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

TL;DR

This paper introduces a measurement-based quantum algorithm, MBHVA, that efficiently simulates quantum many-body systems, reducing resource costs and outperforming existing methods, especially in photonic quantum platforms.

Contribution

Proposes the MBHVA algorithm leveraging MBQC's advantages for resource-efficient quantum simulation of many-body systems.

Findings

MBHVA reduces resource overhead compared to quantum circuit methods.

MBHVA outperforms Measurement-based Hardware Efficient Ansatz (MBHEA).

Numerical results confirm effectiveness for 2D Heisenberg and Fermi-Hubbard models.

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.