Comparing classical and quantum PageRanks

Loke, T.; Tang, Jiangshan; Rodriguez, J. P. J.; Small, Michael; Wang, Jingbo

doi:10.1007/s11128-016-1456-z

Cited by 44 publications

(32 citation statements)

References 31 publications

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“…Therefore, we can use Eq. (7) to find out that there exists one eigenvalue of the form 2(1 − ω)i with corresponding eigenvector |C k |C 2k , where (·) denotes the element-wise conjugation and |C i is the i-th eigenvector of a circulant matrix of the form…”

Section: Directed Graphsmentioning

confidence: 99%

Limiting properties of stochastic quantum walks on directed graphs

Glos

Miszczak

Ostaszewski

2017

J. Phys. A: Math. Theor.

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The main results of our work is determining the differences between limiting properties in various models of quantum stochastic walks. In particular, we prove that in the case of strongly connected and a class of weakly connected directed graphs, local environment interaction evolution is relaxing, and in the case of undirected graphs, global environment interaction evolution is convergent. For other classes of directed graphs we show, that the character of connectivity large influence on the limiting properties. We also study the limiting properties for the non-moralizing global interaction case. We demonstrate that the digraph observance is recovered in this case.

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Section: Directed Graphsmentioning

confidence: 99%

Limiting properties of stochastic quantum walks on directed graphs

Glos

Miszczak

Ostaszewski

2017

J. Phys. A: Math. Theor.

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“…It has been proven that the quantum methods for ranking nodes outperform their classical counterparts [62][63][64][65] on different kinds of networks, but the quantum protocol tested is based on Szegedy's scheme. Szegedy's scheme is a variant of a DTQW that does not require a coin operator, but needs an additional Hilbert space of the same dimension as its position space.…”

Section: Introductionmentioning

confidence: 99%

Discrete-time quantum walk algorithm for ranking nodes on a network

Chawla

Mangal

Chandrashekar

2020

Quantum Inf Process

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We present a quantum algorithm for ranking the nodes on a network in their order of importance. The algorithm is based on a directed discrete-time quantum walk, and works on all directed networks. This algorithm can theoretically be applied to the entire internet, and thus can function as a quantum PageRank algorithm. Our analysis shows that the hierarchy of quantum rank matches well with the hierarchy of classical rank for directed tree network and for non-trivial cyclic networks, the hierarchy of quantum ranks do not exactly match to the hierarchy of the classical rank. This highlights the role of quantum interference and fluctuations in networks and the importance of using quantum algorithms to rank nodes in quantum networks. Another application this algorithm can envision is to model the dynamics on networks mimicking the chemical complexes and rank active centers in order of reactivities. Since discrete-time quantum walks are implementable on current quantum processing systems, this algorithm will also be of practical relevance in analysis of quantum architecture.

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“…They have been used extensively in graph theoretical applications [11][12][13][14] and are the basis of many other quantum algorithms [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

A quantum walk-assisted approximate algorithm for bounded NP optimisation problems

Marsh

Wang

2019

Quantum Inf Process

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This paper describes an application of the Quantum Approximate Optimisation Algorithm (QAOA) to efficiently find approximate solutions for computational problems contained in the polynomially bounded NP optimisation complexity class (NPO PB). We consider a generalisation of the QAOA state evolution to alternating quantum walks and solution-quality-dependent phase shifts, and use the quantum walks to integrate the problem constraints of NPO problems. We apply the recent concept of a hybrid quantum-classical variational scheme to attempt finding the highest expectation value, which contains a high-quality solution. The algorithm is applied to the problem of minimum vertex cover, showing promising results using only a fixed and low number of optimisation parameters.

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Comparing classical and quantum PageRanks

Cited by 44 publications

References 31 publications

Limiting properties of stochastic quantum walks on directed graphs

Limiting properties of stochastic quantum walks on directed graphs

Discrete-time quantum walk algorithm for ranking nodes on a network

A quantum walk-assisted approximate algorithm for bounded NP optimisation problems

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