scholarly journals Analysis of Decoherence in Linear and Cyclic Quantum Walks

Optics ◽  
2021 ◽  
Vol 2 (4) ◽  
pp. 236-250
Author(s):  
Mahesh N. Jayakody ◽  
Asiri Nanayakkara ◽  
Eliahu Cohen
Keyword(s):  
Probability Distributions ◽  
Quantum Walks ◽  
Noisy Environments ◽  
Data Encoding ◽  
Phase Damping ◽  
Initial States ◽  
Binomial Transform ◽  
Bit Flip ◽  
Depolarizing Channel ◽  
Cyclic Path

We theoretically analyze the case of noisy Quantum walks (QWs) by introducing four qubit decoherence models into the coin degree of freedom of linear and cyclic QWs. These models include flipping channels (bit flip, phase flip and bit-phase flip), depolarizing channel, phase damping channel and generalized amplitude damping channel. Explicit expressions for the probability distribution of QWs on a line and on a cyclic path are derived under localized and delocalized initial states. We show that QWs which begin from a delocalized state generate mixture probability distributions, which could give rise to useful algorithmic applications related to data encoding schemes. Specifically, we show how the combination of delocalzed initial states and decoherence can be used for computing the binomial transform of a given set of numbers. However, the sensitivity of QWs to noisy environments may negatively affect various other applications based on QWs.

ENTANGLEMENT-ASSISTED CLASSICAL CAPACITIES OF SOME SINGLE QUBIT QUANTUM NOISY CHANNELS

2002 ◽  
Vol 16 (12) ◽  
pp. 441-448 ◽  
Author(s):  
XIAN-TING LIANG ◽  
HONG-YI FAN
Keyword(s):  
Noisy Channels ◽  
Single Qubit ◽  
Phase Damping ◽  
Analytical Results ◽  
Bit Flip ◽  
Depolarizing Channel ◽  
Quantum Noisy Channels

In this paper, we calculate the entanglement-assisted classical capacities of the depolarizing channel, the phase damping channel, the phase flip channel, the bit flip channel, the bit-phase flip channel, the two-Pauli channel and the amplitude channel, and discuss the analytical results obtained. The Stokes papametrization representation of a qubit and the characteristic of unitary covariance of some quantum noisy channels are used in the calculations.

scholarly journals Entanglement Robustness via Spatial Deformation of Identical Particle Wave Functions

Entropy ◽  
2021 ◽  
Vol 23 (6) ◽  
pp. 708
Author(s):  
Matteo Piccolini ◽  
Farzam Nosrati ◽  
Giuseppe Compagno ◽  
Patrizia Livreri ◽  
Roberto Morandotti ◽  
...  
Keyword(s):  
Identical Particle ◽  
Quantum Correlations ◽  
Wave Functions ◽  
Noisy Environments ◽  
Classical Communication ◽  
Entanglement Protection ◽  
Phase Damping ◽  
Spatial Deformation ◽  
Amplitude Damping Channel ◽  
Depolarizing Channel

We address the problem of entanglement protection against surrounding noise by a procedure suitably exploiting spatial indistinguishability of identical subsystems. To this purpose, we take two initially separated and entangled identical qubits interacting with two independent noisy environments. Three typical models of environments are considered: amplitude damping channel, phase damping channel and depolarizing channel. After the interaction, we deform the wave functions of the two qubits to make them spatially overlap before performing spatially localized operations and classical communication (sLOCC) and eventually computing the entanglement of the resulting state. This way, we show that spatial indistinguishability of identical qubits can be utilized within the sLOCC operational framework to partially recover the quantum correlations spoiled by the environment. A general behavior emerges: the higher the spatial indistinguishability achieved via deformation, the larger the amount of recovered entanglement.

Decoherence of GHZ state under three noisy channels in non-inertial frames

2021 ◽  
pp. 2150209
Author(s):  
Kwang-Il Kim ◽  
Myong Chol Pak ◽  
Son A Kim ◽  
Jin Ju Ri ◽  
Tae-Hyok Kim
Keyword(s):  
Ghz State ◽  
Noisy Environments ◽  
Tripartite Entanglement ◽  
Noisy Channels ◽  
Phase Damping ◽  
Inertial Frames ◽  
Bit Flip

In this paper, we investigate the decoherence of GHZ state under three noisy channels in non-inertial frames. The phase flip, the bit flip and the phase damping channels are considered as noisy channels, respectively. By using three-tangle [Formula: see text] as the measurement of entanglement, we numerically calculate the genuine tripartite entanglement of GHZ state under noisy environments in non-inertial frames. Unlike the case of phase damping channel, in the cases of the phase flip and the bit flip ones, we find that the effect of environment cannot only decay the genuine tripartite entanglement, but also revive it.

scholarly journals Stiffness of probability distributions of work and Jarzynski relation for non-Gibbsian initial states

