The Impact of Logical Errors on Quantum Algorithms

TL;DR

This paper investigates how logical stochastic Pauli and Z-rotation errors affect the resilience of six canonical quantum algorithms, revealing that larger circuits are less resilient and that algorithms can be grouped based on their robustness to logical errors.

Contribution

It provides a comparative analysis of the resilience of six quantum algorithms to logical errors using Monte Carlo simulations and the quantum jump formalism.

Findings

Resilience decreases with more qubits and deeper circuits.

Algorithms split into two groups based on robustness.

Hamiltonian, Simon, and phase estimation are less resilient.

Abstract

In this work, we explore the impact of logical stochastic Pauli and coherent Z-rotation errors on quantum algorithms. We evaluate six canonical quantum algorithms' intrinsic resilience to the logical qubit and gate errors by performing the Monte Carlo simulations guided by the quantum jump formalism. The results suggest that the resilience of the studied quantum algorithms decreases as the number of qubits and the depth of the algorithms' circuits increase for both Pauli and Z-rotation errors. Our results also suggest that the algorithms split into two different groups in terms of algorithmic resilience. The evolution of Hamiltonian, Simon and the quantum phase estimation algorithms are less resilient to logical errors than Grover's search, Deutsch-Jozsa and Bernstein-Vazirani algorithms.