Concepts de base
This paper introduces a new optimization model and symmetry-breaking constraints to efficiently design minimum-cost quantum circuits using Multiple-Control Toffoli (MCT) gates.
Résumé
The paper presents a new optimization model for designing minimum-cost quantum circuits using Multiple-Control Toffoli (MCT) gates. The key contributions are:
- The paper introduces a new optimization model and new symmetry-breaking constraints for the MCT quantum circuit design problem.
- The new model allows both Constraint Programming (CP) and Mixed Integer Programming (MIP) solvers to significantly improve solving time, with up to two orders of magnitude speedup when the CP solver is used.
- Experiments with up to seven qubits and using up to 15 quantum gates result in several new best-known circuits for well-known benchmarks.
- An extensive comparison with other approaches shows that optimization models may require more time but can provide superior circuits with guaranteed optimality.
The paper first provides the necessary terminology and problem description. It then introduces the new optimization model, which uses network flows to model the state transitions caused by the quantum circuit. Symmetry-breaking constraints are also presented to further improve the solving time.
Computational experiments are conducted on well-known benchmarks from RevLib. The results demonstrate the significant performance improvements of the new model compared to prior work, especially when using the CP solver. The new model is able to solve all instances with up to seven gates, and finds several new best-known circuits for larger instances up to 15 gates. The benefits of the symmetry-breaking constraints are also highlighted.
Finally, a comparative analysis is provided that shows the new optimization-based approach outperforms various heuristic and exact methods from the literature in terms of solution quality, while still requiring more computation time.
Stats
The number of qubits used in the circuits ranges from 3 to 7.
The number of quantum gates in the circuits ranges from 6 to 15.
Citations
"This paper provides an introduction to the MCT quantum circuit design problem for reversible Boolean functions without assuming a prior background in quantum computing."
"The new model allows both CP and MIP solvers to significantly improve solving time, with up to two orders of magnitude speedup when the CP solver is used."
"Experiments with up to seven qubits and using up to 15 quantum gates result in several new best-known circuits for well-known benchmarks."