Practical implementation of Toffoli-based qubit rotation

TL;DR

This paper evaluates a Toffoli-based single-qubit rotation algorithm on real and simulated quantum computers, analyzing its performance under noise and proposing its use as a benchmark for quantum hardware.

Contribution

It demonstrates the practical implementation of a Toffoli-based rotation algorithm and assesses its robustness, providing a potential benchmark for quantum processors.

Findings

Algorithm performs well up to 1% noise levels

Results match simulated noise models and live runs

Proposed as a low-complexity benchmark for quantum hardware

Abstract

The Toffoli gate is an important universal quantum gate, and will alongside the Clifford gates be available in future fault-tolerant quantum computing hardware. Many quantum algorithms rely on performing arbitrarily small single-qubit rotations for their function, and these rotations may also be used to construct any unitary from a limited (but universal) gate set. How to carry out such rotations is then of significant interest. In this work, we evaluate the performance of a recently proposed single-qubit rotation algorithm using the Clifford plus Toffoli gate set by implementation of a one-shot version on both a real and a simulated quantum computer. We test the algorithm under various simulated noise levels using a per-qubit depolarizing error noise model and examine how the probabilities and process fidelities are affected. We then conduct live runs and find that the results reasonably match the simulated results. We also attempt to model the hardware noise by combining a number of noise models, matching the results to results of the live runs to approximate the hardware noise. Our results suggest that the algorithm will perform well for up to 1% noise, under the noise models we chose. We further posit the use of our algorithm as a benchmark for quantum processing units, given that it has a low complexity that is easy to fine-tune in small steps. We provide details for how to do this.