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.

References in corpus (21)

• Improved Simulation of Stabilizer Circuits
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Surface code quantum computing by lattice surgery
• Stim: a fast stabilizer circuit simulator
• Improved classical simulation of quantum circuits dominated by Clifford gates
• Classical simulation of commuting quantum computations implies collapse of the polynomial hierarchy
• Simulation of quantum circuits by low-rank stabilizer decompositions
• Polynomial-time T-depth Optimization of Clifford+T circuits via Matroid Partitioning
• Automated optimization of large quantum circuits with continuous parameters
• Reducing T-count with the ZX-calculus
• Quantum Measurements and Gates by Code Deformation
• On the CNOT-complexity of CNOT-PHASE circuits
• Shorter stabilizer circuits via Bruhat decomposition and quantum circuit transformations
• Simulating quantum circuits with ZX-calculus reduced stabiliser decompositions
• Improved upper bounds on the stabilizer rank of magic states
• T-count optimization and Reed-Muller codes
• Techniques to Reduce $\pi /4$-Parity-Phase Circuits, Motivated by the ZX Calculus
• Phase polynomials synthesis algorithms for NISQ architectures and beyond
• Relating Measurement Patterns to Circuits via Pauli Flow
• AND-gates in ZX-calculus: Spider Nest Identities and QBC-completeness
• Classical simulation of quantum circuits with partial and graphical stabiliser decompositions

Cited by in corpus (3)

• Lower T-count with faster algorithms
• Qsyn: A Developer-Friendly Quantum Circuit Synthesis Framework for NISQ Era and Beyond
• On the role of coherence for quantum computational advantage