Noise tolerance via reinforcement in the quantum search problem

TL;DR

Reinforcement dramatically reduces the quantum search computation time from square root to logarithmic scale, significantly increasing noise tolerance and success probability in noisy quantum systems.

Contribution

This work demonstrates that reinforcement can exponentially improve quantum search efficiency and noise resilience, a novel approach in quantum algorithm error mitigation.

Findings

Reinforcement reduces quantum search time from √D to ln D

Reinforcement increases noise threshold exponentially

Success probability and scaling improve with reinforcement

Abstract

We find that reinforcement exponentially reduces computation time of the quantum search problem from $\sqrt{D}$ to $\ln D$ in a $D$-dimensional system. Therefor, a reinforced quantum search is expected to exhibit an exponentially larger noise threshold compared to a standard search algorithm in a noisy environment. We use numerical simulations to characterize the level of noise tolerance via reinforcement in the presence of both coherent and incoherent noise, considering a system of $N$ qubits and a single $D$-level (qudit) system. Our results show that reinforcement significantly enhances the algorithm's success probability and improves the scaling of its computation time with system size. These findings indicate that reinforcement offers a promising strategy for error mitigation, especially when a precise noise model is unavailable.