Designing exceptional-point-based graphs yielding topologically guaranteed quantum search

TL;DR

This paper introduces a novel quantum walk design based on exceptional points that guarantees efficient quantum search with topological robustness, outperforming classical and typical quantum walks.

Contribution

It presents a method to construct quantum walks with eigenvalue coalescence at exceptional points, ensuring bounded-time guaranteed search success and linking it to topological invariants.

Findings

Guaranteed quantum search success in bounded time

Connection between exceptional points and topological winding number

Relation to massless Dirac particle dynamics

Abstract

Quantum walks underlie an important class of quantum computing algorithms, and represent promising approaches in various simulations and practical applications. Here we design stroboscopically monitored quantum walks and their subsequent graphs that can naturally boost target searches. We show how to construct walks with the property that all the eigenvalues of the non-Hermitian survival operator, describing the mixed effects of unitary dynamics and the back-action of measurement, coalesce to zero, corresponding to an exceptional point whose degree is the size of the system. Generally, the resulting search is guaranteed to succeed in a bounded time for any initial condition, which is faster than classical random walks or quantum walks on typical graphs. We then show how this efficient quantum search is related to a quantized topological winding number and further discuss the connection of the problem to an effective massless Dirac particle.