Analytical Error Analysis of Clifford Gates by the Fault-Path Tracer Method

TL;DR

This paper introduces a fault-path tracing method to analytically estimate the success probability of Clifford-based quantum protocols with Pauli errors, enabling precise analysis of complex quantum circuits.

Contribution

It extends the fault-point formalism to a broader class of quantum protocols, providing an efficient way to compute success probabilities and output distributions.

Findings

Accurately estimates success probabilities of quantum protocols with Clifford gates.

Identifies circuit structures enabling efficient exact calculations.

Validates the method against Monte Carlo simulations for specific algorithms.

Abstract

We estimate the success probability of quantum protocols composed of Clifford operations in the presence of Pauli errors. Our method is derived from the fault-point formalism previously used to determine the success rate of low-distance error correction codes. Here we apply it to a wider range of quantum protocols and identify circuit structures that allow for efficient calculation of the exact success probability and even the final distribution of output states. As examples, we apply our method to the Bernstein-Vazirani algorithm and the Steane [[7,1,3]] quantum error correction code and compare the results to Monte Carlo simulations.