Spin systems dynamics and faults detection in threshold networks

TL;DR

This paper explores quantum dynamics in threshold networks to develop an optimal quantum search algorithm, achieving quadratic speed-up over classical methods, but faces challenges in fault detection reliability.

Contribution

It introduces an analytic framework for quantum search in threshold networks and presents an optimal algorithm with quadratic speed-up, expanding quantum search applications.

Findings

Analytic formulas for success probability in quantum search.

Quadratic speed-up over classical search algorithms.

Fragility of fault detection in the quantum setting.

Abstract

We consider an agent on a fixed but arbitrary node of a known threshold network, with the task of detecting an unknown missing link/node. We obtain analytic formulas for the probability of success, when the agent's tool is the free evolution of a single excitation on an XX spin system paired with the network. We completely characterize the parameters allowing for an advantageous solution. From the results emerges an optimal (deterministic) algorithm for quantum search, therefore gaining a quadratic speed-up with respect to the optimal classical analogue, and in line with well-known results in quantum computation. When attempting to detect a faulty node, the chosen setting appears to be very fragile and the probability of success too small to be of any direct use.