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arXiv:2209.12454 · Quantum Machine Intelligence

Shuffle-QUDIO: accelerate distributed VQE with trainability enhancement and measurement reduction

Yang Qian, Yuxuan Du, Dacheng Tao

Published May 24, 2024• 8 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1007/s42484-024-00167-y

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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 \varvecK\varvec{K}\varvecK K subproblems and allocates them to \varvecK\varvec{K}\varvecK 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) 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.
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.
Solving combinatorial optimization problems using variational quantum algorithms (VQAs) might be a promise application in the NISQ era. However, the limited trainability of VQAs could hinder their scalability to large problem sizes. In this paper, we improve the trainability of variational quantum eigensolver (VQE) by utilizing convex interpolation to solve portfolio optimization. Based on convex interpolation, the location of the ground state can be evaluated by learning the property of a small subset of basis states in the Hilbert space. This enlightens naturally the proposals of the strategies of close-to-solution initialization, regular cost function landscape, and recursive ansatz equilibrium partition. The successfully implementation of a 404040-qubit experiment using only 101010 superconducting qubits demonstrates the effectiveness of our proposals. Furthermore, the quantum inspiration has also spurred the development of a prototype greedy algorithm. Extensive numerical simulations indicate that the hybridization of VQE and greedy algorithms achieves a mutual complementarity, combining the advantages of both global and local optimization methods. Our proposals can be extended to improve the trainability for solving other large-scale combinatorial optimization problems that are widely used in real applications, paving the way to unleash quantum advantages of NISQ computers in the near future.
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Variational quantum eigensolver (VQE) is a promising algorithm suitable for near-term quantum computers. VQE aims to approximate solutions to exponentially-sized optimization problems by executing a polynomial number of quantum subproblems. However, the number of subproblems scales as N4for typical problems of interest-a daunting growth rate that poses a serious limitation for emerging applications such as quantum computational chemistry. We mitigate this issue by exploiting the simultaneous measurability of subproblems corresponding to commuting terms. Our technique transpiles VQE instances into a format optimized for simultaneous measurement, ultimately yielding 8-30x lower cost. Our work also encompasses a synthesis tool for compiling simultaneous measurement circuits with minimal overhead. We demonstrate experimental validation of our techniques by estimating the ground state energy of deuteron with a quantum computer. We also investigate the underlying statistics of simultaneous measurement and devise an adaptive strategy for mitigating harmful covariance terms.
The variational quantum eigensolver (VQE) is a hybrid algorithm that has the potential to provide a quantum advantage in practical chemistry problems that are currently intractable on classical computers. VQE trains parameterized quantum circuits using a classical optimizer to approximate the eigenvalues and eigenstates of a given Hamiltonian. However, VQE faces challenges in task-specific design and machine-specific architecture, particularly when running on noisy quantum devices. This can have a negative impact on its trainability, accuracy, and efficiency, resulting in noisy quantum data. We propose variational denoising, an unsupervised learning method that employs a parameterized quantum neural network to improve the solution of VQE by learning from noisy VQE outputs. Our approach can significantly decrease energy estimation errors and increase fidelities with ground states compared to noisy input data for the H2 , LiH, and BeH2 molecular Hamiltonians and the transverse field Ising model. Surprisingly, it only requires noisy data for training. Variational denoising can be integrated into quantum hardware, increasing its versatility as an end-to-end quantum processing for quantum data. Published by the American Physical Society 2024