Quantum Approximate Optimization Algorithm with Sparsified Phase Operator

TL;DR

This paper introduces a sparsification strategy for QAOA that reduces resource requirements by using an alternative phase operator, maintaining performance if the ground state is preserved, and compares it with classical graph sparsification methods.

Contribution

The paper proposes a novel sparsification approach for QAOA's phase operator, reducing gate complexity while preserving approximation quality under certain conditions.

Findings

Sparsified phase operators can replace the original in QAOA without losing ground state fidelity.

Better alignment of the low energy subspace improves QAOA performance.

The proposed sparsification method outperforms some classical graph sparsification techniques.

Abstract

The Quantum Approximate Optimization Algorithm (QAOA) is a promising candidate algorithm for demonstrating quantum advantage in optimization using near-term quantum computers. However, QAOA has high requirements on gate fidelity due to the need to encode the objective function in the phase separating operator, requiring a large number of gates that potentially do not match the hardware connectivity. Using the MaxCut problem as the target, we demonstrate numerically that an easier way to implement an alternative phase operator can be used in lieu of the phase operator encoding the objective function, as long as the ground state is the same. We observe that if the ground state energy is not preserved, the approximation ratio obtained by QAOA with such phase separating operator is likely to decrease. Moreover, we show that a better alignment of the low energy subspace of the alternative operator leads to better performance. Leveraging these observations, we propose a sparsification strategy that reduces the resource requirements of QAOA. We also compare our sparsification strategy with some other classical graph sparsification methods, and demonstrate the efficacy of our approach.