Efficient computation of decoherent quantum walks through eigenvalue perturbation

Torsello, Andrea and Rossi, Luca (2016). Efficient computation of decoherent quantum walks through eigenvalue perturbation. Technical Report. UNSPECIFIED.

Abstract

A number of recent studies have investigated the introduction of decoherence in quantum walks and the resulting transition to classical random walks. Interestingly,it has been shown that algorithmic properties of quantum walks with decoherence such as the spreading rate are sometimes better than their purely quantum counterparts. Not only quantum walks with decoherence provide a generalization of quantum walks that naturally encompasses both the quantum and classical case, but they also give rise to new and different probability distribution. The application of quantum walks with decoherence to large graphs is limited by the necessity of evolving state vector whose sizes quadratic in the number of nodes of the graph, as opposed to the linear state vector of the purely quantum (or classical) case. In this technical report,we show how to use perturbation theory to reduce the computational complexity of evolving a continuous-time quantum walk subject to decoherence. More specifically, given a graph over n nodes, we show how to approximate the eigendecomposition of the n2×n2 Lindblad super-operator from the eigendecomposition of the n×n graph Hamiltonian.

Divisions: Engineering & Applied Sciences
Engineering & Applied Sciences > Systems analytics research institute (SARI)
Additional Information: http://arxiv.org/abs/1601.04691
Full Text Link: http://arxiv.or ... 601.04691v1.pdf
Related URLs:
Published Date: 2016
Authors: Torsello, Andrea
Rossi, Luca ( 0000-0002-6116-9761)

Download

[img]

Version: Published Version


Export / Share Citation


Statistics

Additional statistics for this record