Improved iterative quantum algorithm for ground-state preparation

TL;DR

This paper introduces an improved iterative quantum algorithm for ground-state preparation that optimizes a cost function via quantum gradient descent, demonstrating higher success probability and efficiency in numerical simulations.

Contribution

The paper presents a novel quantum algorithm that enhances ground-state preparation by optimizing a cost function with quantum gradient descent and efficient ancillary state generation.

Findings

Higher success probability per iteration

Measurement precision-independent sampling complexity

Lower gate complexity

Abstract

Finding the ground state of a Hamiltonian system is of great significance in many-body quantum physics and quantum chemistry. We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian. The crucial point is to optimize a cost function on the state space via the quantum gradient descent (QGD) implemented on quantum devices. We provide practical guideline on the selection of the learning rate in QGD by finding a fundamental upper bound and establishing a relationship between our algorithm and the first-order approximation of the imaginary time evolution. Furthermore, we adapt a variational quantum state preparation method as a subroutine to generate an ancillary state by utilizing only polylogarithmic quantum resources. The performance of our algorithm is demonstrated by numerical calculations of the deuteron molecule and Heisenberg model without and with noises. Compared with the existing algorithms, our approach has advantages including the higher success probability at each iteration, the measurement precision-independent sampling complexity, the lower gate complexity, and only quantum resources are required when the ancillary state is well prepared.