T Count as a Numerically Solvable Minimization Problem

2026-03-26

AI Summary

This work addresses the problem of synthesizing quantum circuits for a given unitary operator with the minimal number of T gates. It introduces, for the first time, a formulation of the minimal-T-count synthesis problem as a continuous optimization problem amenable to numerical solution, combined with a binary search strategy to efficiently approximate the optimal T count. To enhance scalability, the approach further incorporates a circuit partitioning technique that substantially extends the range of solvable instances. The method not only reproduces known optimal T counts for small-scale circuits but also surpasses existing limits on circuit size that can be practically optimized, thereby offering a promising new pathway toward the efficient compilation of large-scale quantum circuits.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

Abstract

We present a formulation of the problem of finding the smallest T -Count circuit that implements a given unitary as a binary search over a sequence of continuous minimization problems, and demonstrate that these problems are numerically solvable in practice. We reproduce best-known results for synthesis of circuits with a small number of qubits, and push the bounds of the largest circuits that can be solved for in this way. Additionally, we show that circuit partitioning can be used to adapt this technique to be used to optimize the T -Count of circuits with large numbers of qubits by breaking the circuit into a series of smaller sub-circuits that can be optimized independently.

Problem

• T-Count
• quantum circuit synthesis
• unitary implementation
• circuit optimization

Innovation

• T-Count
• numerical optimization
• quantum circuit synthesis
• circuit partitioning
• binary search