Quantum Analogues of Markov Chains

Nayak, Ashwin; Richter, Peter C.; Szegedy, Márió

doi:10.1007/978-1-4939-2864-4_302

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Bounds On the Extended Hitting Time1

An Efficient Quantum Algorithm For the Torus1

Introduction1

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2016

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Cited by 1 publication

(3 citation statements)

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“…Lemma 1 (see e.g. [33,31,22]) The hitting time of a reversible ergodic Markov chain P with marked elements M is…”

Section: Bounds On the Extended Hitting Timementioning

confidence: 99%

“…A quantum walk is implemented similarly [33,32,31]. We first create some initial state |init from the state |π = v∈V √ π v |v , where π is the stationary distribution.…”

Section: An Efficient Quantum Algorithm For the Torusmentioning

confidence: 99%

“…Quantum walks have proven very successful in quantum computing, with applications in diverse settings such as communication complexity [1], element distinctness problems [3,8], testing group commutativity [24], and triangle finding [27,16]. Excellent surveys on quantum walks, their history and applications, include [2,19,32,36,31].…”

Section: Introductionmentioning

confidence: 99%

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Efficient quantum walk on the grid with multiple marked elements

Hoyer,

Komeili

2016

Preprint

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We give a quantum algorithm for finding a marked element on the grid when there are multiple marked elements. Our algorithm uses quadratically fewer steps than a random walk on the grid, ignoring logarithmic factors. This is the first known quantum walk that finds a marked element in a number of steps less than the square-root of the extended hitting time. We also give a new tighter upper bound on the extended hitting time of a marked subset, expressed in terms of the hitting times of its members.

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“…Lemma 1 (see e.g. [33,31,22]) The hitting time of a reversible ergodic Markov chain P with marked elements M is…”

Section: Bounds On the Extended Hitting Timementioning

confidence: 99%

“…A quantum walk is implemented similarly [33,32,31]. We first create some initial state |init from the state |π = v∈V √ π v |v , where π is the stationary distribution.…”

Section: An Efficient Quantum Algorithm For the Torusmentioning

confidence: 99%