NISQ circuit compilation is the travelling salesman problem on a torus

TL;DR

This paper models NISQ circuit compilation as a traveling salesman problem on a torus, leveraging the circular nature of quantum gate lists to optimize qubit allocation and gate scheduling.

Contribution

It introduces a novel torus-based model for quantum circuit compilation, connecting classical optimization techniques with quantum circuit design.

Findings

QCC landscape is a two-dimensional discrete torus.

Compilation can start from any gate due to circuit circularity.

The approach bridges classical automation and quantum optimization.

Abstract

Noisy, intermediate-scale quantum (NISQ) computers are expected to execute quantum circuits of up to a few hundred qubits. The circuits have to conform to NISQ architectural constraints regarding qubit allocation and the execution of multi-qubit gates. Quantum circuit compilation (QCC) takes a nonconforming circuit and outputs a compatible circuit. Can classical optimisation methods be used for QCC? Compilation is a known combinatorial problem shown to be solvable by two types of operations: 1) qubit allocation, and 2) gate scheduling. We show informally that the two operations form a discrete ring. The search landscape of QCC is a two dimensional discrete torus where vertices represent configurations of how circuit qubits are allocated to NISQ registers. Torus edges are weighted by the cost of scheduling circuit gates. The novelty of our approach uses the fact that a circuit's gate list is circular: compilation can start from any gate as long as all the gates will be processed, and the compiled circuit has the correct gate order. Our work bridges a theoretical and practical gap between classical circuit design automation and the emerging field of quantum circuit optimisation.