arXiv subjects

C. M. Chandrashekar

Publications and source records attributed to C. M. Chandrashekar.

At least 73 records · Page 4Linked to original sources

arXiv2018

Bounds on the dynamics of periodic quantum walks and emergence of the gapless and gapped Dirac equation

We study the dynamics of discrete-time quantum walk using quantum coin operations, $\hat{C}(θ_1)$ and $\hat{C}(θ_2)$ in time-dependent periodic sequence. For the two-period quantum walk with the parameters $θ_1$ and $θ_2$ in the coin operations we show that the standard deviation [$σ_{θ_1, θ_2} (t)$] is the same as the minimum of standard deviation obtained from one of the one-period quantum walks with coin operations $θ_1$ or $θ_2$, $σ_{θ_1, θ_2}(t) = \min \{σ_{θ_1}(t), σ_{θ_2}(t) \}$. Our numerical result is analytically corroborated using the dispersion relation obtained from the continuum limit of the dynamics. Using the dispersion relation for one- and two-period quantum walks, we present the bounds on the dynamics of three- and higher period quantum walks. We also show that the bounds for the two-period quantum walk will hold good for the split-step quantum walk which is also defined using two coin operators using $θ_1$ and $θ_2$. Unlike the previous known connection of discrete-time quantum walks with the massless Dirac equation where coin parameter $θ=0$, here we show the recovery of the massless Dirac equation with non-zero $θ$ parameters contributing to the intriguing interference in the dynamics in a totally non-relativistic situation. We also present the effect of periodic sequence on the entanglement between coin and position space.

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arXiv2017

Quantum ratchet in disordered quantum walk

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 $\propto$ 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.

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arXiv2017

Neutrino oscillations in discrete-time quantum walk framework

Here we present neutrino oscillation in the frame-work of quantum walks. Starting from a one spatial dimensional discrete-time quantum walk we present a scheme of evolutions that will simulate neutrino oscillation. The set of quantum walk parameters which is required to reproduce the oscillation probability profile obtained in both, long range and short range neutrino experiment is explicitly presented. Our scheme to simulate three-generation neutrino oscillation from quantum walk evolution operators can be physically realized in any low energy experimental set-up with access to control a single six-level system, a multiparticle three-qubit or a qubit-qutrit system. We also present the entanglement between spins and position space, during neutrino propagation that will quantify the wave function delocalization around instantaneous average position of the neutrino. This work will contribute towards understanding neutrino oscillation in the framework of the quantum information perspective.

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arXiv2016

Dynamics and energy spectra of aperiodic discrete-time quantum walks

Deterministically aperiodic sequences are an intermediary between periodic sequences and completely random sequences. Materials which are translationally periodic have Bloch-like extended states, while random media exhibit Anderson localisation. Materials constructed on the basis of deterministic aperiodic sequences such as Fibonacci, Thue-Morse, and Rudin-Shapiro exhibit different properties, which can be related to their spectrum. Here, by investigating the dynamics of discrete-time quantum walks using different aperiodic sequences of coin operations in position space and time we establish the role of the diffraction spectra in characterizing the spreading of the wavepacket.

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arXiv2016

Dirac Quantum Cellular Automaton from Split-step Quantum Walk

Simulations of one quantum system by an other has an implication in realization of quantum machine that can imitate any quantum system and solve problems that are not accessible to classical computers. One of the approach to engineer quantum simulations is to discretize the space-time degree of freedom in quantum dynamics and define the quantum cellular automata (QCA), a local unitary update rule on a lattice. Different models of QCA are constructed using set of conditions which are not unique and are not always in implementable configuration on any other system. Dirac Cellular Automata (DCA) is one such model constructed for Dirac Hamiltonian (DH) in free quantum field theory. Here, starting from a split-step discrete-time quantum walk (QW) which is uniquely defined for experimental implementation, we recover the DCA along with all the fine oscillations in position space and bridge the missing connection between DH-DCA-QW. We will present the contribution of the parameters resulting in the fine oscillations on the Zitterbewegung frequency and entanglement. The tuneability of the evolution parameters demonstrated in experimental implementation of QW will establish it as an efficient tool to design quantum simulator and approach quantum field theory from principles of quantum information theory.

