Modular Parity Quantum Approximate Optimization

TL;DR

This paper introduces a modular parallelization method for the Quantum Approximate Optimization Algorithm (QAOA) applied to parity-encoded spin models, enhancing performance and scalability by combining explicit and implicit constraint enforcement.

Contribution

It proposes a novel modular parallelization approach that partitions QAOA circuits into clusters, balancing performance and circuit depth for large-scale quantum optimization.

Findings

Improved QAOA performance with combined explicit and implicit constraint enforcement.

Scalable circuit partitioning method for large quantum systems.

Enhanced parallelization without increasing circuit depth.

Abstract

The parity transformation encodes spin models in the low-energy subspace of a larger Hilbert-space with constraints on a planar lattice. Applying the Quantum Approximate Optimization Algorithm (QAOA), the constraints can either be enforced explicitly, by energy penalties, or implicitly, by restricting the dynamics to the low-energy subspace via the driver Hamiltonian. While the explicit approach allows for parallelization with a system-size-independent circuit depth, the implicit approach shows better QAOA performance. Here we combine the two approaches in order to improve the QAOA performance while keeping the circuit parallelizable. In particular, we introduce a modular parallelization method that partitions the circuit into clusters of subcircuits with fixed maximal circuit depth, relevant for scaling up to large system sizes.