Reducing the Depth of Linear Reversible Quantum Circuits

In quantum computing the decoherence time of the qubits determines the computation time available and this time is very limited when using current hardware. In this paper we minimize the execution time (the depth) for a class of circuits referred to as linear reversible circuits, which has many applications in quantum computing (e.g., stabilizer circuits, CNOT+T circuits, etc.). We propose a practical formulation of a divide and conquer algorithm that produces quantum circuits that are twice as shallow as those produced by existing algorithms. We improve the theoretical upper bound of the depth in the worst case for some range of qubits. We also propose greedy algorithms based on cost minimization to find more optimal circuits for small or simple operators. Overall, we manage to consistently reduce the total depth of a class of reversible functions, with up to 92% savings in an ancilla-free case and up to 99% when ancillary qubits are available.