Abstract The search for useful applications of noisy intermediate-scale quantum (NISQ) devices in quantum simulation has been hindered by their intrinsic noise and the high costs associated with achieving high accuracy. A promising approach to finding utility despite these challenges involves using quantum devices to generate training data for classical machine learning (ML) models. In this study, we explore the use of noisy data generated by quantum algorithms in training an ML model to learn a density functional for the Fermi–Hubbard model. We benchmark various ML models against exact solutions, demonstrating that a neural-network ML model can successfully generalize from small datasets subject to noise typical of NISQ algorithms. The learning procedure can effectively filter out unbiased sampling noise, resulting in a trained model that outperforms any individual training data point. Conversely, when trained on data with expressibility and optimization error typical of the variational quantum eigensolver, the model replicates the biases present in the training data. The trained models can be applied to solving new problem instances in a Kohn–Sham-like density optimization scheme, benefiting from automatic differentiability and achieving reasonably accurate solutions on most problem instances. Our findings suggest a promising pathway for leveraging NISQ devices in practical quantum simulations, highlighting both the potential benefits and the challenges that need to be addressed for successful integration of quantum computing and ML techniques.
Abstract The search for useful applications of noisy intermediate-scale quantum (NISQ) devices in quantum simulation has been hindered by their intrinsic noise and the high costs associated with achieving high accuracy. A promising approach to finding utility despite these challenges involves using quantum devices to generate training data for classical machine learning (ML) models. In this study, we explore the use of noisy data generated by quantum algorithms in training an ML model to learn a density functional for the Fermi–Hubbard model. We benchmark various ML models against exact solutions, demonstrating that a neural-network ML model can successfully generalize from small datasets subject to noise typical of NISQ algorithms. The learning procedure can effectively filter out unbiased sampling noise, resulting in a trained model that outperforms any individual training data point. Conversely, when trained on data with expressibility and optimization error typical of the variational quantum eigensolver, the model replicates the biases present in the training data. The trained models can be applied to solving new problem instances in a Kohn–Sham-like density optimization scheme, benefiting from automatic differentiability and achieving reasonably accurate solutions on most problem instances. Our findings suggest a promising pathway for leveraging NISQ devices in practical quantum simulations, highlighting both the potential benefits and the challenges that need to be addressed for successful integration of quantum computing and ML techniques.
As medium-scale quantum computers progress, the application of quantum algorithms across diverse fields like simulating physical systems, chemistry, optimization, and cryptography becomes more prevalent. However, these quantum computers, known as Noisy Intermediate Scale Quantum (NISQ), are susceptible to noise, prompting the search for applications that can capitalize on quantum advantage without extensive error correction procedures. Since, Machine Learning (ML), particularly Deep Learning (DL), faces challenges due to resource-intensive training and algorithmic opacity. Therefore, this study explores the intersection of quantum computing and ML, focusing on computer vision tasks. Specifically, it evaluates the effectiveness of hybrid quantum-classical algorithms, such as the data re-uploading scheme and the patch Generative Adversarial Networks (GAN) model, on small-scale quantum devices. Through practical implementation and testing, the study reveals comparable or superior performance of these algorithms compared to classical counterparts, highlighting the potential of leveraging quantum algorithms in ML tasks.
The rapid advancement of quantum computing hardware and software has ushered in a new era for computational science, promising to tackle problems that are intractable for classical computers. Parallelly, machine learning (ML) has revolutionized data analysis and artificial intelligence. The confluence of these two fields, known as Quantum Machine Learning (QML), aims to harness the principles of quantum mechanics-such as superposition, entanglement, and interference-to enhance and redefine classical machine learning algorithms. This survey provides a comprehensive overview of the burgeoning field of QML. We begin by elucidating the fundamental quantum concepts that underpin QML approaches. We then present a detailed taxonomy and analysis of prominent QML algorithms, categorizing them into quantum-enhanced classical models and fully quantum models. Key families of algorithms discussed include Quantum Support Vector Machines (QSVM), Quantum Neural Networks (QNNs), and Quantum Generative Adversarial Networks (QGANs). For each, we explain the theoretical quantum advantage, the circuit implementation, and the current limitations. Furthermore, we delve into the critical challenges facing the practical realization of QML, including the pervasive issue of noise in Noisy Intermediate-Scale Quantum (NISQ) devices, the problem of barren plateaus in training quantum circuits, and the complexities of efficient data encoding (quantum feature maps). We also present a small-scale experimental simulation of a variational quantum classifier on a standardized dataset, demonstrating its principle and comparing its performance with a classical counterpart. Finally, the paper discusses the future trajectory of QML, highlighting the importance of error mitigation, hybrid quantum-classical architectures, and the development of quantum-specific learning inductive biases. We conclude that while fault-tolerant quantum computers remain on the horizon, QML represents a paradigm shift with the potential to deliver profound computational advantages in the coming decades.
