Efficiently Solve the Max-cut Problem via a Quantum Qubit Rotation Algorithm

TL;DR

This paper introduces QQRA, a simple quantum algorithm for the max-cut problem that uses single-qubit rotations, offering high trainability and near-certain approximate solutions, outperforming some existing algorithms.

Contribution

The paper proposes QQRA, a novel quantum algorithm that simplifies circuit design for max-cut, improving trainability and solution accuracy compared to existing methods.

Findings

QQRA achieves near 100% probability of correct max-cut solutions.

QQRA outperforms the quantum approximate optimization algorithm.

QQRA compares favorably with the classical Goemans-Williamson algorithm.

Abstract

Optimizing parameterized quantum circuits promises efficient use of near-term quantum computers to achieve the potential quantum advantage. However, there is a notorious tradeoff between the expressibility and trainability of the parameter ansatz. We find that in combinatorial optimization problems, since the solutions are described by bit strings, one can trade the expressiveness of the ansatz for high trainability. To be specific, by focusing on the max-cut problem we introduce a simple yet efficient algorithm named Quantum Qubit Rotation Algorithm (QQRA). The quantum circuits are comprised with single-qubit rotation gates implementing on each qubit. The rotation angles of the gates can be trained free of barren plateaus. Thus, the approximate solution of the max-cut problem can be obtained with probability close to 1. To illustrate the effectiveness of QQRA, we compare it with the well known quantum approximate optimization algorithm and the classical Goemans-Williamson algorithm.