Quantum search degeneration under amplitude noise in queries to the oracle

TL;DR

This paper investigates how amplitude damping noise in quantum oracle queries affects the success probability of quantum search algorithms, revealing significant degradation even with minor errors and exploring coherence-success trade-offs.

Contribution

It introduces a simple model for amplitude damping noise in quantum search and analyzes its impact on success probability and quantum coherence.

Findings

Success probability drops to near 50% with small amplitude errors

Amplitude damping significantly degrades quantum search performance

Trade-offs between quantum coherence and success probability are identified

Abstract

We examine how amplitude noise in queries to the oracle degrades a performance of quantum search algorithm. The Grover search and similar techniques are widely used in various quantum algorithms, including cases where rival parties are fighting over confidential data. Hence, the oracle-box wires become the subject of competing activity with an alteration of their normal functioning. Of course, many kinds of errors could arise in this way. Possible influence of dephasing on quantum search was already addressed in the literature. Amplitude damping is another type of errors that should be analyzed first. To study the problem, we introduce a simple model of collective distortions with the use of amplitude damping channel. All the quantities of interest should be considered as functions of the number of Grover's iterations. In particular, we investigate the success probability with respect to the parameter that characterizes the level of amplitude errors. The success probability degrades significantly even if the error amount is not essential. Namely, this probability soon enough reduces to a value close to one half. We also study trade-off relations between quantum coherence and the success probability in the presence of amplitude noise.