Asymptotic properties of the Dirac quantum cellular automaton

Perez, A.

doi:10.1103/physreva.93.012328

Cited by 16 publications

(20 citation statements)

References 68 publications

(111 reference statements)

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“…Continuous-time quantum walk is defined only on position Hilbert space, whereas discrete-time quantum walk is defined on a joint position and coin Hilbert space, thus providing an additional degree of freedom to control the dynamics. Upon tuning the different parameters of the evolution operators of DTQW, one may control and engineer the dynamics in order to simulate various quantum phenomena such as localization [21][22][23], topological phase [24,25], neutrino oscillation [26,27], and relativistic quantum dynamics [28][29][30][31][32][33][34]. Quantum walks have been experimentally implemented in various physical systems such as NMR [35], photonics [36][37][38][39], cold atoms [40], and trapped ions [41,42].…”

Section: Introductionmentioning

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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Section: Introductionmentioning

confidence: 99%

Quantum walker as a probe for its coin parameter

2019

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“…It is remarked that the massless Dirac equation can simulate the trivial DTQW. Note that similar approaches are well known as Dirac quantum cellular automata [44][45][46][47]. They have also exhibited various quantum dynamics by the massive Dirac equation.…”

Section: Dtqw Implementation By Dirac Particlementioning

confidence: 90%

How to Realize One-dimensional Discrete-time Quantum Walk by Dirac Particle

Shikano

2017

IIS

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One-dimensional discrete-time quantum walks (DTQWs) can simulate various quantum and classical dynamics and have already been implemented in several physical systems. This implementation needs a well-controlled quantum dynamical system, which is the same requirement for implementing quantum information processing tasks. Here, we consider how to realize DTQWs by Dirac particles toward a solid-state implementation of DTQWs.

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“…It yields, whatever the values of the entries, two propagation fronts, one to the left, and the other to the right, and thus exhibits, in particular, ballistic spread, i.e., O(t) spread. In the long-time limit, the spread is exactly σ ∞ (t) = (a/ )t √ 1 − sin θ [53,54]. Notice in particular that this spread 2 is independent of ξ 0 , ξ 1 and χ.…”

Section: Cξ0mentioning

confidence: 99%

Quantum simulation of quantum relativistic diffusion via quantum walks

Arnault¹,

Macquet²,

Anglés-Castillo³

et al. 2020

J. Phys. A: Math. Theor.

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Two models are first presented, of one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: The diffusion arises via the byconstruction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position.

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Asymptotic properties of the Dirac quantum cellular automaton

Cited by 16 publications

References 68 publications

Quantum walker as a probe for its coin parameter

Quantum walker as a probe for its coin parameter

How to Realize One-dimensional Discrete-time Quantum Walk by Dirac Particle

Quantum simulation of quantum relativistic diffusion via quantum walks

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