Qubit Mapping and Routing via MaxSAT

TL;DR

This paper introduces a MAXSAT-based method for optimal qubit mapping and routing in noisy quantum computers, significantly improving scalability and reducing costs compared to existing approaches.

Contribution

It presents a novel MAXSAT reduction for QMR and two relaxation techniques that enhance scalability and efficiency of the solution.

Findings

Solves over 3x more benchmarks than previous methods

Achieves approximately 5x reduction in swap costs

Demonstrates the effectiveness of proposed relaxations

Abstract

Near-term quantum computers will operate in a noisy environment, without error correction. A critical problem for near-term quantum computing is laying out a logical circuit onto a physical device with limited connectivity between qubits. This is known as the qubit mapping and routing (QMR) problem, an intractable combinatorial problem. It is important to solve QMR as optimally as possible to reduce the amount of added noise, which may render a quantum computation useless. In this paper, we present a novel approach for optimally solving the QMR problem via a reduction to maximum satisfiability (MAXSAT). Additionally, we present two novel relaxation ideas that shrink the size of the MAXSAT constraints by exploiting the structure of a quantum circuit. Our thorough empirical evaluation demonstrates (1) the scalability of our approach compared to state-of-the-art optimal QMR techniques (solves more than 3x benchmarks with 40x speedup), (2) the significant cost reduction compared to state-of-the-art heuristic approaches (an average of ~5x swap reduction), and (3) the power of our proposed constraint relaxations.