From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks

Arrighi, Pablo; Molfetta, Giuseppe Di; Márquez-Martín, Iván; Perez, A.

doi:10.1038/s41598-019-47535-4

Cited by 23 publications

(22 citation statements)

References 52 publications

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“…More particularly, we would like to have two already elegant theories to work together. On the one hand, the family of QWs considered here is the one described in [23], as while being very simple, it has the Dirac Equation as a continuous limit and can easily be extended to account for a curved metric [24]. Similar results had already been obtained on a rectangular lattice and generalized to higher dimensions [11][12][13].…”

Section: Introductionsupporting

confidence: 53%

Dynamical Triangulation Induced by Quantum Walk

2020

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We present the single-particle sector of a quantum cellular automaton, namely a quantum walk, on a simple dynamical triangulated 2 - manifold. The triangulation is changed through Pachner moves, induced by the walker density itself, allowing the surface to transform into any topologically equivalent one. This model extends the quantum walk over triangular grid, introduced in a previous work, by one of the authors, whose space-time limit recovers the Dirac equation in (2+1)-dimensions. Numerical simulations show that the number of triangles and the local curvature grow as t α e − β t 2 , where α and β parametrize the way geometry changes upon the local density of the walker, and that, in the long run, flatness emerges. Finally, we also prove that the global behavior of the walker, remains the same under spacetime random fluctuations.

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Section: Introductionsupporting

confidence: 53%

Dynamical Triangulation Induced by Quantum Walk

2020

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“…Let us rewrite our system of equations, Eq. (42), not in momentum space as above in Eq. (45), but in position space, by applying x| on the left of Eq.…”

Section: System Of Equations In Position Space and Remarksmentioning

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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“…In fact, QW are a universal computational model 7,8 , that spans a large spectrum of physical and biological phenomena, relevant both for fundamental science and for applications. Applications include search algorithms [9][10][11][12] and graph isomorphism algorithms 13 to modeling and simulating quantum [14][15][16][17][18] and classical dynamics 19,20 . These models have sparked various theoretical investigations covering areas in mathematics, computer science, quantum information and statistical mechanics and have been defined in any physical dimensions 21,22 and over several topologies [23][24][25] .…”

Section: Quantum Control Using Quantum Memorymentioning

confidence: 99%

Quantum control using quantum memory

Roget¹,

Herzog²,

Molfetta³

2020

Sci Rep

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We propose a new quantum numerical scheme to control the dynamics of a quantum walker in a two dimensional space–time grid. More specifically, we show how, introducing a quantum memory for each of the spatial grid, this result can be achieved simply by acting on the initial state of the whole system, and therefore can be exactly controlled once for all. As example we prove analytically how to encode in the initial state any arbitrary walker’s mean trajectory and variance. This brings significantly closer the possibility of implementing dynamically interesting physics models on medium term quantum devices, and introduces a new direction in simulating aspects of quantum field theories (QFTs), notably on curved manifold.

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From curved spacetime to spacetime-dependent local unitaries over the honeycomb and triangular Quantum Walks

Cited by 23 publications

References 52 publications

Dynamical Triangulation Induced by Quantum Walk

Dynamical Triangulation Induced by Quantum Walk

Quantum simulation of quantum relativistic diffusion via quantum walks

Quantum control using quantum memory

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