State-space gradient descent and metastability in quantum systems

TL;DR

This paper introduces a quantum algorithm inspired by ADAPT-VQE that efficiently finds ground or metastable states of quantum systems, avoiding barren plateaus and using experimentally accessible gradient and Hessian information.

Contribution

The proposed algorithm is the first to reliably produce ground or metastable states without suffering from barren plateaus, using local operations and experimental gradient/Hessian data.

Findings

Algorithm successfully finds ground or metastable states in simulations.

It avoids barren plateau issues common in variational quantum algorithms.

Numerical results demonstrate reliable state preparation in typical systems.

Abstract

We propose a quantum algorithm, inspired by ADAPT-VQE, to variationally prepare the ground state of a quantum Hamiltonian, with the desirable property that if it fails to find the ground state, it still yields a physically meaningful local-minimum state that oftentimes corresponds to a metastable state of the quantum system. At each iteration, our algorithm reduces the energy using a set of local physical operations. The operations to perform are chosen using gradient and Hessian information that can be efficiently extracted from experiments. We show that our algorithm does not suffer from the barren plateau problem, which is a significant issue in many variational quantum algorithms. We use numerical simulation to demonstrate that our method reliably produces either the true ground state or a physically meaningful metastable state in typical physical systems with such states.