Continuous-time quantum-walk spatial search on the Bollobás scale-free network

Osada, Takuma; Coutinho, Bruno C.; Omar, Yasser; Sanaka, Kaoru; Munro, William J.; Nemoto, Kae

doi:10.1103/physreva.101.022310

Cited by 18 publications

(10 citation statements)

References 43 publications

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“…Philipp et al [13] analyzed spatial search on balanced trees, and showed that the efficiency depends on whether the marked vertex is close to the root or the leaves of the graph. Osada et al [14] explored the spatial search on scale-free networks and found that the efficiency is determined by the global structure around the marked vertex. Recently, new experimental implementations of quantum walk search were proposed in [15,16].…”

Section: Introductionmentioning

confidence: 99%

Spatial Search on Johnson Graphs by Continuous-Time Quantum Walk

Tanaka,

Sabri,

Portugal

2021

Preprint

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Spatial search on graphs is one of the most important algorithmic applications of quantum walks. To show that a quantum-walk-based search is more efficient than a random-walk-based search is a difficult problem, which has been addressed in several ways. Usually, graph symmetries aid in the calculation of the algorithm's computational complexity, and Johnson graphs are an interesting class regarding symmetries because they are regular, Hamiltonconnected, vertex-and distance-transitive. In this work, we show that spatial search on Johnson graphs by continuous-time quantum walk achieves the Grover lower bound π √ N /2 with success probability 1 asymptotically for every fixed diameter, where N is the number of vertices. The proof is mathematically rigorous and can be used for other graph classes.

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Section: Introductionmentioning

confidence: 99%

Spatial Search on Johnson Graphs by Continuous-Time Quantum Walk

Tanaka,

Sabri,

Portugal

2021

Preprint

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“…It appears that the most successful strategies consist in using unitary QWs which (i) incorporate the basic idea behind Grover abstract search algorithm [30,31] and (ii) admit, similarly to massless Dirac equation, a linear dispersion relation at large scales [32][33][34]. Some of these unitary QWs work in continuous time [35][36][37][38][39], while others work in discrete time [40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

Dirac Spatial Search with Electric Fields

Zylberman

2021

Entropy

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Electric Dirac quantum walks, which are a discretisation of the Dirac equation for a spinor coupled to an electric field, are revisited in order to perform spatial searches. The Coulomb electric field of a point charge is used as a non local oracle to perform a spatial search on a 2D grid of N points. As other quantum walks proposed for spatial search, these walks localise partially on the charge after a finite period of time. However, contrary to other walks, this localisation time scales as N for small values of N and tends asymptotically to a constant for larger Ns, thus offering a speed-up over conventional methods.

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“…Spatial search on graphs by means of CTQWs has been thoroughly investigated in the last decades. Starting from the seminal work from Childs and Goldstone [8], the advantage provided by CTQW to quantum spatial search on different families of graphs has been analyzed [20][21][22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Quantum spatial search in two-dimensional waveguide arrays

Benedetti,

Tamascelli,

Paris

et al. 2021

Preprint

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Continuous-time quantum walks (CTQW) have shown the capability to perform efficiently the spatial search of a marked site on many kinds of graphs. However, most of such graphs are hard to realize in an experimental setting. Here we study CTQW spatial search on a planar triangular lattice by means of both numerical simulations and experiments. The experiments are performed using three-dimensional waveguide arrays fabricated by femtosecond laser pulses, illuminated by coherent light. We show that the retrieval of the marked site by the quantum walker is accomplished with higher probability than the classical counterpart, in a convenient time window placed early in the evolution.

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Continuous-time quantum-walk spatial search on the Bollobás scale-free network

Cited by 18 publications

References 43 publications

Spatial Search on Johnson Graphs by Continuous-Time Quantum Walk

Spatial Search on Johnson Graphs by Continuous-Time Quantum Walk

Dirac Spatial Search with Electric Fields

Quantum spatial search in two-dimensional waveguide arrays

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