T Count as a Numerically Solvable Minimization Problem
This work addresses the optimization of quantum circuits for researchers in quantum computing, offering incremental improvements in scalability and efficiency.
The paper tackles the problem of finding the smallest T-count circuit for a given unitary by formulating it as a binary search over continuous minimization problems, demonstrating numerical solvability and reproducing best-known results for small qubit circuits while extending to larger ones through circuit partitioning.
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.