Fractional recurrence in discrete-time quantum walk

Chandrashekar, C. M.

doi:10.2478/s11534-010-0023-y

Cited by 18 publications

(16 citation statements)

References 38 publications

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“…In Fig. 5(b), we have shown simulations with 16 and 32 lattice sites for 50 and 100 timesteps respectively, but no complete recurrence has been observed, which is consistent with earlier studies on DTQW on a circle [52].…”

Section: A Dtqw Without Disordersupporting

confidence: 90%

Simulating Anderson localization via a quantum walk on a one-dimensional lattice of superconducting qubits

Ghosh

2014

Phys. Rev. A

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Quantum walk (QW) on a disordered lattice leads to a multitude of interesting phenomena, such as Anderson localization. While QW has been realized in various optical and atomic systems, its implementation with superconducting qubits still remains pending. The major challenge in simulating QW with superconducting qubits emerges from the fact that on-chip superconducting qubits cannot hop between two adjacent lattice sites. Here we overcome this barrier and develop a novel gate-based scheme to realize the discrete time QW by placing a pair of qubits on each site of a 1D lattice and treating an excitation as a walker. It is also shown that various lattice disorders can be introduced and fully controlled by tuning the qubit parameters in our quantum walk circuit. We observe a distinct signature of transition from the ballistic regime to a localized QW with an increasing strength of disorder. Finally, an eight-qubit experiment is proposed where the signatures of such localized and delocalized regimes can be detected with existing superconducting technology. Our proposal opens up the possibility to explore various quantum transport processes with promising superconducting qubits.

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Section: A Dtqw Without Disordersupporting

confidence: 90%

Simulating Anderson localization via a quantum walk on a one-dimensional lattice of superconducting qubits

Ghosh

2014

Phys. Rev. A

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“…Besides the approach we take in this paper, there is an alternative route, an "ensemble approach", useful to obtain estimations for efficiency of quantum protocols. This consists in letting the quantum walk run undisturbed and after a fixed time measure the position distribution of the walker 31 , or its full quantum state 32 . The expected return time, defined in this way, does not necessarily take on an integer value even in the fully coherent case: it can exceed or stay below the dimension of the Hilbert space 20 .…”

Section: Discussionmentioning

confidence: 99%

Quantized recurrence time in unital iterated open quantum dynamics

et al. 2015

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The expected return time to the original state is a key concept characterizing systems obeying both classical or quantum dynamics. We consider iterated open quantum dynamical systems in finite dimensional Hilbert spaces, a broad class of systems that includes classical Markov chains and unitary discrete time quantum walks on networks. Starting from a pure state, the time evolution is induced by repeated applications of a general quantum channel, in each timestep followed by a measurement to detect whether the system has returned to the original state. We prove that if the superoperator is unital in the relevant Hilbert space (the part of the Hilbert space explored by the system), then the expectation value of the return time is an integer, equal to the dimension of this relevant Hilbert space. We illustrate our results on partially coherent quantum walks on finite graphs. Our work connects the previously known quantization of the expected return time for bistochastic Markov chains and for unitary quantum walks, and shows that these are special cases of a more general statement. The expected return time is thus a quantitative measure of the size of the part of the Hilbert space available to the system when the dynamics is started from a certain state.

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“…However, some striking differences between the two cases appear after 2a time steps, [−a, a] being the spatial interval for bounded DTQW. Those differences may be traced back to interference [58] and recurrence [59,60] in the position space. In order to illustrate this phenomenon, in Fig.…”

Section: Quantum Estimation In Discrete-time Quantum Walkmentioning

confidence: 99%

Quantum walker as a probe for its coin parameter

2019

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In discrete-time quantum walk (DTQW) the walker's coin space entangles with the position space after the very first step of the evolution. This phenomenon may be exploited to obtain the value of the coin parameter θ by performing measurements on the sole position space of the walker. In this paper, we evaluate the ultimate quantum limits to precision for this class of estimation protocols, and use this result to assess measurement schemes having limited access to the position space of the walker in one dimension. We find that the quantum Fisher information (QFI) of the walker's position space Hw(θ) increases with θ and with time which, in turn, may be seen as a metrological resource. We also find a difference in the QFI of bounded and unbounded DTQWs, and provide an interpretation of the different behaviors in terms of interference in the position space. Finally, we compare Hw(θ) to the full QFI H f (θ), i.e., the QFI of the walkers position plus coin state, and find that their ratio is dependent on θ, but saturates to a constant value, meaning that the walker may probe its coin parameter quite faithfully.

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Fractional recurrence in discrete-time quantum walk

Cited by 18 publications

References 38 publications

Simulating Anderson localization via a quantum walk on a one-dimensional lattice of superconducting qubits

Simulating Anderson localization via a quantum walk on a one-dimensional lattice of superconducting qubits

Quantized recurrence time in unital iterated open quantum dynamics

Quantum walker as a probe for its coin parameter

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