Dirac Cellular Automaton from Split-step Quantum Walk

Mallick, Arindam; Chandrashekar, C. M.

doi:10.1038/srep25779

Cited by 43 publications

(58 citation statements)

References 64 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Multiple evolution parameters give more control over the evolution of the walk to engineer the dynamics at our desire. The general single-particle SS-DQW in + ( ) 1 1 dimensional space-time can be defined as a unitary evolution operator that evolves a state y ñ | ( ) t at time t to a state y t Here the unitary coin operation is defined as , we have a general U(2) group operation on coin space [25]. These position shift operators act homogeneously on all positions, at all time steps.…”

Section: General Split-step Dqwmentioning

confidence: 99%

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

et al. 2019

Self Cite

View full text Add to dashboard Cite

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...

show abstract

Section: General Split-step Dqwmentioning

confidence: 99%

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

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…With a demonstration of steering of random walk in ultracold atoms, [30] quantum random walk of Bose-Einstein condensate (BEC) in momentum space [31] and initial state dependence of quantum ratchet in BEC, [32] one can anticipate realization of our ratchet model in BEC system. With the connection of DQW with Dirac cellular automaton, [33] system in which dynamics can be described using Dirac equations can also be effectively explore to implement our scheme for coherent transport.…”

Section: Entanglement Entropy In Ratchetmentioning

confidence: 99%

“…With the connection of DQW with Dirac cellular automaton [33], system in which dynamics can be described using Dirac equations can also be effectively explore to implement our scheme for coherent transport.…”

Section: Entanglement Entropy In Ratchetmentioning

confidence: 99%

Quantum Ratchet in Disordered Quantum Walk

et al. 2017

Self Cite

View full text Add to dashboard Cite

Symmetrically evolving discrete quantum walk results in dynamic localization with zero mean displacement when the standard evolution operations are replaced by a temporal disorder evolution operation. In this work we show that the quantum ratchet action, that is, a directed transport in standard or disordered discrete-time quantum walk can be realized by introducing a pawl like effect realized by using a fixed coin operation at marked positions that is, different from the ones used for evolution at other positions. We also show that the combination of standard and disordered evolution operations can be optimized to get the mean displacement of order ∝ t (number of walk steps). This model of quantum ratchet in quantum walk is defined using only a set of entangling unitary operators resulting in the coherent quantum transport.

show abstract

“…We give another possible interpretation of Equation (34). The boson approximation Equation (34) can be obtained by applying coarse graining to Equation (18) using the following seemingly reasonable weight matrix for the adjacent grid pair subspace.…”

Section: I C Is C Is a A C Is A A C Is A A E E Is C Is C A A Is C Amentioning

confidence: 99%

“…The boson approximation Equation (34) can be obtained by applying coarse graining to Equation (18) using the following seemingly reasonable weight matrix for the adjacent grid pair subspace. Namely the 11 -11 component of Equation (34) (=1) is obtained also by…”

Section: I C Is C Is a A C Is A A C Is A A E E Is C Is C A A Is C Amentioning

confidence: 99%

The Approximation of Bosonic System by Fermion in Quantum Cellular Automaton

Hamada¹,

Sekino²

2017

JQIS

View full text Add to dashboard Cite

In one-dimensional multiparticle Quantum Cellular Automaton (QCA), the approximation of the bosonic system by fermion (boson-fermion correspondence) can be derived in a rather simple and intriguing way, where the principle to impose zero-derivative boundary conditions of one-particle QCA is also analogously used in particle-exchange boundary conditions. As a clear cut demonstration of this approximation, we calculate the ground state of few-particle systems in a box using imaginary time evolution simulation in 2nd quantization form as well as in 1st quantization form. Moreover in this 2nd quantized form of QCA calculation, we use Time Evolving Block Decimation (TEBD) algorithm. We present this demonstration to emphasize that the TEBD is most naturally regarded as an approximation method to the 2nd quantized form of QCA.

show abstract

Dirac Cellular Automaton from Split-step Quantum Walk

Cited by 43 publications

References 64 publications

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

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

Quantum Ratchet in Disordered Quantum Walk

The Approximation of Bosonic System by Fermion in Quantum Cellular Automaton

Contact Info

Product

Resources

About