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Decoherence in the Three-State Quantum Walk

M. C. de Oliveira, Luísa Toledo Tude

Jan 1, 20221 citation

Decoherence in a one-dimensional quantum walk

Mostafa Annabestani, Seyed Javad Akhtarshenas, Mohamad Reza Abolhassani

In this article we study decoherence in the discrete-time quantum walk on the line. We generalize the method of decoherent coin quantum walk, introduced by Brun et al. [Phys. Rev. A 67, 32304 (2003)]. Our analytical expressions are applicable for all kinds of decoherence. As an example of the coin-position decoherence, we study the broken line quantum walk and compare our results with the numerical one. We also show that our analytical results reduce to the Brun formalism when only the coin is subjected to decoherence.In this article we study decoherence in the discrete-time quantum walk on the line. We generalize the method of decoherent coin quantum walk, introduced by Brun et al. [Phys. Rev. A 67, 32304 (2003)]. Our analytical expressions are applicable for all kinds of decoherence. As an example of the coin-position decoherence, we study the broken line quantum walk and compare our results with the numerical one. We also show that our analytical results reduce to the Brun formalism when only the coin is subjected to decoherence.

arXiv:0910.1986Physical Review AMar 24, 201053 citations

Decoherence in the three-state quantum walk

Luísa Toledo Tude, M. C. de Oliveira

arXiv:2107.09124Physica A Statistical Mechanics and its ApplicationsAug 4, 20225 citations

Decoherence in a quantum walk on the line

Viv M. Kendon, Ben Tregenna

We have studied how decoherence affects a quantum walk on the line. As expected, it is highly sensitive, consisting as it does of an extremely delocalized particle. We obtain an expression for the rate at which the standard deviation falls from the quantum value as decoherence increases and show that it is proportional to the number of decoherence "events" occuring during the walk.

arXiv:quant-ph/0210047Oct 8, 200227 citations

Decoherence is useful in quantum walks

Viv M. Kendon, Ben Tregenna

We present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalised with each step. However, the effect of a small amount of decoherence is to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms. Specifically, we observe a highly uniform distribution on the line, a very fast mixing time on the cycle, and more reliable hitting times across the hypercube.We present a study of the effects of decoherence in the operation of a discrete quantum walk on a line, cycle and hypercube. We find high sensitivity to decoherence, increasing with the number of steps in the walk, as the particle is becoming more delocalised with each step. However, the effect of a small amount of decoherence is to enhance the properties of the quantum walk that are desirable for the development of quantum algorithms. Specifically, we observe a highly uniform distribution on the line, a very fast mixing time on the cycle, and more reliable hitting times across the hypercube.

Aug 31, 200213 citations

Decoherence in Discrete Quantum Walks

Viv M. Kendon, Ben Tregenna

arXiv:quant-ph/0301182Lecture notes in physicsDec 9, 200329 citations

Decoherence in the quantum walk on the line

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