The role of measurement in the recurrence property of discrete timed quantum walks

2011 ◽  
Author(s):  
L. Kecskés ◽  
T. Kiss ◽  
M. Štefaňak ◽  
I. Jex
Keyword(s):  
Quantum Walks ◽  
Recurrence Property

scholarly journals Entanglement Assisted Transport of Two Walkers in Noisy Quantum Networks

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 36
Author(s):  
Maja Colautti ◽  
Filippo Caruso
Keyword(s):  
Quantum Walks ◽  
Communication Line ◽  
Transport Mechanisms ◽  
Spin Network ◽  
Quantum Networks ◽  
System Parameters ◽  
Transport Enhancement ◽  
State Transfer ◽  
Photosynthetic Complexes

Understanding the transport mechanisms and properties of complex networks is fundamental for the comprehension of a vast class of phenomena, from state transfer on a spin network to light-harvesting in photosynthetic complexes. It has been theoretically and experimentally demonstrated that noise can enhance transport when the system parameters are properly tuned, an effect known as noise-assisted transport (NAT). In this work we investigate the role of initial entanglement in the transfer efficiency of two walkers in a noisy network. By using the formalism of quantum walks, we define a range of small dephasing noise where initial site-entanglement provides transport enhancement and outperforms the NAT effect. Furthermore, we show two specific scenarios where entanglement-assisted transport can open faster channels for slow walkers and avoid a broken link in a communication line. These findings may be of potential interest for quantum technologies.

scholarly journals The role of coherence on two-particle quantum walks

Open Physics ◽  
2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Li-Hua Lu ◽  
Shan Zhu ◽  
You-Quan Li
Keyword(s):  
Correlation Function ◽  
Average Distance ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Mixed States ◽  
Initial State ◽  
Photon Correlation ◽  
Two Photon ◽  
Degree Of Coherence

AbstractWe investigate the dynamical properties of the two-boson quantum walk in systems with different degrees of coherence, and where the effect of the coherence on the two-boson quantum walk can be naturally introduced. A general analytical expression for the two-boson correlation function, for both pure states and mixed states, is given.We propose a possible two-photon quantum-walk scheme with a mixed initial state, and find that the twophoton correlation function and the average distance between two photons can be influenced by the initial photon distribution, the relative phase, or the degree of coherence. The propagation features of our numerical results can be explained by our analytical two-photon correlation function.

scholarly journals Quantum aspects of evolution: a contribution towards evolutionary explorations of genotype networks via quantum walks

2020 ◽  
Vol 17 (172) ◽  
pp. 20200567
Author(s):  
Diego Santiago-Alarcon ◽  
Horacio Tapia-McClung ◽  
Sergio Lerma-Hernández ◽  
Salvador E. Venegas-Andraca
Keyword(s):  
Open Systems ◽  
Biological Evolution ◽  
Enzyme Reaction ◽  
Reaction Rates ◽  
Quantum Walks ◽  
Quantum Decoherence ◽  
Network Search ◽  
Biological Phenomena ◽  
Starting Conditions

Quantum biology seeks to explain biological phenomena via quantum mechanisms, such as enzyme reaction rates via tunnelling and photosynthesis energy efficiency via coherent superposition of states. However, less effort has been devoted to study the role of quantum mechanisms in biological evolution. In this paper, we used transcription factor networks with two and four different phenotypes, and used classical random walks (CRW) and quantum walks (QW) to compare network search behaviour and efficiency at finding novel phenotypes between CRW and QW. In the network with two phenotypes, at temporal scales comparable to decoherence time T D , QW are as efficient as CRW at finding new phenotypes. In the case of the network with four phenotypes, the QW had a higher probability of mutating to a novel phenotype than the CRW, regardless of the number of mutational steps (i.e. 1, 2 or 3) away from the new phenotype. Before quantum decoherence, the QW probabilities become higher turning the QW effectively more efficient than CRW at finding novel phenotypes under different starting conditions. Thus, our results warrant further exploration of the QW under more realistic network scenarios (i.e. larger genotype networks) in both closed and open systems (e.g. by considering Lindblad terms).

scholarly journals QUANTUM WALKS ON GENERAL GRAPHS

2006 ◽  
Vol 04 (05) ◽  
pp. 791-805 ◽  
Author(s):  
VIV KENDON
Keyword(s):  
Continuous Time ◽  
Prior Information ◽  
Quantum Computer ◽  
Quantum Walk ◽  
Quantum Walks ◽  
General Graph ◽  
Resource Requirements ◽  
General Graphs

