Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages over classical methods. Nevertheless, modern VQAs suffer from cumbersome computational overhead, hampered by the tradition of employing a solitary quantum processor to handle large-volume data. As such, to better exert the superiority of VQAs, it is of great significance to improve their runtime efficiency. Here we devise an efficient distributed optimization scheme, called QUDIO, to address this issue. Specifically, in QUDIO, a classical central server partitions the learning problem into multiple subproblems and allocate them to multiple local nodes where each of them consists of a quantum processor and a classical optimizer. During the training procedure, all local nodes proceed parallel optimization and the classical server synchronizes optimization information among local nodes timely. In doing so, we prove a sublinear convergence rate of QUDIO in terms of the number of global iteration under the ideal scenario, while the system imperfection may incur divergent optimization. Numerical results on standard benchmarks demonstrate that QUDIO can surprisingly achieve a superlinear runtime speedup with respect to the number of local nodes. Our proposal can be readily mixed with other advanced VQAs-based techniques to narrow the gap between the state of the art and applications with quantum advantage.
Variational quantum algorithms (VQAs) have the potential of utilizing near-term quantum machines to gain certain computational advantages over classical methods. Nevertheless, modern VQAs suffer from cumbersome computational overhead, hampered by the tradition of employing a solitary quantum processor to handle large-volume data. As such, to better exert the superiority of VQAs, it is of great significance to improve their runtime efficiency. Here we devise an efficient distributed optimization scheme, called QUDIO, to address this issue. Specifically, in QUDIO, a classical central server partitions the learning problem into multiple subproblems and allocate them to multiple local nodes where each of them consists of a quantum processor and a classical optimizer. During the training procedure, all local nodes proceed parallel optimization and the classical server synchronizes optimization information among local nodes timely. In doing so, we prove a sublinear convergence rate of QUDIO in terms of the number of global iteration under the ideal scenario, while the system imperfection may incur divergent optimization. Numerical results on standard benchmarks demonstrate that QUDIO can surprisingly achieve a superlinear runtime speedup with respect to the number of local nodes. Our proposal can be readily mixed with other advanced VQAs-based techniques to narrow the gap between the state of the art and applications with quantum advantage.
Variational quantum algorithms (VQAs) are prime contenders to gain computational advantages over classical algorithms using near-term quantum machines. As such, many endeavors have been made to accelerate the optimization of modern VQAs in past years. To further improve the capability of VQAs, here we propose a QUantum DIstributed Optimization scheme (dubbed as QUDIO), whose backends support both real quantum devices and various quantum simulators. Unlike traditional VQAs subsuming a single quantum chip or simulator, QUDIO collaborates with multiple quantum machines or simulators to complete learning tasks. In doing so, the required wall-clock time for optimization can be continuously reduced by increasing the accessible computational resources when ignoring the communication and synchronization time. Moreover, through the lens of optimization theory, we unveil the potential factors that could affect the convergence of QUDIO. In addition, we systematically understand the ability of QUDIO to reduce wall-clock time via two standard benchmarks, which are hand-written image classification and the ground energy estimation of the dihydrogen. Our proposal facilitates the development of advanced VQAs to narrow the gap between the state of the art and applications with the quantum advantage.
Abstract The variational quantum eigensolver (VQE) is a leading strategy that exploits noisy intermediate-scale quantum (NISQ) machines to tackle chemical problems. It is expected to demonstrate quantum advantage when handling a large number of qubits, where the density matrix cannot be processed efficiently on classical computers. To gain such computational advantages on large-scale problems, a feasible solution is the QUantum DIstributed Optimization (QUDIO) scheme, which partitions the original problem into $$\varvec{K}$$ K subproblems and allocates them to $$\varvec{K}$$ K quantum machines followed by the parallel optimization. Despite the provable acceleration ratio, the efficiency of QUDIO may heavily degrade by the synchronization operation. To conquer this issue, here we propose Shuffle-QUDIO to involve shuffle operations into local Hamiltonians during the quantum distributed optimization. Compared with QUDIO, Shuffle-QUDIO significantly reduces the communication frequency among quantum processors and simultaneously achieves better trainability. Particularly, we prove that Shuffle-QUDIO enables a faster convergence rate over QUDIO. Extensive numerical experiments are conducted to verify that Shuffle-QUDIO allows both a wall-clock time speedup and low approximation error in the tasks of estimating the ground state energy of a molecule. We empirically demonstrate that our proposal can be seamlessly integrated with other acceleration techniques, such as operator grouping, to further improve the efficacy of VQE.
