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

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.

References added. Modification of introduction to remove an erroneous "intractable"

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Cited by in corpus (7)

• Errors and pseudo-thresholds for incoherent and coherent noise
• Fault Tolerance with Bare Ancillae for a [[7,1,3]] Code
• Controlling error orientation to improve quantum algorithm success rates
• Propagation of generalized Pauli errors in qudit Clifford circuits
• Imperfect quantum networks with tailored resource states
• Improved performance of the Bacon-Shor code with Steane's syndrome extraction method
• Comparison of spin-qubit architectures for quantum error-correcting codes