Quantum Circuit Optimization by Hadamard Gate Reduction

Abstract. Due to its fault-tolerant gates, the Clifford+T library con-sisting of Hadamard (denoted by H), T, and CNOT gates has attracted interest in the synthesis of quantum circuits. Since the implementation of T gates is expensive, recent research is aiming at minimizing the use of such gates. It has been shown that T-depth optimizations can be im-plemented efficiently for circuits consisting only of T and CNOT gates and that H gates impede the optimization significantly. In this paper, we investigate the role of H gates in reducing the T-count and T-depth for quantum circuits. To reduce the number of H gates, we propose several algorithms targeting different steps in the synthesis of reversible functions as quantum circuits. Experiments show the effect of H gate reductions on the costs for T-count and T-depth. Our approach yields a significant improvement of up to 88 % in the final T-depth compared to the best known T-depth optimization technique.