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Conference Papers Year : 2023

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

Simon Martiel
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Simon Perdrix

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 π/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-04318278 , version 1 (01-12-2023)

Identifiers

  • HAL Id : hal-04318278 , version 1

Cite

Vivien Vandaele, Simon Martiel, Simon Perdrix, Christophe Vuillot. Optimal Hadamard gate count for Clifford+T synthesis of Pauli rotations sequences. TQC 2023: 18th Theory of Quantum Computation, Communication and Cryptography, Jul 2023, Aveiro, Portugal. ⟨hal-04318278⟩
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