We study synthesis of optimal Clifford circuits and apply the results to peephole optimization of quantum circuits. We report optimal circuits for all Clifford operations with up to four inputs. We perform peephole optimization of Clifford circuits with up to 40 inputs found in the literature, and demonstrate a reduction in the number of gates by about 50%. We extend our methods to the synthesis of optimal linear reversible circuits, partially specified Clifford unitaries, and optimal Clifford circuits with five inputs up to input-output permutation. The results find their application in randomized benchmarking protocols, quantum error correction, and quantum circuit optimization.

• Received 3 May 2013

DOI:https://doi.org/10.1103/PhysRevA.88.052307