2018 ◽  
Vol 98 (1) ◽  
Author(s):  
Daniel Schmidtke ◽  
Lars Knipschild ◽  
Michele Campisi ◽  
Robin Steinigeweg ◽  
Jochen Gemmer
Keyword(s):  
Probability Distributions ◽  
Initial States

Photonic Quantum Walks on Finite Graphs and with Non-Localised Initial States

CLEO: 2015 ◽  
2015 ◽  
Author(s):  
Sonja Barkhofen ◽  
Fabian Elster ◽  
Thomas Nitsche ◽  
Jaroslav Novotný ◽  
Aurél Gábris ◽  
...  
Keyword(s):  
Quantum Walks ◽  
Finite Graphs ◽  
Initial States

scholarly journals Efficient circuits for quantum walks

2010 ◽  
Vol 10 (5&6) ◽  
pp. 420-434
Author(s):  
C.-F. Chiang ◽  
D. Nagaj ◽  
P. Wocjan
Keyword(s):  
Markov Chain ◽  
Random Walk ◽  
Random Walks ◽  
Probability Distributions ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Problem Size ◽  
Integrable Probability ◽  
The Difference ◽  
General Method

We present an efficient general method for realizing a quantum walk operator corresponding to an arbitrary sparse classical random walk. Our approach is based on Grover and Rudolph's method for preparing coherent versions of efficiently integrable probability distributions \cite{GroverRudolph}. This method is intended for use in quantum walk algorithms with polynomial speedups, whose complexity is usually measured in terms of how many times we have to apply a step of a quantum walk \cite{Szegedy}, compared to the number of necessary classical Markov chain steps. We consider a finer notion of complexity including the number of elementary gates it takes to implement each step of the quantum walk with some desired accuracy. The difference in complexity for various implementation approaches is that our method scales linearly in the sparsity parameter and poly-logarithmically with the inverse of the desired precision. The best previously known general methods either scale quadratically in the sparsity parameter, or polynomially in the inverse precision. Our approach is especially relevant for implementing quantum walks corresponding to classical random walks like those used in the classical algorithms for approximating permanents \cite{Vigoda, Vazirani} and sampling from binary contingency tables \cite{Stefankovi}. In those algorithms, the sparsity parameter grows with the problem size, while maintaining high precision is required.

scholarly journals Two component quantum walk in one-dimensional lattice with hopping imbalance

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Mrinal Kanti Giri ◽  
Suman Mondal ◽  
Bhanu Pratap Das ◽  
Tapan Mishra
Keyword(s):  
Interaction Strength ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Fast Particle ◽  
Particle Correlation ◽  
Dimensional Lattice ◽  
One Dimensional ◽  
Slow Particle ◽  
Two Component ◽  
Initial States

AbstractWe investigate the two-component quantum walk in one-dimensional lattice. We show that the inter-component interaction strength together with the hopping imbalance between the components exhibit distinct features in the quantum walk for different initial states. When the walkers are initially on the same site, both the slow and fast particles perform independent particle quantum walks when the interaction between them is weak. However, stronger inter-particle interactions result in quantum walks by the repulsively bound pair formed between the two particles. For different initial states when the walkers are on different sites initially, the quantum walk performed by the slow particle is almost independent of that of the fast particle, which exhibits reflected and transmitted components across the particle with large hopping strength for weak interactions. Beyond a critical value of the interaction strength, the wave function of the fast particle ceases to penetrate through the slow particle signalling a spatial phase separation. However, when the two particles are initially at the two opposite edges of the lattice, then the interaction facilitates the complete reflection of both of them from each other. We analyze the above mentioned features by examining various physical quantities such as the on-site density evolution, two-particle correlation functions and transmission coefficients.

scholarly journals Quantum speedup of Monte Carlo methods

2015 ◽  
Vol 471 (2181) ◽  
pp. 20150301 ◽  
Author(s):  
Ashley Montanaro
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Methods ◽  
Statistical Physics ◽  
Probability Distributions ◽  
General Setting ◽  
Quantum Algorithm ◽  
Quantum Walks ◽  
Partition Functions ◽  
Performance Bounds ◽  
Quantum Speedup

Monte Carlo methods use random sampling to estimate numerical quantities which are hard to compute deterministically. One important example is the use in statistical physics of rapidly mixing Markov chains to approximately compute partition functions. In this work, we describe a quantum algorithm which can accelerate Monte Carlo methods in a very general setting. The algorithm estimates the expected output value of an arbitrary randomized or quantum subroutine with bounded variance, achieving a near-quadratic speedup over the best possible classical algorithm. Combining the algorithm with the use of quantum walks gives a quantum speedup of the fastest known classical algorithms with rigorous performance bounds for computing partition functions, which use multiple-stage Markov chain Monte Carlo techniques. The quantum algorithm can also be used to estimate the total variation distance between probability distributions efficiently.

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