Enumerating Optimal Quantum Circuits using Spectral Classification

This work targets fault-tolerant quantum computing and focuses on the problem of mapping reversible circuits into the Clifford+T quantum gate library. We present an automatically-generated database containing minimal-cost quantum circuits for Boolean functions up to 5 inputs. The database contains three circuits for each spectral-equivalent class representative, which are respectively optimized for the T-count, the T-depth, and the number of qubits. We show that any Boolean function can be derived from the implementation of its class representative without increasing any of the stated cost functions.