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arXiv2015

Localization and limit laws of a three-state alternate quantum walk on a two-dimensional lattice

A two-dimensional discrete-time quantum walk (DTQW) can be realized by alternating a two-state DTQW in one spatial dimension followed by an evolution in the other dimension. This was shown to reproduce a probability distribution for a certain configuration of a four-state DTQW on a two-dimensional lattice. In this work we present a three-state alternate DTQW with a parameterized coin-flip operator and show that it can produce localization that is also observed for a certain other configuration of the four-state DTQW and non-reproducible using the two-state alternate DTQW. We will present two limit theorems for the three-state alternate DTQW. One of the limit theorems describes a long-time limit of a return probability, and the other presents a convergence in distribution for the position of the walker on a rescaled space by time. We will also outline the relevance of these walks in physical systems.

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arXiv2015

Localized quantum walks as secured quantum memory

We show that a quantum walk process can be used to construct and secure quantum memory. More precisely, we show that a localized quantum walk with temporal disorder can be engineered to store the information of a single, unknown qubit on a compact position space and faithfully recover it on demand. Since the localization occurss with a finite spread in position space, the stored information of the qubit will be naturally secured from the simple eavesdropper. Our protocol can be adopted to any quantum system for which experimental control over quantum walk dynamics can be achieved.

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arXiv2015

Entanglement Properties of Localized States in 1D Topological Quantum Walks

The symmetries associated with discrete-time quantum walks (DTQWs) and the flexibilities in controlling their dynamical parameters allow to create a large number of topological phases. An interface in position space, which separates two regions with different topological numbers, can, for example, be effectively modelled using different coin parameters for the walk on either side of the interface. Depending on the neighbouring numbers, this can lead to localized states in one-dimensional configurations and here we carry out a detailed study into the strength of such localized states. We show that it can be related to the amount of entanglement created by the walks, with minima appearing for strong localizations. This feature also persists in the presence of small amounts of $σ_x$ (bit flip) noise.

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arXiv2014

Quantum percolation and transition point of a directed discrete-time quantum walk

Quantum percolation describes the problem of a quantum particle moving through a disordered system. While certain similarities to classical percolation exist, the quantum case has additional complexity due to the possibility of Anderson localisation. Here, we consider a directed discrete-time quantum walk as a model to study quantum percolation of a two-state particle on a two-dimensional lattice. Using numerical analysis we determine the fraction of connected edges required (transition point) in the lattice for the two-state particle to percolate with finite (non-zero) probability for three fundamental lattice geometries, finite square lattice, honeycomb lattice, and nanotube structure and show that it tends towards unity for increasing lattice sizes. To support the numerical results we also use a continuum approximation to analytically derive the expression for the percolation probability for the case of the square lattice and show that it agrees with the numerically obtained results for the discrete case. Beyond the fundamental interest to understand the dynamics of a two-state particle on a lattice (network) with disconnected vertices, our study has the potential to shed light on the transport dynamics in various quantum condensed matter systems and the construction of quantum information processing and communication protocols.

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arXiv2014

Single photons in an imperfect array of beam-splitters: Interplay between percolation, backscattering and transient localization

Photons in optical networks can be used in multi-path interferometry and various quantum information processing and communication protocols. Large networks, however, are often not free from defects, which can appear randomly between the lattice sites and are caused either by production faults or deliberate introduction. In this work we present numerical simulations of the behaviour of a single photon injected into a regular lattice of beam-splitting components in the presence of defects that cause perfect backward reflections. We find that the photon dynamics is quickly dominated by the backscattering processes, and a small fraction of reflectors in the paths of the beam-splitting array strongly affects the percolation probability of the photon. We carefully examine such systems and show an interesting interplay between the probabilities of percolation, backscattering and temporary localization. We also discuss the sensitivity of these probabilities to lattice size, timescale, injection point, fraction of reflectors and boundary conditions.

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arXiv2014

Noise-enhanced quantum transport on a closed loop using quantum walks

We study the effect of noise on the transport of a quantum state from a closed loop of $n-$sites with one of the sites as a sink. Using a discrete-time quantum walk dynamics, we demonstrate that the transport efficiency can be enhanced with noise when the number of sites in the loop is small and reduced when the number of sites in the loop grows. By using the concept of measurement induced disturbance we identify the regimes in which genuine quantum effects are responsible for the enhanced transport.

