Imaginary Hamiltonian variational ansatz for the Schwinger model and combinatorial optimization problems

Abstract

Variational quantum algorithms hold promise for efficiently solving combinatorial optimization problems that are difficult to solve classically on near-term quantum devices. The commonly used quantum approximate optimization algorithm (QAOA) suffers from adiabatic bottlenecks, leading to deep quantum circuits or longer evolution time. In contrast, imaginary time evolution algorithm often requires a constant evolution time. In this work, we propose the imaginary Hamiltonian variational ansatz (iHVA) to the ground state preparation of the Schwinger model and solve the MaxCut problem. This variational ansatz is inspired by the quantum imaginary time evolution algorithm. We introduce a tree arrangement of the parametrized quantum gates, enabling the exact solution of the MaxCut problem for any tree graphs. For randomly generated regular graphs, we numerically demonstrate that the MaxCut problem can be exactly solved using iHVA with a constant number of rounds. In contrast, QAOA requires the number of rounds that increases with system size, and the classically near-optimal Goemans-Williamson algorithm often yields only approximate solutions. We validate our algorithm’s advantage over QAOA through hardware experiments on a graph with 67 nodes.

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