### Abstract

*n*

^{2}×

*n*

^{2}Lindblad super-operator from the eigendecomposition of the

*n*×

*n*graph Hamiltonian.

Original language | English |
---|---|

Number of pages | 8 |

Publication status | Published - 2016 |

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### Bibliographical note

http://arxiv.org/abs/1601.04691### Cite this

*Efficient computation of decoherent quantum walks through eigenvalue perturbation*.

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**Efficient computation of decoherent quantum walks through eigenvalue perturbation.** / Torsello, Andrea; Rossi, Luca.

Research output: Working paper › Technical report

TY - UNPB

T1 - Efficient computation of decoherent quantum walks through eigenvalue perturbation

AU - Torsello, Andrea

AU - Rossi, Luca

N1 - http://arxiv.org/abs/1601.04691

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

M3 - Technical report

BT - Efficient computation of decoherent quantum walks through eigenvalue perturbation

ER -