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arXiv · 2307.10324

Applicability of Measurement-based Quantum Computation towards Physically-driven Variational Quantum Eigensolver

Zheng Qin·Xiufan Li·Yang Zhou·Shikun Zhang·Rui Li·Chunxiao Du·Zhisong Xiao
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Abstract

Variational quantum algorithms are considered one of the most promising methods for obtaining near-term quantum advantages; however, most of these algorithms are only expressed in the conventional quantum circuit scheme. The roadblock to developing quantum algorithms with the measurement-based quantum computation (MBQC) scheme is resource cost. Recently, we discovered that the realization of multi-qubit rotation operations requires a constant number of single-qubit measurements with the MBQC scheme, providing a potential advantage in terms of resource cost. The structure of the Hamiltonian variational ansatz (HVA) aligns well with this characteristic. Thus, we propose an efficient measurement-based quantum algorithm for quantum many-body system simulation tasks, called measurement-based Hamiltonian variational ansatz (MBHVA). We then demonstrate the effectiveness, efficiency, and advantages of the two-dimensional Heisenberg model and the Fermi-Hubbard chain. Numerical experiments show that MBHVA is expected to reduce resource overhead compared to quantum circuits, especially in the presence of large multi-qubit rotation operations. Furthermore, when compared to Measurement-based Hardware Efficient Ansatz (MBHEA), MBHVA also demonstrates superior performance. We conclude that the MBQC scheme is potentially feasible for achieving near-term quantum advantages in terms of both resource efficiency and error mitigation, particularly for photonic platforms.

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Zheng Qin, Xiufan Li, Yang Zhou, Shikun Zhang, Rui Li, Chunxiao Du, Zhisong Xiao. 2023-07-19. Applicability of Measurement-based Quantum Computation towards Physically-driven Variational Quantum Eigensolver. https://doi.org/10.1088/1367-2630%2Fad634a

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