Practical approximation of single-qubit unitaries by single-qubit quantum Clifford and T circuits

TL;DR

This paper introduces an algorithm that efficiently finds optimal single-qubit Clifford+T circuits approximating Z-rotations with extremely high precision, aiding scalable quantum algorithm implementation.

Contribution

The paper presents a novel algorithm and implementation for T-optimal approximation of single-qubit Z-rotations with high precision, improving quantum circuit design.

Findings

Handles approximation errors down to 10^{-15}

Provides publicly available implementation and experimental results

Achieves optimal circuit designs for scalable quantum algorithms

Abstract

We present an algorithm, along with its implementation that finds T-optimal approximations of single-qubit Z-rotations using quantum circuits consisting of Clifford and T gates. Our algorithm is capable of handling errors in approximation down to size $10^{-15}$, resulting in optimal single-qubit circuit designs required for implementation of scalable quantum algorithms. Our implementation along with the experimental results are available in the public domain.