Projection theorem for discrete-time quantum walks

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21340/20:00345798

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Projection theorem for discrete-time quantum walks

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Projection theorem for discrete-time quantum walks

Popis výsledku anglicky

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.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GJ19-15744Y" target="_blank" >GJ19-15744Y: Kvantové a klasické náhodné procházky</a><br>

Návaznosti

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

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings 9th International Conference on Quantum Simulation and Quantum Walks

ISBN

—

ISSN

2075-2180

e-ISSN

2075-2180

Počet stran výsledku

11

Strana od-do

48-58

Název nakladatele

Open Publishing Association

Místo vydání

Sydney

Místo konání akce

Marseille

Datum konání akce

20. 1. 2020

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

—