Symmetry enhanced variational quantum spin eigensolver

TL;DR

This paper enhances the variational quantum eigensolver by exploiting Hamiltonian symmetries, significantly improving the efficiency of excited state simulations through two novel symmetry integration methods.

Contribution

It introduces two symmetry-based methods for VQE, including a hybrid approach, to improve excited state calculations without complex circuit design.

Findings

Hardware symmetry preserving method outperforms the second approach.

Hybrid symmetry method balances circuit complexity and symmetry benefits.

Symmetry exploitation significantly reduces resource demands for excited states.

Abstract

The variational quantum-classical algorithms are the most promising approach for achieving quantum advantage on near-term quantum simulators. Among these methods, the variational quantum eigensolver has attracted a lot of attention in recent years. While it is very effective for simulating the ground state of many-body systems, its generalization to excited states becomes very resource demanding. Here, we show that this issue can significantly be improved by exploiting the symmetries of the Hamiltonian. The improvement is even more effective for higher energy eigenstates. We introduce two methods for incorporating the symmetries. In the first approach, called hardware symmetry preserving, all the symmetries are included in the design of the circuit. In the second approach, the cost function is updated to include the symmetries. The hardware symmetry preserving approach indeed outperforms the second approach. However, integrating all symmetries in the design of the circuit could be extremely challenging. Therefore, we introduce hybrid symmetry preserving method in which symmetries are divided between the circuit and the classical cost function. This allows to harness the advantage of symmetries while preventing sophisticated circuit design.