Pseudo-Hermitian continuous-time quantum walks

TL;DR

This paper introduces a novel pseudo-Hermitian continuous-time quantum walk model with real spectra, enabling faster quantum transport on networks, which could enhance search algorithms.

Contribution

It presents a new type of quantum walk based on non-Hermitian Hamiltonians with real spectra and a method to compute probability distributions on networks.

Findings

Probability distribution increases on certain vertices compared to Hermitian case

Transport process is faster with the pseudo-Hermitian model

Potential applications in quantum search algorithms

Abstract

In this paper we present a model exhibiting a new type of continuous-time quantum walk (as a quantum mechanical transport process) on networks, which is described by a non-Hermitian Hamiltonian possessing a real spectrum. We call it pseudo-Hermitian continuous-time quantum walk. We introduce a method to obtain the probability distribution of walk on any vertex and then study a specific system. We observe that the probability distribution on certain vertices increases compared to that of the Hermitian case. This formalism makes the transport process faster and can be useful for search algorithms.