Quantum phase estimation in presence of glassy disorder

TL;DR

This paper studies how glassy disorder in circuit elements affects the success probability of quantum phase estimation, showing that the probability depends on disorder mean and strength, with implications for precision and robustness.

Contribution

It demonstrates that success probability depends only on disorder parameters in large circuits and analyzes the effects of different disorder distributions on quantum phase estimation.

Findings

Success probability depends on disorder mean and strength, not type.

Increasing auxiliary qubits improves phase precision despite disorder.

Identifies a transition from concave to convex probability dependence on disorder strength.

Abstract

We investigate the response to noise, in the form of glassy disorder present in circuit elements, in the success probability of the quantum phase estimation algorithm, a subroutine used to determine the eigenvalue - a phase - corresponding to an eigenvector of a unitary gate. We prove that when a large number of auxiliary qubits are involved in the circuit, the probability does not depend on the actual type of disorder but only on the mean and strength of the disorder. For further analysis, we consider three types of disorder distributions: Haar-uniform with a circular cut-off, Haar-uniform with an elliptical or squeezed cut-off, and spherical normal. There is generally a depreciation of the disorder-averaged success probability in response to the disorder incorporation. Even in the presence of the disorder, increasing the number of auxiliary qubits helps to get a better precision of the phase, albeit to a lesser extent (probability) than that in the clean case. We find a concave to convex transition in the dependence of probability on the strength of disorder, and a log-log dependence is witnessed between the point of inflection and the number of auxiliary qubits used.