Constraint programming models for depth-optimal qubit assignment and SWAP-based routing

TL;DR

This paper introduces constraint programming models for depth-optimal qubit assignment and routing in quantum circuits, demonstrating superior performance over existing ILP models in solution quality and runtime.

Contribution

It presents novel CP models for qubit routing, comparing their effectiveness against ILP models on various quantum device topologies.

Findings

CP models outperform ILP in solution quality

CP models have faster runtimes

Effective for linear and 2D grid topologies

Abstract

Due to the limited connectivity of gate model quantum devices, logical quantum circuits must be compiled to target hardware before they can be executed. Often, this process involves the insertion of SWAP gates into the logical circuit, usually increasing the depth of the circuit, achieved by solving a so-called qubit assignment and routing problem. Recently, a number of integer linear programming (ILP) models have been proposed for solving the qubit assignment and routing problem to proven optimality. These models encode the objective function and constraints of the problem, and leverage the use of automated solver technology to find hardware-compliant quantum circuits. In this work, we propose constraint programming (CP) models for this problem and compare their performance against ILP for circuit depth minimization for both linear and two-dimensional grid lattice device topologies on a set of randomly generated instances. Our empirical analysis indicates that the proposed CP approaches outperform the ILP models both in terms of solution quality and runtime.