Optimal Hadamard gate count for Clifford$+T$ synthesis of Pauli rotations sequences

• URL: http://arxiv.org/abs/2302.07040v3
• Date: Sat, 24 Feb 2024 13:43:10 GMT
• Title: Optimal Hadamard gate count for Clifford$+T$ synthesis of Pauli rotations sequences
• Authors: Vivien Vandaele, Simon Martiel, Simon Perdrix, Christophe Vuillot
• Abstract summary: We propose an algorithm for synthesizing a sequence of $pi/4$ Pauli rotations with a minimal number of Hadamard gates. We present an algorithm which optimally minimizes the number of Hadamard gates lying between the first and the last $T$ gate of the circuit.
• Score: 4.423586186569902
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Clifford$+T$ gate set is commonly used to perform universal quantum computation. In such setup the $T$ gate is typically much more expensive to implement in a fault-tolerant way than Clifford gates. To improve the feasibility of fault-tolerant quantum computing it is then crucial to minimize the number of $T$ gates. Many algorithms, yielding effective results, have been designed to address this problem. It has been demonstrated that performing a pre-processing step consisting of reducing the number of Hadamard gates in the circuit can help to exploit the full potential of these algorithms and thereby lead to a substantial $T$-count reduction. Moreover, minimizing the number of Hadamard gates also restrains the number of additional qubits and operations resulting from the gadgetization of Hadamard gates, a procedure used by some compilers to further reduce the number of $T$ gates. In this work we tackle the Hadamard gate reduction problem, and propose an algorithm for synthesizing a sequence of $\pi/4$ Pauli rotations with a minimal number of Hadamard gates. Based on this result, we present an algorithm which optimally minimizes the number of Hadamard gates lying between the first and the last $T$ gate of the circuit.

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