Improved variational quantum eigensolver via quasi-dynamical evolution

TL;DR

This paper introduces an enhanced variational quantum eigensolver (VQE) that incorporates a quasi-dynamical evolution inspired by quantum annealing, improving ground state energy estimation on near-term quantum devices and scaling towards quantum advantage.

Contribution

It proposes a novel heuristic supplementing VQE with quasi-dynamical evolution, enabling efficient initial state preparation and better scaling for larger quantum systems.

Findings

Avoids barren plateaus and local minima

Works with low-depth circuits

Enables estimation beyond 50 qubits

Abstract

The variational quantum eigensolver (VQE) is a hybrid quantum-classical algorithm designed for current and near-term quantum devices. Despite its initial success, there is a lack of understanding involving several of its key aspects. There are problems with VQE that forbid a favourable scaling towards quantum advantage. In order to alleviate the problems, we propose and extensively test a quantum annealing inspired heuristic that supplements VQE. The improved VQE enables an efficient initial state preparation mechanism, in a recursive manner, for a quasi-dynamical unitary evolution. We conduct an in-depth scaling analysis of finding the ground state energies with increasing lattice sizes of the Heisenberg model, employing simulations of up to $40$ qubits that manipulate the complete state vector. For the current devices, we further propose a benchmarking toolkit using a mean-field model and test it on IBM Q devices. The improved VQE avoids barren plateaus, exits local minima, and works with low-depth circuits. Realistic gate execution times estimate a longer computational time to complete the same computation on a fully functional error-free quantum computer than on a quantum computer emulator implemented on a classical computer. However, our proposal can be expected to help accurate estimations of the ground state energies beyond $50$ qubits when the complete state vector can no longer be stored on a classical computer, thus enabling quantum advantage.