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arXiv2013

Two-component Dirac-like Hamiltonian for generating quantum walk on one-, two- and three-dimensional lattices

From the unitary operator used for implementing two-state discrete-time quantum walk on one-, two- and three- dimensional lattice we obtain a two-component Dirac-like Hamiltonian. In particular, using different pairs of Pauli basis as position translation states we obtain three different form of Hamiltonians for evolution on one-dimensional lattice. We extend this to two- and three-dimensional lattices using different Pauli basis states as position translation states for each dimension and show that the external coin operation, which is necessary for one-dimensional walk is not a necessary requirement for a walk on higher dimensions but can serve as an additional resource to control the dynamics. The two-component Hamiltonian we present here for quantum walk on different lattices can serve as a general framework to simulate, control, and study the dynamics of quantum systems governed by Dirac-like Hamiltonian.

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arXiv2013

Self-avoiding quantum walks: realisations in subspaces and limit theorems

While completely self-avoiding quantum walks have the distinct property of leading to a trivial unidirectional transport of a quantum state, an interesting and non-trivial dynamics can be constructed by restricting the self-avoidance to a subspace of the complete Hilbert space. Here, we present a comprehensive study of three two-dimensional quantum walks, which are self-avoiding in coin space, in position space and in both, coin and position space. We discuss the properties of these walks and show that all result in delocalisation of the probability distribution for initial states which are strongly localised for a walk with a standard Grover coin operation. We also present analytical results for the evolution in the form of limit distributions for the self-avoiding walks in coin space and in both, coin and position space.

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arXiv2013

Disorder induced localization and enhancement of entanglement in one- and two-dimensional quantum walks

The time evolution of one- and two-dimensional discrete-time quantum walk with increase in disorder is studied. We use spatial, temporal and spatio-temporal broken periodicity of the unitary evolution as disorder to mimic the effect of disordered/random medium in our study. Disorder induces a dramatic change in the interference pattern leading to localization of the quantum walks in one- and two-dimensions. Spatial disorder results in the decreases of the particle and position entanglement in one-dimension and counter intuitively, an enhancement in entanglement with temporal and spatio-temporal disorder is seen. The study signifies that the Anderson localization of quantum state without compromising on the degree of entanglement could be implement in a large variety of physical settings where quantum walks has been realized. The study presented here could make it feasible to explore, theoretically and experimentally the interplay between disorder and entanglement. This also brings up a variety of intriguing questions relating to the negative and positive implications on algorithmic and other applications.

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arXiv2013

Enhancement of Geometric Phase by Frustration of Decoherence: A Parrondo like Effect

Geometric phase plays an important role in evolution of pure or mixed quantum states. However, when a system undergoes decoherence the development of geometric phase may be inhibited. Here, we show that when a quantum system interacts with two competing environments there can be enhancement of geometric phase. This effect is akin to Parrondo like effect on the geometric phase which results from quantum frustration of decoherence. Our result suggests that the mechanism of two competing decoherence can be useful in fault-tolerant holonomic quantum computation.

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arXiv2013

Decoherence on a two-dimensional quantum walk using four- and two-state particle

We study the decoherence effects originating from state flipping and depolarization for two-dimensional discrete-time quantum walks using four-state and two-state particles. By quantifying the quantum correlations between the particle and position degree of freedom and between the two spatial ($x-y$) degrees of freedom using measurement induced disturbance (MID), we show that the two schemes using a two-state particle are more robust against decoherence than the Grover walk, which uses a four-state particle. We also show that the symmetries which hold for two-state quantum walks breakdown for the Grover walk, adding to the various other advantages of using two-state particles over four-state particles.

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arXiv2012

Two-state quantum walk on two- and three-dimensional lattices

We present a new scheme for a discrete-time quantum walk on two- and three-dimensional lattices using a two-state particle. We use different Pauli basis as translational eigestates for different axis and show that the coin operation, which is necessary for one-dimensional walk is not a necessary requirement for two- and three- dimensional walk but can serve as an additional resource. Using this scheme, the probability distribution from Grover walk using four-state particle and other equivalent schemes on a square lattice using coin operation is reproduced. We also present the Hamiltonian form of evolution which can serve as a general framework to simulate, control, and study the dynamics in different physical systems.

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arXiv2012

Entanglement generation in spatially separated systems using quantum walk

We present a novel scheme to generate entanglement between two spatially separated systems. The scheme makes use of spatial entanglement generated by a single-particle quantum walk which is used to entangle two spatially separated, not necessarily correlated, systems. This scheme can be used to entangle any two systems which can interact with the spatial modes entangled during the quantum walk evolution. A notable feature is that we can control the quantum walk dynamics and its ability to localize leads to a substantial control and improvement in the entanglement output.

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