Limiting distribution of decoherent quantum random walks

Zhang, Kai

doi:10.1103/physreva.77.062302

Cited by 25 publications

(15 citation statements)

References 27 publications

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“…Environment, of which the description corresponds to that of quantum measurement in quantum mechanics [16], seems intuitively to be the origin of randomness. In such studies, the description of the periodic quantum measurement is used and the quantum-classical transition, which means an immediate change from the QW to the RW due to the decoherence effect, is shown [17][18][19][20]. However, the contribution to the quantum walk behavior from environment has not been shown analytically.…”

Section: Introductionmentioning

confidence: 99%

Emergence of randomness and arrow of time in quantum walks

et al. 2010

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CitationShikano, Yutaka et al. "Emergence of randomness and arrow of time in quantum walks." Physical Review A 81.6 (2010): 062129.Quantum walks are powerful tools not only for constructing the quantum speedup algorithms but also for describing specific models in physical processes. Furthermore, the discrete time quantum walk has been experimentally realized in various setups. We apply the concept of the quantum walk to the problems in quantum foundations. We show that randomness and the arrow of time in the quantum walk gradually emerge by periodic projective measurements from the mathematically obtained limit distribution under the time-scale transformation.

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Section: Introductionmentioning

confidence: 99%

Emergence of randomness and arrow of time in quantum walks

et al. 2010

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“…This concept was first introduced by H. Zeh [23] in 1970, and then formulated mathematically for quantum walks by T. Brun [3]. For both coin and position space partially decoherent Hadamard walk with strength 0 < p ≤ 1, K. Zhang proved in [24] that with symmetric initial conditions, it has Gaussian limiting distribution. More recently, the fact that the limiting distribution of the rescaled position discrete-time quantum random walks with general unitary operators subject to only coin space partially decoherence with strength 0 < p < 1 is a convex combination of normal distributions under certain conditions is proved by S. Fan, Z. Feng, S. Xiong and W. Yang [9].…”

Section: Introductionmentioning

confidence: 99%

Time-inhomogeneous Quantum Walks with Decoherence on Discrete Infinite Spaces

Chou,

Yang

2021

Preprint

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In quantum computation theory, quantum random walks have been utilized by many quantum search algorithms which provide improved performance over their classical counterparts. However, due to the importance of the quantum decoherence phenomenon, decoherent quantum walks and their applications have been studied on a wide variety of structures. Recently, a unified timeinhomogeneous coin-turning random walk with rescaled limiting distributions, Bernoulli, uniform, arcsine and semi-circle laws as parameter varies have been obtained. In this paper we study the quantum analogue of these models. We obtained a representation theorem for time-inhomogeneous quantum walk on discrete infinite state space. Additionally, the convergence of the distributions of the decoherent quantum walks are numerically estimated as an application of the representation theorem, and the convergence in distribution of the quantum analogues of Bernoulli, uniform, arcsine and semicircle laws are statistically analyzed.

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“…Recently, QW has been realized in experiment with different physical systems, such as trapped atoms or ions [15][16][17][18], optical systems [19][20][21][22], and superconducting qubit Yan et al [23]. Theoretical studies provide the transition from QW to CRW in different fashions, with decoherence approach [7,[24][25][26], or with random phase approach [27]. Actually, QW is the quantum extension of CRW from the singlecoin interpretation.…”

Section: Introductionmentioning

confidence: 99%

Directional quantum random walk induced by coherence

Chen

Sun

2020

Front. Phys.

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Quantum walk (QW), which is considered as the quantum counterpart of the classical random walk (CRW), is actually the quantum extension of CRW from the single-coin interpretation. The sequential unitary evolution engenders correlation between different steps in QW and leads to a ballistic position distribution. In this paper, we propose an alternative quantum extension of CRW from the ensemble interpretation, named quantum random walk (QRW), where the walker has many unrelated coins, modeled as two-level systems, initially prepared in the same state. We calculate the walker's position distribution in QRW for different initial coin states with the coin operator chosen as Hadamard matrix. In one-dimensional case, the walker's position is the asymmetric binomial distribution. We further demonstrate that in QRW, coherence leads the walker to perform directional movement. For an initially decoherenced coin state, the walker's position distribution is exactly the same as that of CRW. Moreover, we study QRW in 2D lattice, where the coherence plays a more diversified role in the walker's position distribution.

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Limiting distribution of decoherent quantum random walks

Cited by 25 publications

References 27 publications

Emergence of randomness and arrow of time in quantum walks

Emergence of randomness and arrow of time in quantum walks

Time-inhomogeneous Quantum Walks with Decoherence on Discrete Infinite Spaces

Directional quantum random walk induced by coherence

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