Controlling quantum random walk with a step-dependent coin

Panahiyan, S.; Fritzsche, S.

doi:10.1088/1367-2630/aad899

Cited by 38 publications

(34 citation statements)

References 75 publications

(133 reference statements)

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“…Initially, a space-dependent coin was introduced in the quantum walk 20 . Later, a quantum walk with time-dependent coins was studied [21][22][23][24][25] . The resulting probability distribution for the quantum walk changed significantly.…”

Section: Floquet-engineered Quantum Walksmentioning

confidence: 99%

Floquet-engineered quantum walks

Katayama

Hatakenaka

Fujii

2020

Sci Rep

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The quantum walk is the quantum-mechanical analogue of the classical random walk, which offers an advanced tool for both simulating highly complex quantum systems and building quantum algorithms in a wide range of research areas. One prominent application is in computational models capable of performing any quantum computation, in which precisely controlled state transfer is required. It is, however, generally difficult to control the behavior of quantum walks due to stochastic processes. Here we unveil the walking mechanism based on its particle-wave duality and then present tailoring quantum walks using the walking mechanism (Floquet oscillations) under designed time-dependent coins, to manipulate the desired state on demand, as in universal quantum computation primitives. Our results open the path towards control of quantum walks.

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Section: Floquet-engineered Quantum Walksmentioning

confidence: 99%

Floquet-engineered quantum walks

Katayama

Hatakenaka

Fujii

2020

Sci Rep

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“…In previous study [33], we confirmed that by utilizing step-dependent coins [34] in splitstep quantum walk, we can simulate exotic cell-like structure for topological phenomena [33]. In this paper, we mainly focus on these cell-like structures and address the following issues.…”

mentioning

confidence: 79%

Simulation of novel cell-like topological structures with quantum walk

Panahiyan

Fritzsche

2020

Eur. Phys. J. Plus

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We demonstrate how quantum walk can simulate exotic cell-like structures for topological phases and boundary states. These cell-like structures contain the three known boundary states of Dirac cone, Fermi arc and flat bands alongside of all trivial and non-trivial phases of BDI family of topological phases. We also characterize the behavior of boundary states through Bloch spheres. In addition, we investigate the topological phase transitions and critical behavior of the system that take place over boundary states through curvature function. We confirm that critical behavior of the simulated topological phenomena can be described by peak-divergence scenario. We extract the critical exponents and length scale, establish a scaling law and show that band crossing is 1. Furthermore, we find the correlation function through Wannier states and show that it decays as a function of length scale.

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“…However, when either of these conditions are violated, a naive classical MCMC fails to produce the correct probability distribution over final states. While quantum walks with time/space dependence have been studied in the literature [4,[7][8][9][10] and there are some similarities to quantum algorithms for decision trees [11], our quantum tree requires a new approach.…”

Section: Introductionmentioning

confidence: 99%

A quantum algorithm to efficiently sample from interfering binary trees

Provasoli¹,

Nachman²,

Bauer³

et al. 2020

Quantum Sci. Technol.

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Quantum computers provide an opportunity to efficiently sample from probability distributions that include non-trivial interference effects between amplitudes. Using a simple process wherein all possible state histories can be specified by a binary tree, we construct an explicit quantum algorithm that runs in polynomial time to sample from the process once. The corresponding naive Markov Chain algorithm does not produce the correct probability distribution and an explicit classical calculation of the full distribution requires exponentially many operations. However, the problem can be reduced to a system of two qubits with repeated measurements, shedding light on a quantuminspired efficient classical algorithm. arXiv:1901.08148v2 [quant-ph]

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Controlling quantum random walk with a step-dependent coin

Cited by 38 publications

References 75 publications

Floquet-engineered quantum walks

Floquet-engineered quantum walks

Simulation of novel cell-like topological structures with quantum walk

A quantum algorithm to efficiently sample from interfering binary trees

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