Optimizing Multiple-Control Toffoli Quantum Circuit Design with Constraint Programming

TL;DR

This paper introduces a new optimization model with symmetry-breaking constraints for designing efficient multiple-control Toffoli quantum circuits, significantly improving solving time and achieving new best-known circuits for benchmarks.

Contribution

It presents a novel optimization model and symmetry-breaking constraints that enhance quantum circuit design efficiency and optimality guarantees compared to prior methods.

Findings

Up to 100x faster solving times with the new model

Achieved several new best-known quantum circuits for benchmarks

Optimization models can produce superior circuits despite longer computation times

Abstract

As quantum technology advances, the efficient design of quantum circuits has become an important area of research. This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions with the necessary background in quantum computing to comprehend the problem. While this is a well-studied problem, optimization models that minimize the true objective have only been explored recently. This paper introduces a new optimization model and symmetry-breaking constraints that improve solving time by up to two orders of magnitude compared to earlier work when a Constraint Programming solver is used. Experiments with up to seven qubits and using up to 15 quantum gates result in several new best-known circuits, obtained by any method, for well-known benchmarks. Several in-depth analyses are presented to validate the effectiveness of the symmetry-breaking constraints from multiple perspectives. Finally, an extensive comparison with other approaches shows that optimization models may require more time but can provide superior circuits with optimality guarantees.