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Journal Articles ACM Transactions on Quantum Computing Year : 2023

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

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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Dates and versions

hal-03991154 , version 1 (15-02-2023)
hal-03991154 , version 2 (09-04-2023)
hal-03991154 , version 3 (24-02-2024)

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Cite

Vivien Vandaele, Simon Martiel, Simon Perdrix, Christophe Vuillot. Optimal Hadamard gate count for Clifford+T synthesis of Pauli rotations sequences. ACM Transactions on Quantum Computing, 2023, ⟨10.1145/3639062⟩. ⟨hal-03991154v3⟩
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