Quantum spatial search on graphs subject to dynamical noise

TL;DR

This paper investigates the robustness of quantum spatial search algorithms on graphs under dynamical noise, showing that certain graph topologies like the star graph maintain near-optimal performance despite noise.

Contribution

It demonstrates that quantum spatial search remains effective on complete and star graphs under dynamical noise, highlighting the star graph's suitability for noisy quantum walk implementations.

Findings

Fast noise slightly degrades performance

Slow noise significantly reduces success probability

Quadratic speed-up persists under certain noise conditions

Abstract

We address quantum spatial search on graphs and its implementation by continuous-time quantum walks in the presence of dynamical noise. In particular, we focus on search on the complete graph and on the star graph of order $N$, proving that also the latter is optimal in the computational limit $N \gg 1$, being nearly optimal also for small $N$. The noise is modeled by independent sources of random telegraph noise (RTN), dynamically perturbing the links of the graph. We observe two different behaviours depending on the switching rate of RTN: fast noise only slightly degrades performance, whereas slow noise is more detrimental and, in general, lowers the success probability. In particular, we still find a quadratic speed-up for the average running time of the algorithm, while for the star graph with external target node we observe a transition to classical scaling. We also address how the effects of noise depend on the order of the graphs, and discuss the role of the graph topology. Overall, our results suggest that realizations of quantum spatial search are possible with current technology, and also indicate the star graph as the perfect candidate for the implementation by noisy quantum walks, owing to its simple topology and nearly optimal performance also for just few nodes.