Neutrino oscillations in discrete-time quantum walk framework

Mallick, Arindam; Mandal, Sanjoy; Chandrashekar, C. M.

doi:10.1140/epjc/s10052-017-4636-9

Cited by 40 publications

(37 citation statements)

References 41 publications

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“…It has also been mapped to two period standard discrete-time quantum walks [65,66]. The evolution operator for split-step quantum walk is given by (26) and the coin operator is given by, where j = 1, 2.…”

Section: Qfi In Split-step Quantum Walkmentioning

confidence: 99%

“…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%

“…The most general unitary coin operator in one dimension has three independent parameters [43] and provides an ample control over the dynamics, but already one and two parameter coins are extremely useful in simulating various physical systems in one dimension. For example, different combinations of evolution parameters in split-step DTQW describes topological phases [24,25] and neutrino oscillation [26,27]. Indeed, coin parameters play a relevant role in the evolution of the state of the walker in the position space and, in turn, in controlling and engineering DTQWs.…”

Section: Introductionmentioning

confidence: 99%

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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: Qfi In Split-step Quantum Walkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum walker as a probe for its coin parameter

2019

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“…The zeroth order should be equal to the identity operator both in position and coin space in order to make the Hamiltonian, a bounded operator at  a 0, t  0 for the validity of Taylor series expansion in equation (13).…”

Section: General Split-step Dqwmentioning

confidence: 99%

“…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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Exact simulation of coined quantum walks with the continuous-time model

Pascal

Portugal

2016

Quantum Inf Process

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The connection between coined and continuous-time quantum walk models has been addressed in a number of papers. In most of those studies, the continuous-time model is derived from coined quantum walks by employing dimensional reduction and taking appropriate limits. In this work, we produce the evolution of a coined quantum walk on a generic graph using a continuous-time quantum walk on a larger graph. In addition to expanding the underlying structure, we also have to switch on and off edges during the continuous-time evolution to accommodate the alternation between the shift and coin operators from the coined model. In one particular case, the connection is very natural, and the continuous-time quantum walk that simulates the coined quantum walk is driven by the graph Laplacian on the dynamically changing expanded graph. 1 Let nt be a Poisson random variable and denote the expected value by · . For the continuous-time transition matrix M CT (t) and the discrete-time transition matrix M DT (k) of the RW, we have M CT (t) = M DT (nt) = ∞ k=0 P (nt = k)M DT (k) = exp[t(M DT − I)].

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Neutrino oscillations in discrete-time quantum walk framework

Cited by 40 publications

References 41 publications

Quantum walker as a probe for its coin parameter

Quantum walker as a probe for its coin parameter

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

Exact simulation of coined quantum walks with the continuous-time model

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