The Impact of Logical Errors on Quantum Algorithms

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.