Improving the performance of quantum approximate optimization for preparing non-trivial quantum states without translational symmetry

TL;DR

This paper investigates how translational symmetry affects QAOA performance in preparing complex quantum states and introduces a generalized method to improve efficiency, enabling high-fidelity GHZ state generation on non-symmetric systems.

Contribution

It proposes a parameterized resource Hamiltonian-enhanced QAOA and a low-depth circuit design for non-translationally invariant systems, improving quantum state preparation.

Findings

QAOA performance decreases without translational symmetry.

PRH-QAOA improves efficiency and fidelity.

Successful design of GHZ state generation circuit.

Abstract

The variational preparation of complex quantum states using the quantum approximate optimization algorithm (QAOA) is of fundamental interest, and becomes a promising application of quantum computers. Here, we systematically study the performance of QAOA for preparing ground states of target Hamiltonians near the critical points of their quantum phase transitions, and generating Greenberger-Horne-Zeilinger (GHZ) states. We reveal that the performance of QAOA is related to the translational invariance of the target Hamiltonian: Without the translational symmetry, for instance due to the open boundary condition (OBC) or randomness in the system, the QAOA becomes less efficient. We then propose a generalized QAOA assisted by the parameterized resource Hamiltonian (PRH-QAOA), to achieve a better performance. In addition, based on the PRH-QAOA, we design a low-depth quantum circuit beyond one-dimensional geometry, to generate GHZ states with perfect fidelity. The experimental realization of the proposed scheme for generating GHZ states on Rydberg-dressed atoms is discussed. Our work paves the way for performing QAOA on programmable quantum processors without translational symmetry, especially for recently developed two-dimensional quantum processors with OBC.