Spin systems dynamics and faults detection in threshold networks

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.

6 pages

References in corpus (9)

• Strengths and Weaknesses of Quantum Computing
• Quantum random walks - an introductory overview
• Perfect state transfer in quantum spin networks
• A Quantum Random Walk Search Algorithm
• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Quantum computers can search arbitrarily large databases by a single query
• Spatial search and the Dirac equation
• Searching via walking: How to find a marked subgraph of a graph using quantum walks
• State Transfer in Highly Connected Networks and a Quantum Babinet Principle

Cited by in corpus (6)

• Transport of Quantum Correlations across a spin chain
• Quantum walks on complex networks with connection instabilities and community structure
• Quantum state transfer between twins in weighted graphs
• Sedentariness in quantum walks
• Bounds on probability of state transfer with respect to readout time and edge weight
• Local subgraph structure can cause localization in continuous-time quantum walk