Multi-angle Quantum Approximate Optimization Algorithm

TL;DR

This paper introduces a multi-angle ansatz for QAOA that reduces circuit depth and enhances approximation ratios, making it more suitable for near-term quantum devices by optimizing parameters efficiently.

Contribution

The authors propose a multi-angle ansatz for QAOA that increases classical parameters to improve performance while reducing circuit depth, demonstrating significant improvements over traditional QAOA.

Findings

33% increase in approximation ratio for MaxCut instances

Comparable performance with fewer layers, reducing circuit complexity

Higher approximation ratios on larger graphs at same depth

Abstract

The quantum approximate optimization algorithm (QAOA) generates an approximate solution to combinatorial optimization problems using a variational ansatz circuit defined by parameterized layers of quantum evolution. In theory, the approximation improves with increasing ansatz depth but gate noise and circuit complexity undermine performance in practice. Here, we introduce a multi-angle ansatz for QAOA that reduces circuit depth and improves the approximation ratio by increasing the number of classical parameters. Even though the number of parameters increases, our results indicate that good parameters can be found in polynomial time. This new ansatz gives a 33\% increase in the approximation ratio for an infinite family of MaxCut instances over QAOA. The optimal performance is lower bounded by the conventional ansatz, and we present empirical results for graphs on eight vertices that one layer of the multi-angle anstaz is comparable to three layers of the traditional ansatz on MaxCut problems. Similarly, multi-angle QAOA yields a higher approximation ratio than QAOA at the same depth on a collection of MaxCut instances on fifty and one-hundred vertex graphs. Many of the optimized parameters are found to be zero, so their associated gates can be removed from the circuit, further decreasing the circuit depth. These results indicate that multi-angle QAOA requires shallower circuits to solve problems than QAOA, making it more viable for near-term intermediate-scale quantum devices.