Projection theorem for discrete-time quantum walks

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00341403" target="_blank" >RIV/68407700:21340/20:00341403 - isvavai.cz</a>

Alternative codes found

RIV/68407700:21340/20:00345798

Result on the web

<a href="https://doi.org/10.4204/EPTCS.315.5" target="_blank" >https://doi.org/10.4204/EPTCS.315.5</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.4204/EPTCS.315.5" target="_blank" >10.4204/EPTCS.315.5</a>

Result language

angličtina

Original language name

Projection theorem for discrete-time quantum walks

Original language description

We make and generalize the observation that summing of probability amplitudes of a discrete-time quantum walk over partitions of the walking graph consistent with the step operator results in a unitary evolution on the reduced graph which is also a quantum walk. Since the effective walking graph of the projected walk is not necessarily simpler than the original, this may bring new insights into the dynamics of some kinds of quantum walks using known results from thoroughly studied cases like Euclidean lattices. We use abstract treatment of the walking space and walker displacements in aim for a generality of the presented statements. Using this approach we also identify some pathological cases in which the projection mapping breaks down. For walks on lattices, the operation typically results in quantum walks with hyper-dimensional coin spaces. Such walks can, conversely, be viewed as projections of walks on inaccessible, larger spaces, and their properties can be inferred from the parental walk. We show that this is is the case for a lazy quantum walk, a walk with large coherent jumps and a walk on a circle with a twisted boundary condition. We also discuss the relation of this theory to the time-multiplexing optical implementations of quantum walks. Moreover, this manifestly irreversible operation can, in some cases and with a minor adjustment, be undone, and a quantum walk can be reconstructed from a set of its projections.

Czech name

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Czech description

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Type

D - Article in proceedings

CEP classification

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OECD FORD branch

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Project

<a href="/en/project/GJ19-15744Y" target="_blank" >GJ19-15744Y: Quantum and classical random walks</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

Proceedings 9th International Conference on Quantum Simulation and Quantum Walks

ISBN

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ISSN

2075-2180

e-ISSN

2075-2180

Number of pages

11

Pages from-to

48-58

Publisher name

Open Publishing Association

Place of publication

Sydney

Event location

Marseille

Event date

Jan 20, 2020

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

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