Mixing and decoherence in continuous-time quantum walks on long-range interacting cycles

Salimi, S.; Radgohar, Roya

doi:10.1088/1751-8113/42/47/475302

Cited by 10 publications

(13 citation statements)

References 39 publications

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“…29 and for long-range interacting cycles in Ref. 38. Moreover, we show that for small rates of decoherence, the mixing time is independent of the distance parameter l ðl !…”

Section: Introductionsupporting

confidence: 55%

“…The e®ect of decoherence on CTQWs has been studied on hypercube, 27,28 cycles, 29 lines, 30,31 N-cycles 32 and long-range interaction cycles. 38 Here, we study CTQWs on one-dimension (1D) networks with distance parameter l ! 2, which can be constructed as follows 33 : we construct a 1D ring lattice of N nodes, with each node connected to its 2l nearest neighbors (l on either side).…”

Section: Introductionmentioning

confidence: 99%

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The Effect of Decoherence on Mixing Time in Continuous-Time Quantum Walks on One-Dimensional Regular Networks

Salimi

Radgohar

2010

Int. J. Quantum Inform.

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In this paper, we study decoherence in continuous-time quantum walks (CTQWs) on onedimensional regular networks. For this purpose, we assume that every node is represented by a quantum dot continuously monitored by an individual point contact (Gurvitz's model). This measuring process induces decoherence. We focus on small rates of decoherence and then obtain the mixing time bound of the CTQWs on the one-dimensional regular network, whose distance parameter is l ! 2. Our results show that the mixing time is inversely proportional to the rate of decoherence, which is in agreement with the mentioned results for cycles in Refs. 29 and 37. Also, the same result is provided in Ref. 38 for long-range interacting cycles. Moreover, we¯nd that this quantity is independent of the distance parameter l ðl ! 2Þ and that the small values of decoherence make short the mixing time on these networks. 795 Int. J. Quantum Inform. 2010.08:795-806. Downloaded from www.worldscientific.com by UNIVERSITY OF AUCKLAND LIBRARY -SERIALS UNIT on 03/15/15. For personal use only. Ne ÀÀ NÀ1 N t : ð37Þ E®ect of Decoherence on Mixing Time in CTQWs 803 Int. J. Quantum Inform. 2010.08:795-806. Downloaded from www.worldscientific.com by UNIVERSITY OF AUCKLAND LIBRARY -SERIALS UNIT on 03/15/15. For personal use only.

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“…29 and for long-range interacting cycles in Ref. 38. Moreover, we show that for small rates of decoherence, the mixing time is independent of the distance parameter l ðl !…”

Section: Introductionsupporting

confidence: 55%

Section: Introductionmentioning

confidence: 99%

The Effect of Decoherence on Mixing Time in Continuous-Time Quantum Walks on One-Dimensional Regular Networks

Salimi

Radgohar

2010

Int. J. Quantum Inform.

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“…Salimi and Radgohar have considered the long-range case of the single cycle, where a given node interacts with its 2m nearest neighbors (m to each side) [128], see also Sec. V A.…”

Section: Decoherence On Ringsmentioning

confidence: 99%

Continuous-time quantum walks: Models for coherent transport on complex networks

2011

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This paper reviews recent advances in continuous-time quantum walks (CTQW) and their application to transport in various systems. The introduction gives a brief survey of the historical background of CTQW. After a short outline of the theoretical ideas behind CTQW and of its relation to classical continuous-time random walks (CTRW) in Sec. 2, implications for the efficiency of the transport are presented in Sec. 3. The fourth section gives an overview of different types of networks on which CTQW have been studied so far. Extensions of CTQW to systems with long-range interactions and with static disorder are discussed in section V. Systems with traps, i.e., systems in which the walker's probability to remain inside the system is not conserved, are presented in section IV. Relations to similar approaches to the transport are studied in section VII. The paper closes with an outlook on possible future directions.

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“…Firstly, we review the results obtained in [49] for the decoherent CTQWs on LRICs with small rate of decoherence. The mixing time upper bound for the odd values of m is as T mix (ǫ) < 1 Γ ln( N ǫ )[ N N −2 ] and for the even ms is as…”

Section: Large Decoherencementioning

confidence: 99%

The effect of large decoherence on mixing time in continuous-time quantum walks on long-range interacting cycles

Salimi

Radgohar

2010

J. Phys. B: At. Mol. Opt. Phys.

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In this paper, we consider decoherence in continuous-time quantum walks on long-range interacting cycles (LRICs), which are the extensions of the cycle graphs. For this purpose, we use Gurvitz's model and assume that every node is monitored by the corresponding point contact induced the decoherence process. Then, we focus on large rates of decoherence and calculate the probability distribution analytically and obtain the lower and upper bounds of the mixing time. Our results prove that the mixing time is proportional to the rate of decoherence and the inverse of the distance parameter (m) squared. This shows that the mixing time decreases with increasing the range of interaction. Also, what we obtain for m = 0 is in agreement with Fedichkin, Solenov and Tamon's results [48] for cycle, and see that the mixing time of CTQWs on cycle improves with adding interacting edges.

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Mixing and decoherence in continuous-time quantum walks on long-range interacting cycles

Cited by 10 publications

References 39 publications

The Effect of Decoherence on Mixing Time in Continuous-Time Quantum Walks on One-Dimensional Regular Networks

The Effect of Decoherence on Mixing Time in Continuous-Time Quantum Walks on One-Dimensional Regular Networks

Continuous-time quantum walks: Models for coherent transport on complex networks

The effect of large decoherence on mixing time in continuous-time quantum walks on long-range interacting cycles

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