pyCTQW: A continuous-time quantum walk simulator on distributed memory computers

Izaac, Josh; Wang, Jingbo

doi:10.1016/j.cpc.2014.09.011

Cited by 18 publications

(10 citation statements)

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“…The wavefunction that evolves from an initial wavefunction satisfies

where |Ψ( z )〉 = ∑ j a j ( z )| j 〉, and | a j ( z )| 2 = |〈 j |Ψ( z )||〉 2 = P j ( z ), respectively. | a j ( z )| 2 or P j ( z ) is the probability of the walker ( 27 ) being found at waveguide j at the propagation length z . As shown in Fig.…”

Section: Resultsmentioning

confidence: 99%

Experimental two-dimensional quantum walk on a photonic chip

et al. 2018

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“…The wavefunction that evolves from an initial wavefunction satisfies

Section: Resultsmentioning

confidence: 99%

Experimental two-dimensional quantum walk on a photonic chip

et al. 2018

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“…In this paper, we construct a quantum Hash function (QHF) by subtly modifying the quantum walks (QW) model 5 6 7 8 9 10 11 12 13 and it can be used for the privacy amplification process of QKD systems with higher security by means of the physical principles of quantum mechanics. As a byproduct, QHF can also be used for pseudo-random number generation due to its inherent chaotic dynamics and further we propose a novel QHF-based image encryption algorithm.…”

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confidence: 99%

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption

Yang

et al. 2016

Sci Rep

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Quantum information and quantum computation have achieved a huge success during the last years. In this paper, we investigate the capability of quantum Hash function, which can be constructed by subtly modifying quantum walks, a famous quantum computation model. It is found that quantum Hash function can act as a hash function for the privacy amplification process of quantum key distribution systems with higher security. As a byproduct, quantum Hash function can also be used for pseudo-random number generation due to its inherent chaotic dynamics. Further we discuss the application of quantum Hash function to image encryption and propose a novel image encryption algorithm. Numerical simulations and performance comparisons show that quantum Hash function is eligible for privacy amplification in quantum key distribution, pseudo-random number generation and image encryption in terms of various hash tests and randomness tests. It extends the scope of application of quantum computation and quantum information.

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“…One possibility for a future version of QSWalk, therefore, would be to incorporate calls to a program using parallelized linear algebra libraries running in an HPC environment; an approach along these lines was used successfully in Ref. [23] to simulate phase-coherent quantum walks.…”

Section: Resultsmentioning

confidence: 99%

QSWalk: A Mathematica package for quantum stochastic walks on arbitrary graphs

Falloon

Rodriguez

Wang

2017

Computer Physics Communications

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We present a Mathematica package, QSWalk, to simulate the time evaluation of Quantum Stochastic Walks (QSWs) on arbitrary directed and weighted graphs. QSWs are a generalization of continuous time quantum walks that incorporate both coherent and incoherent dynamics and as such, include both quantum walks and classical random walks as special cases. The incoherent component allows for quantum walks along directed graph edges. The dynamics of QSWs are expressed using the Lindblad formalism, originally developed for open quantum systems, which frames the problem in the language of density matrices. For a QSW on a graph of N vertices, we have a sparse superoperator in an N 2 -dimensional space, which can be solved efficiently using the built-in MatrixExp function in Mathematica. We illustrate the use of the QSWalk package through several example case studies. Nature of problem:The QSWalk package provides a method for simulating quantum stochastic walks on arbitrary (directed/undirected, weighted/unweighted) graphs. Solution method:For an N -vertex graph, the solution of a quantum stochastic walk can be expressed as an N 2 ×N 2 sparse matrix exponential. The QSWalk package makes use of Mathematica's sparse linear algebra routines to solve this efficiently. Restrictions:The size of graphs that can be treated is constrained by available memory. Running time:Running time depends on the size of the graph and the propagation time of the walk.

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pyCTQW: A continuous-time quantum walk simulator on distributed memory computers

Cited by 18 publications

References 50 publications

Experimental two-dimensional quantum walk on a photonic chip

Experimental two-dimensional quantum walk on a photonic chip

Quantum Hash function and its application to privacy amplification in quantum key distribution, pseudo-random number generation and image encryption

QSWalk: A Mathematica package for quantum stochastic walks on arbitrary graphs

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