NISQ circuit compilation is the travelling salesman problem on a torus

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