Variational quantum algorithms (VQAs) have emerged as a promising near-term technique to explore practical quantum advantage on noisy intermediate-scale quantum (NISQ) devices. However, the inefficient parameter training process due to the incompatibility with backpropagation and the cost of a large number of measurements, posing a great challenge to the large-scale development of VQAs. Here, we propose a parameter-parallel distributed variational quantum algorithm (PPD-VQA), to accelerate the training process by parameter-parallel training with multiple quantum processors. To maintain the high performance of PPD-VQA in the realistic noise scenarios, a alternate training strategy is proposed to alleviate the acceleration attenuation caused by noise differences among multiple quantum processors, which is an unavoidable common problem of distributed VQA. Besides, the gradient compression is also employed to overcome the potential communication bottlenecks. The achieved results suggest that the PPD-VQA could provide a practical solution for coordinating multiple quantum processors to handle large-scale real-word applications.
Variational quantum algorithms (VQAs) provide a promising approach to achieve quantum advantage in the noisy intermediate-scale quantum era. In this era, quantum computers experience high error rates and quantum error detection and correction is not feasible. VQAs can utilize noisy qubits in tandem with classical optimization algorithms to solve hard problems. However, VQAs are still slow relative to their classical counterparts. Hence, improving the performance of VQAs will be necessary to make them competitive. While VQAs are expected perform better as the problem sizes increase, increasing their performance will make them a viable option sooner. In this work we show that circuit-level concurrency provides a means to increase the performance of variational quantum algorithms on noisy quantum computers. This involves mapping multiple instances of the same circuit (program) onto the quantum computer at the same time, which allows multiple samples in a variational quantum algorithm to be gathered in parallel for each training iteration. We demonstrate that this technique provides a linear increase in training speed when increasing the number of concurrently running quantum circuits. Furthermore, even with pessimistic error rates concurrent quantum circuit sampling can speed up the quantum approximate optimization algorithm by up to 20x with low mapping and run time overhead.
The exponential runtime of quantum simulators on classical machines, along with long queue times and high costs associated with real quantum devices, presents significant challenges for the efficient optimization of Variational Quantum Algorithms (VQAs) such as the Variational Quantum Eigensolver (VQE), Quantum Approximate Optimization Algorithm (QAOA), and Quantum Neural Networks (QNNs). To address these limitations, we propose a novel approach, DyPP (Dynamic Parameter Prediction), which accelerates the convergence of VQAs by leveraging regular trends in the parameter weights to update parameters efficiently. We introduce two techniques for optimal prediction performance: Naive Prediction (NaP) and Adaptive Prediction (AdaP). Through extensive experimentation and training of multiple QNN models on various datasets, we demonstrate that DyPP achieves a speedup of approximately 2.25×compared to standard training methods, while also providing improved accuracy (up to 2.3% higher) and lower loss (up to 6.1% reduction) with minimal storage and computational overhead. We further evaluate DyPP’s effectiveness in VQE for molecular ground-state energy estimation and in QAOA for graph MaxCut. Our results show that, on average, DyPP leads to a speedup of up to 3.1× for VQE and 2.91× for QAOA compared to traditional optimization, while requiring up to 3.3× fewer shots (i.e., repeated circuit executions). Even in the presence of hardware noise, DyPP outperforms existing optimization techniques, delivering up to 3.33× speedup and requiring 2.5× fewer shots, thereby enhancing the efficiency of VQAs.
Variational quantum algorithms (VQAs) are leading strategies to reach practical utilities of near-term quantum devices. However, the no-cloning theorem in quantum mechanics precludes standard backpropagation, leading to prohibitive quantum resource costs when applying VQAs to large-scale tasks. To address this challenge, we reformulate the training dynamics of VQAs as a nonlinear partial differential equation and propose a novel protocol that leverages physics-informed neural networks (PINNs) to model this dynamical system efficiently. Given a small amount of training trajectory data collected from quantum devices, our protocol predicts the parameter updates of VQAs over multiple iterations on the classical side, dramatically reducing quantum resource costs. Through systematic numerical experiments, we demonstrate that our method achieves up to a 30x speedup compared to conventional methods and reduces quantum resource costs by as much as 90\% for tasks involving up to 40 qubits, including ground state preparation of different quantum systems, while maintaining competitive accuracy. Our approach complements existing techniques aimed at improving the efficiency of VQAs and further strengthens their potential for practical applications.