Optimized Qubit Routing for Commuting Gates via Integer Programming

TL;DR

This paper introduces an optimal integer programming-based method for qubit routing of commuting gates, improving quantum circuit compilation by providing optimal solutions and bounds.

Contribution

It presents a novel two-step integer programming approach for qubit routing, including proofs of NP-hardness and bounds, outperforming heuristics in quality and exact methods in runtime.

Findings

Outperforms existing heuristics in solution quality

Provides exact solutions with guaranteed optimality

Develops generalized polytope descriptions for broader applications

Abstract

Quantum computers promise to outperform their classical counterparts at certain tasks. However, existing quantum devices are error-prone and restricted in size. Thus, effective compilation methods are crucial to exploit limited quantum resources. In this work, we address the problem of qubit routing for commuting gates, which arises, for example, during the compilation of the well-known Quantum Approximate Optimization Algorithm. We propose a two-step decomposition approach based on integer programming, which is guaranteed to return an optimal solution. To justify the use of integer programming, we prove NP-hardness of the underlying optimization problem. Furthermore, we derive asymptotic upper and lower bounds on the quality of a solution. We develop several integer programming models and derive linear descriptions of related polytopes, which generalize to applications beyond this work. Finally, we conduct a computational study showing that our approach outperforms existing heuristics in terms of quality and exact methods in terms of runtime.