Quantum walks over a square lattice

Ghosal, Arkaprabha; Deb, Prasenjit

doi:10.1103/physreva.98.032104

Cited by 7 publications

(4 citation statements)

References 32 publications

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“…The way to build an attractor from these blocks is provided by the shift conditions. Rewriting the equation (17) as…”

Section: Percolated Quantum Walksmentioning

confidence: 99%

“…Another possibility is to consider quantum walks in media randomized by static or dynamical percolation [9]. For discrete-time quantum walks on infinite lattices dynamical percolation was considered as a source of decoherence [10,11], and the research focused on spreading properties and transition to classical diffusive behaviour [12][13][14][15], non-markovianity of the evolution of the reduced coin state [16], or mixing times [17]. On finite graphs, the effect of percolation on quantum transport was investigated [18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

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Two-particle Hadamard walk on dynamically percolated line and circle

Parýzková,

Štefaňák,

Novotný

et al. 2024

Phys. Scr.

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Asymptotic dynamics of a Hadamard walk of two non-interacting quantum particles on a dynamically percolated finite line or a circle is investigated. We construct a basis of the attractor space of the corresponding random-unitary dynamics and prove the completeness of our solution. In comparison to the one-particle case, the structure of the attractor space is much more complex, resulting in intriguing asymptotic dynamics. General results are illustrated on two examples. First, for circles of length not divisible by 4 the boundary conditions reduces the number of attractors considerably, allowing for fully analytic solution. Second, we investigate line of length 4 and determine the asymptotic cycle of reduced coin states and position distributions, focusing on the correlations between the two particles. Our results show that a random unitary evolution, which is a combination of quantum dynamics and a classical stochasticity, leads to correlations between initially uncorrelated particles. This is not possible for purely unitary evolution of non-interacting quantum particles. The shared dynamically percolated graph can thus be considered as a weak form of interaction.

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“…The way to build an attractor from these blocks is provided by the shift conditions. Rewriting the equation (17) as…”

Section: Percolated Quantum Walksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Two-particle Hadamard walk on dynamically percolated line and circle

Parýzková,

Štefaňák,

Novotný

et al. 2024

Phys. Scr.

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“…A quantum walk algorithm can be implemented on many graph structures, and its function is very significant [7][8][9][10][11][12][13][14]. Also, quantum walks have important applications in quantum cryptography and quantum communication [15,16].…”

Section: Introductionmentioning

confidence: 99%

Multiparticle quantum walk–based error correction algorithm with two-lattice Bose–Hubbard model

Wang

et al. 2022

Front. Phys.

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When the evolution of discrete time quantum walk is carried out for particles, the ramble state is prone to error due to the influence of system noise. A multiparticle quantum walk error correction algorithm based on the two-lattice Bose–Hubbard model is proposed in this study. First, two point Bose–Hubbard models are constructed according to the local Euclidean generator, and it is proved that the two elements in the model can be replaced arbitrarily. Second, the relationship between the transition intensity and entanglement degree of the particles in the model is obtained by using the Bethe hypothesis method. Third, the position of the quantum lattice is coded and the quantum state exchange gate is constructed. Finally, the state replacement of quantum walk on the lattice point is carried out by switching the walker to the lattice point of quantum error correction code, and the replacement is carried out again. The entanglement of quantum particles in the double-lattice Bose–Hubbard model is simulated numerically. When the ratio of the interaction between particles and the transition intensity of particles is close to 0, the entanglement operation of quantum particles in the model can be realized by using this algorithm. According to the properties of the Bose–Hubbard model, quantum walking error correction can be realized after particle entanglement. This study introduces the popular restnet network as a training model, which increases the decoding speed of the error correction circuit by about 33%. More importantly, the lower threshold limit of the convolutional neural network (CNN) decoder is increased from 0.0058 under the traditional minimum weight perfect matching (MWPM) to 0.0085, which realizes the stable progress of quantum walk with high fault tolerance rate.

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“…In both cases, quantum speedups were found as a result of the SQRW causing nearly all of the probability in the systems to concentrate along the path of states leading to F. This paper is an extension to the study of SQRWs, showcasing a new geometry that one can obtain a speedup on. Specifically, we extend the study of previous discrete quantum random walks on square lattices [27,28], now using the SQRW scheme rather than coin quantum random walks.…”

Section: Introductionmentioning

confidence: 99%

Scattering quantum random walks on square grids and randomly generated mazes

Koch

2019

Phys. Rev. A

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The Scattering Quantum Random Walk scheme has found success as a basis for search algorithms on highly symmetric graph structures. In this paper we examine its effectiveness at locating a specially marked vertex on square grid graphs, consisting of N 2 nodes. We simulate these quantum systems using classical computational methods, and find that the probability distributions that arise are very favorable for a hybrid quantum / classical algorithm. We then examine how this hybrid algorithm handles varying types of randomness in both location of the special vertex and later random obstacles placed throughout the geometry, showing that that the algorithm is resilient to both cases.

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Quantum walks over a square lattice

Cited by 7 publications

References 32 publications

Two-particle Hadamard walk on dynamically percolated line and circle

Two-particle Hadamard walk on dynamically percolated line and circle

Multiparticle quantum walk–based error correction algorithm with two-lattice Bose–Hubbard model

Scattering quantum random walks on square grids and randomly generated mazes

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