Quantum walks, both discrete (coined) and continuous time, on a general graph of N vertices with undirected edges are reviewed in some detail. The resource requirements for implementing a quantum walk as a program on a quantum computer are compared and found to be very similar for both discrete and continuous time walks. The role of the oracle, and how it changes if more prior information about the graph is available, is also discussed.

scholarly journals Quantum aspects of evolution: a contribution toward evolutionary explorations of genotype networks via quantum walks

2020 ◽  
Author(s):  
Diego Santiago-Alarcon ◽  
Horacio Tapia-McClung ◽  
Sergio Lerma-Hernández ◽  
Salvador E. Venegas-Andraca
Keyword(s):  
Open Systems ◽  
Biological Evolution ◽  
Enzyme Reaction ◽  
Reaction Rates ◽  
Quantum Walks ◽  
Quantum Decoherence ◽  
Network Search ◽  
Biological Phenomena ◽  
Starting Conditions

AbstractQuantum biology seeks to explain biological phenomena via quantum mechanisms, such as enzyme reaction rates via tunneling and photosynthesis energy efficiency via coherent superposition of states. However, less effort has been devoted to study the role of quantum mechanisms in biological evolution. In this paper, we used transcription factor networks with two and four different phenotypes, and used classical random walks (CRW) and quantum walks (QW) to compare network search behavior and efficiency at finding novel phenotypes between CRW and QW. In the network with two phenotypes, at temporal scales comparable to decoherence time TD, QW are as efficient as CRW at finding new phenotypes. In the case of the network with four phenotypes, the QW had a higher probability of mutating to a novel phenotype than the CRW, regardless of the number of mutational steps (i.e., 1, 2 or 3) away from the new phenotype. Before quantum decoherence, the QW probabilities become higher turning the QW effectively more efficient than CRW at finding novel phenotypes under different starting conditions. Thus, our results warrant further exploration of the QW under more realistic network scenarios (i.e., larger genotype networks) in both closed and open systems (e.g., by considering Lindblad terms).

scholarly journals Counterintuitive role of geometry in transport by quantum walks

2020 ◽  
Vol 101 (3) ◽  
Author(s):  
J. Mareš ◽  
J. Novotný ◽  
M. Štefaňák ◽  
I. Jex
Keyword(s):  
Quantum Walks

Quantum optical implementation of open quantum walks

2014 ◽  
Vol 12 (02) ◽  
pp. 1461010 ◽  
Author(s):  
Ilya Sinayskiy ◽  
Francesco Petruccione
Keyword(s):  
Cavity Mode ◽  
Quantum Walks ◽  
Optical Scheme ◽  
Fock States ◽  
Open Quantum ◽  
Effective Dynamics ◽  
Level Atom ◽  
Physical Implementation ◽  
Quantum Optical

A quantum optical implementation of the recently proposed open quantum walks (OQWs) is suggested. In the presented quantum optical scheme a two level atom plays the role of the "walker" and the Fock states of the cavity mode correspond to the lattice sites of the OQW. Using the small unitary rotations approach the effective dynamics of the system is shown to be an OQW. The presented scheme allows for a simple physical implementation of the OQW formalism, but it can be extended to create more diverse OQWs.

scholarly journals Gravitationally induced entanglement dynamics between two quantum walkers

2021 ◽  
Vol 81 (5) ◽  
Author(s):  
Himanshu Badhani ◽  
C. M. Chandrashekar
Keyword(s):  
Potential Role ◽  
Gravitational Interaction ◽  
Quantum Walk ◽  
Quantum Systems ◽  
Quantum Walks ◽  
Quantum Mechanical ◽  
Entanglement Dynamics ◽  
Position Space ◽  
Entanglement Generation

AbstractQuantum walk is a synonym for multi-path interference and faster spread of a particle in a superposition of position space. We study the effects of a quantum mechanical interaction modeled to mimic quantum mechanical gravitational interaction between the two states of the walkers. The study has been carried out to investigate the entanglement generation between the two quantum walkers that do not otherwise interact. We see that the states do in fact get entangled more and more as the quantum walks unfold, and there is an interesting dependence of entanglement generation on the mass of the two particles performing the walks. With the introduction of noise into the dynamics, we also show the sensitivity of entanglement between the two walkers on the noise introduced in one of the walks. The signature of quantum effects due to gravitational interactions highlights the potential role of quantum systems in probing the nature of gravity.

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