A New Optimization Model for Multiple-Control Toffoli Quantum Circuit Design

2024-04-22

International Conference on Principles and Practice of Constraint Programming

AI Summary

Synthesis of reversible Boolean functions as multi-controlled Toffoli (MCT) quantum circuits, with the objective of minimizing the actual gate count under physical constraints. Method: We propose the first end-to-end integer optimization model that directly minimizes the number of physical quantum gates. The model integrates constraint programming (CP), integer nonlinear modeling, symmetry analysis, and custom symmetry-breaking constraints to drastically improve computational efficiency. Contribution/Results: Our approach achieves up to two orders of magnitude speedup over prior methods. For 7-qubit benchmarks with at most 15 gates, it delivers the first provably optimal solutions for multiple classical benchmarks, establishing new records for minimal MCT circuits. Unlike heuristic approaches, our method provides mathematically verifiable optimality guarantees and yields strictly smaller circuits. The key innovation lies in embedding the physical gate-count objective into a compact, rigorous optimization framework while systematically exploiting symmetries for pruning—thereby unifying theoretical soundness with computational tractability.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Quantum Machine Learning

Application Category

• Security and Privacy: Large-scale security measurements
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

As quantum technology is advancing, 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 without assuming a prior background in quantum computing. 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. Finally, an extensive comparison with other approaches shows that optimization models may require more time but can provide superior circuits with optimality guarantees.

Problem

• Optimize MCT quantum circuit design for reversible Boolean functions
• Improve solving time with new optimization model and symmetry-breaking constraints
• Achieve superior circuits with optimality guarantees compared to other approaches

Innovation

• Constraint Programming for quantum circuit optimization
• Symmetry-breaking constraints improve solving speed
• Optimality guarantees for superior quantum circuits