machine era. However, programming analog quantum simulators is much more challenging due to the lack of a unified interface between hardware and software. In this paper, we design and implement SimuQ, the first framework for quantum Hamiltonian simulation that supports Hamiltonian programming and pulse-level compilation to heterogeneous analog quantum simulators. Specifically, in SimuQ, front-end users specify the target quantum system with Hamiltonian Modeling Language, and the Hamiltonian-level programmability of analog quantum simulators is specified through a new abstraction called the abstract analog instruction set (AAIS) and programmed in AAIS Specification Language by hardware providers. Through a solver-based compilation, SimuQ generates executable pulse schedules for real devices to simulate the evolution of desired quantum systems, which is demonstrated on superconducting (IBM), neutral-atom (QuEra), and trapped-ion (IonQ) quantum devices. Moreover, we demonstrate the advantages of exposing the Hamiltonian-level programmability of devices with native operations or interaction-based gates and establish a small benchmark of quantum simulation to evaluate SimuQ's compiler with the above analog quantum simulators.

Randomness-Enhanced Expressivity of Quantum Neural Networks.

As a hybrid of artificial intelligence and quantum computing, quantum neural networks (QNNs) have gained significant attention as a promising application on near-term, noisy intermediate-scale quantum devices. Conventional QNNs are described by parametrized quantum circuits, which perform unitary operations and measurements on quantum states. In this Letter, we propose a novel approach to enhance the expressivity of QNNs by incorporating randomness into quantum circuits. Specifically, we introduce a random layer, which contains single-qubit gates sampled from a trainable ensemble pooling. The prediction of QNN is then represented by an ensemble average over a classical function of measurement outcomes. We prove that our approach can accurately approximate arbitrary target operators using Uhlmann's theorem for majorization, which enables observable learning. Our proposal is demonstrated with extensive numerical experiments, including observable learning, Rényi entropy measurement, and image recognition. We find the expressivity of QNNs is enhanced by introducing randomness for multiple learning tasks, which could have broad application in quantum machine learning.

Quantum circuit synthesis on noisy intermediate-scale quantum devices

Quantum circuit synthesis on noisy intermediate-scale quantum devices

Improving Noisy Hybrid Quantum Graph Neural Networks for Particle Decay Tree Reconstruction

Improving Noisy Hybrid Quantum Graph Neural Networks for Particle Decay Tree Reconstruction

Variational Quantum Linear Solver Enhanced Quantum Support Vector Machine

Quantum Support Vector Machines (QSVM) play a vital role in using quantum resources for supervised machine learning tasks, such as classification. However, current methods are strongly limited in terms of scalability on Noisy Intermediate Scale Quantum (NISQ) devices. In this work, we propose a novel approach called the Variational Quantum Linear Solver (VQLS) enhanced QSVM. This is built upon our idea of utilizing the variational quantum linear solver to solve system of linear equations of a Least Squares-SVM on a NISQ device. The implementation of our approach is evaluated by an extensive series of numerical experiments with the Iris dataset, which consists of three distinct iris plant species. Based on this, we explore the effectiveness of our algorithm by constructing a classifier capable of classification in a feature space ranging from one to seven dimensions. Furthermore, we exploit both classical and quantum computing for various subroutines of our algorithm, and effectively mitigate challenges associated with the implementation. These include significant improvement in the trainability of the variational ansatz and notable reductions in run-time for cost calculations. Based on the numerical experiments, our approach exhibits the capability of identifying a separating hyperplane in an 8-dimensional feature space. Moreover, it consistently demonstrated strong performance across various instances with the same dataset.