Quantum search degeneration under amplitude noise in queries to the oracle

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 oraclebox 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 variations 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 the value of one half. We also study trade-off relations between quantum coherence and the success probability in the presence of amplitude noise.

Complementarity between Success Probability and Coherence in Grover Search Algorithm

“…Soon after GSA was proposed, scientists began to study the performance of GSA under different noisy environments [33][34][35][36][37][38][39][40][41][42][43][44][45][46]. In [40,47], Rastegin et al showed the trade-off between the success probability and coherence in GSA with collective phase flip and amplitude damping noises on Oracles.…”