Fermion confinement via quantum walks in (2+1)-dimensional and (3+1)-dimensional space-time

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

doi:10.1103/physreva.95.042112

Cited by 24 publications

(29 citation statements)

References 31 publications

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“…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] . QW appear in multiple variants and can be defined on arbitrary graphs.…”

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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Section: Quantum Control Using Quantum Memorymentioning

confidence: 99%

Quantum control using quantum memory

Roget¹,

Herzog²,

Molfetta³

2020

Sci Rep

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“…from Eqs. (24) and (26). But this is possible precisely because f was chosen such that | δ |δ | ≤ δ · δ .…”

Section: A2 Building the Solutionsmentioning

confidence: 99%

“…Whilst some Quantum Computing algorithms are formulated in terms of QWs, see [35], we focus here on their ability to simulate certain quantum physical phenomena, in the continuum limit. After it became clear that QWs can simulate the Dirac equation [34,11,27,16,12,9], the Klein-Gordon equation [14,6,17] and the Schrödinger equation [33,25], the focus moved towards simulating particles in some background field [13,19,26,20,5], with the difficult topic of interactions initiated in [28,1]. The question of the impact, of these inhomogeneous fields, upon the propagation of the walker gave rise to lattice models of Anderson localization [2,23].…”

Section: Introductionmentioning

confidence: 99%

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Quantum walking in curved spacetime: discrete metric

Arrighi

Molfetta

Facchini

2018

Quantum

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A discrete-time quantum walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs have familiar physics PDEs as their continuum limit. Some slight generalization of them (allowing for prior encoding and larger neighbourhoods) even have the curved spacetime Dirac equation, as their continuum limit. In the (1 + 1)−dimensional massless case, this equation decouples as scalar transport equations with tunable speeds. We characterise and construct all those QWs that lead to scalar transport with tunable speeds. The local coin operator dictates that speed; we provide concrete techniques to tune the speed of propagation, by making use only of a finite number of coin operatorsdifferently from previous models, in which the speed of propagation depends upon a continuous parameter of the quantum coin. The interest of such a discretization is twofold : to allow for easier experimental implementations on the one hand, and to evaluate ways of quantizing the metric field, on the other.

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“…Quantum walk, an effective algorithmic tool for simulating quantum physical phenomena where classical simulator fails or when the computational task is hard to realize via classical algorithm, has been shown to be very useful for realization of universal quantum computation [1][2][3]. The similarity between discrete quantum walk (DQW) and the dynamics of Dirac particles [4][5][6][7][8][9][10][11][12], at the continuum limit, elevates the DQW as a potential candidate to simulate various phenomena where the Dirac fermions play a crucial role [13][14][15]. With advancement in field of quantum simulations where many quantum phenomena are mimicked in table-top experiments, algorithmic schemes which can simulate Dirac particle dynamics in quantum field theory has garnered considerable interest in recent days.…”

Section: Introductionmentioning

confidence: 99%

Simulating Dirac Hamiltonian in curved space-time by split-step quantum walk

et al. 2019

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Dirac particle represents a fundamental constituent of our nature. Simulation of Dirac particle dynamics by a controllable quantum system using quantum walks will allow us to investigate the nonclassical nature of dynamics in its discrete form. In this work, starting from a modified version of onespatial dimensional general inhomogeneous split-step discrete quantum walk we derive an effective Hamiltonian which mimics a single massive Dirac particle dynamics in curved (1+1) space-time dimension coupled to U(1) gauge potential-which is a forward step towards the simulation of the unification of electromagnetic and gravitational forces in lower dimension and at the single particle level. Implementation of this simulation scheme in simple qubit-system has been demonstrated. We show that the same Hamiltonian can represent (2+1) space-time dimensional Dirac particle dynamics when one of the spatial momenta remains fixed. We also discuss how we can include U(N) gauge potential in our scheme, in order to capture other fundamental force effects on the Dirac particle. The emergence of curvature in the two-particle split-step quantum walk has also been investigated while the particles are interacting through their entangled coin operation.operations-mimics the Dirac evolution under influence of gravitational waves in (2+1) dimension-was also recently reported in [24]. In [25], it is shown that the SS-DQW, where the coin parameters are space and timestep independent, can capture properties of the discretized Dirac particle dynamics in flat (1+1) dimension, while conventional DQW is unable to capture all properties of it. This motivates us to generalize the SS-DQW operation and study the consequences of it.In this paper starting from a slightly modified version of the single-step split-step DQW (SS-DQW) [26] whose coin operators are time and position-step dependent (inhomogeneous both in time and space), we derive a SS-DQW version of the (1+1) dimensional massive Dirac particle Hamiltonian under the influence of the U(1) gauge potential in curved space-time. This scheme is realizable in various physical table-top system as the SS-DQW has been proposed and successfully implemented in various systems like cold atoms [27], superconducting qubits [28,29], photonic systems [30,31]. Our scheme can also describe the (2+1) dimensional Dirac Hamiltonian in curved space-time when one component of momentum of the particle remains fixed. We provide realization of our simulation scheme using qubit systems. This scheme doesn't require any prior encoding or decoding, nor it demands extra conditions on the coin parameters in order to satisfy the boundedness (well-defined eigenvalues) of the generator which is the effective Hamiltonian in our case, i.e.the unitary operator should start evolution from identity while the parameter of the corresponding lie group evolves from zero to a nonzero real value. Our coin operations are general U(2) group elements in coinspace. After considering all the terms up to first order in time-step s...

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Fermion confinement via quantum walks in (2+1)-dimensional and (3+1)-dimensional space-time

Cited by 24 publications

References 31 publications

Quantum control using quantum memory

Quantum control using quantum memory

Quantum walking in curved spacetime: discrete metric

Simulating Dirac Hamiltonian in curved space-time by split-step quantum walk

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