Optimization of Clifford Circuits

TL;DR

This paper presents methods for optimal synthesis and optimization of Clifford circuits, significantly reducing gate counts and extending to related quantum circuit classes, with applications in quantum error correction and benchmarking.

Contribution

It introduces new algorithms for optimal Clifford circuit synthesis, achieving reductions in gate counts and extending to larger and related circuit classes.

Findings

Optimal circuits for all Clifford operations with up to four inputs.

50% reduction in gate count through peep-hole optimization.

Extended methods to five-input Clifford circuits and related classes.

Abstract

We study optimal synthesis of Clifford circuits, and apply the results to peep-hole optimization of quantum circuits. We report optimal circuits for all Clifford operations with up to four inputs. We perform peep-hole optimization of Clifford circuits with up to 40 inputs found in the literature, and demonstrate the reduction in the number of gates by about 50%. We extend our methods to the optimal synthesis of linear reversible circuits, partially specified Clifford functions, 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.