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

Quantum Walks on Finite Graphs

2013 ◽  
pp. 85-120
Author(s):  
Renato Portugal
Keyword(s):  
Quantum Walks ◽  
Finite Graphs

scholarly journals A remark on zeta functions of finite graphs via quantum walks

2014 ◽  
Vol 6 (1) ◽  
Author(s):  
Yusuke Higuchi ◽  
Norio Konno ◽  
Iwao Sato ◽  
Etsuo Segawa
Keyword(s):  
Zeta Functions ◽  
Quantum Walks ◽  
Finite Graphs

scholarly journals Asymptotic entanglement in quantum walks from delocalized initial states

2017 ◽  
Vol 16 (9) ◽  
Author(s):  
Alexandre C. Orthey ◽  
Edgard P. M. Amorim
Keyword(s):  
Quantum Walks ◽  
Initial States

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 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.

Localization of quantum walks on finite graphs

2016 ◽  
Vol 25 (12) ◽  
pp. 120303
Author(s):  
Yang-Yi Hu ◽  
Ping-Xing Chen
Keyword(s):  
Quantum Walks ◽  
Finite Graphs

scholarly journals Relation between Quantum Walks with Tails and Quantum Walks with Sinks on Finite Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1169
Author(s):  
Norio Konno ◽  
Etsuo Segawa ◽  
Martin Štefaňák
Keyword(s):  
Graph Theory ◽  
Random Walk ◽  
Survival Probability ◽  
Quantum Walks ◽  
Time Limit ◽  
Finite Graphs ◽  
Long Time

We connect the Grover walk with sinks to the Grover walk with tails. The survival probability of the Grover walk with sinks in the long time limit is characterized by the centered generalized eigenspace of the Grover walk with tails. The centered eigenspace of the Grover walk is the attractor eigenspace of the Grover walk with sinks. It is described by the persistent eigenspace of the underlying random walk whose support has no overlap to the boundaries of the graph and combinatorial flow in graph theory.

scholarly journals Controlling discrete quantum walks: coins and initial states

2003 ◽  
Vol 5 ◽  
pp. 83-83 ◽  
Author(s):  
Ben Tregenna ◽  
Will Flanagan ◽  
Rik Maile ◽  
Viv Kendon
Keyword(s):  
Quantum Walks ◽  
Initial States

scholarly journals Creating cat states in one-dimensional quantum walks using delocalized initial states

2016 ◽  
Vol 18 (9) ◽  
pp. 093025 ◽  
Author(s):  
Wei-Wei Zhang ◽  
Sandeep K Goyal ◽  
Fei Gao ◽  
Barry C Sanders ◽  
Christoph Simon
Keyword(s):  
Quantum Walks ◽  
One Dimensional ◽  
Initial States ◽  
Cat States
Sign in / Sign up

Export Citation Format

Share Document