Compact Quantum Circuits for Autosymmetric and Dimension Reducible Functions

A quantum oracle is a reversible quantum subroutine that implements a classical Boolean function within a quantum algorithm. Classical synthesis methods for quantum oracles typically involve two steps: reversible logic synthesis and quantum compilation. In the reversible logic synthesis phase, producing a compact reversible circuit is crucial to minimizing the quantum cost of the final quantum circuit. In this paper, we investigate Boolean functions that simultaneously exhibit two distinct XOR-based regularities: autosymmetry and D-reducibility. These regularities can be effectively utilized for efficient reversible circuit synthesis of Boolean functions. In particular, we propose and implement a new method for the quantum synthesis of autosymmetric and D-reducible Boolean functions. The experimental results demonstrate the effectiveness of our approach on the considered benchmarks, showing reductions in T-count and CNOT-count after Clifford+T quantum compilation.