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 (NISQ) 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. The training data is generated on-the-fly during ansatz construction thus removing the computational overhead. We demonstrate orders of magnitude improvements in predicted energy over a few strongly correlated molecules.
Hybridizing machine learning (ML) with quantum computing has become an attractive strategy to increase computational power on Noisy Intermediate Scale Quantum (NISQ) devices. Although these can be potentially quantum advantage devices, their qubit numbers and noise are bounded and there are challenges when it comes to practical quantum circuit realization. This work concentrates on the creation of optimized quantum circuits via ML-based strategies, to enhance the performance of the circuits, to reduce the error rate and to accommodate the particular noise profile of the hardware of NISQ devices. The resulting suboptimal mappings with little or no consideration of noise and hardware topology in traditional quantum compilers can ruin the fidelity of quantum algorithm. Leveraging machine learning, and specifically reinforcement and supervised learning methods, our method learns to optimize compilation strategy for specific quantum hardware architecture. The paper proposes a framework that uses machine learning models to predict qubit mappings, gate decompositions, and transpilation paths that minimize gate depth and error accumulation. We also investigate transfer learning methods for propagating the learned compilation strategies to novel NISQ machines. Such methods are empirically validated on both simulated and real quantum hardware backends, providing evidence of circuit depth, execution time and error reductions. The results show that ML-assisted compilation can achieve better success probabilities for benchmark quantum algorithms like VQE and QAOA than conventional compilers. Furthermore, the work examines the interpretability of ML models providing hardware-aware optimization recommendations and understanding the noise patterns and methods of error correction. Our work highlights the key role of ML for transferring between theoretical quantum algorithms and their practical NISQ implementations. This integration boosts the immediate applicability of existing quantum devices and provides a basis for adaptive and scalable likelihood-based compilation for the era of fault-tolerant quantum computation. Our results motivate further investigation of hybrid classical-quantum workflows, in which ML iteratively improves compilation in accordance with changing hardware noise and capabilities. By improving quantum circuit compilation onNISQ computers, this work is taking steps toward the realization of quantum advantage in application scenarios such as optimization, cryptography, and quantum simulation without needing to wait for fully fault-tolerant large-scale quantum computers.
In the noisy intermediate-scale quantum (NISQ) era, one of the key questions is how to deal with the high noise level existing in physical quantum bits (qubits). Quantum error correction is promising but requires an extensive number (e.g., over 1,000) of physical qubits to create one ”perfect” qubit, exceeding the capacity of the existing quantum computers. This paper aims to tackle the noise issue from another angle: instead of creating perfect qubits for general quantum algorithms, we investigate the potential to mitigate the noise issue for dedicate algorithms. Specifically, this paper targets quantum neural network (QNN), and proposes to learn the errors in the training phase, so that the identified QNN model can be resilient to noise. As a result, the implementation of QNN needs no or a small number of additional physical qubits, which is more realistic for the near-term quantum computers. To achieve this goal, an application-specific compiler is essential: on the one hand, the error cannot be learned if the mapping from logical qubits to physical qubits exists randomness; on the other hand, the compiler needs to be efficient so that the lengthy training procedure can be completed in a reasonable time. In this paper, we utilize the recent QNN framework, QuantumFlow, as a case study. Experimental results show that the proposed approach can optimize QNN models for different errors in qubits, achieving up to 28% accuracy improvement compared with the model obtained by the error-agnostic training.
In the noisy intermediate-scale quantum (NISQ) era, one of the key questions is how to deal with the high noise level existing in physical quantum bits (qubits). Quantum error correction is promising but requires an extensive number (e.g., over 1,000) of physical qubits to create one "perfect" qubit, exceeding the capacity of the existing quantum computers. This paper aims to tackle the noise issue from another angle: instead of creating perfect qubits for general quantum algorithms, we investigate the potential to mitigate the noise issue for dedicate algorithms. Specifically, this paper targets quantum neural network (QNN), and proposes to learn the errors in the training phase, so that the identified QNN model can be resilient to noise. As a result, the implementation of QNN needs no or a small number of additional physical qubits, which is more realistic for the near-term quantum computers. To achieve this goal, an application-specific compiler is essential: on the one hand, the error cannot be learned if the mapping from logical qubits to physical qubits exists randomness; on the other hand, the compiler needs to be efficient so that the lengthy training procedure can be completed in a reasonable time. In this paper, we utilize the recent QNN framework, QuantumFlow, as a case study. Experimental results show that the proposed approach can optimize QNN models for different errors in qubits, achieving up to 28% accuracy improvement compared with the model obtained by the error-agnostic training.