scholarly journals Improved upper bounds for the hitting times of quantum walks

2021 ◽  
Vol 104 (3) ◽  
Author(s):  
Yosi Atia ◽  
Shantanav Chakraborty
Keyword(s):  
Upper Bounds ◽  
Quantum Walks ◽  
Hitting Times

scholarly journals On training a classifier of hitting times for quantum walks

2020 ◽  
Author(s):  
Alexey A. Melnikov ◽  
Leonid E. Fedichkin ◽  
Alexander Alodjants
Keyword(s):  
Quantum Walks ◽  
Hitting Times

scholarly journals Quantum walks with infinite hitting times

2006 ◽  
Vol 74 (4) ◽  
Author(s):  
Hari Krovi ◽  
Todd A. Brun
Keyword(s):  
Quantum Walks ◽  
Hitting Times

A simulator for discrete quantum walks on lattices

2017 ◽  
Vol 28 (04) ◽  
pp. 1750055
Author(s):  
J. Rodrigues ◽  
N. Paunković ◽  
P. Mateus
Keyword(s):  
Average Distance ◽  
Joint Probability ◽  
Quantum Walks ◽  
Hitting Times ◽  
Joint Probability Distribution ◽  
Two Dimensional ◽  
Line Lattice ◽  
Various Boundary Conditions ◽  
Open Circular ◽  
Particle Localization

In this paper, we present a simulator for two-particle quantum walks on the line and one-particle on a two-dimensional squared lattice. It can be used to investigate the equivalence between the two cases (one- and two-particle walks) for various boundary conditions (open, circular, reflecting, absorbing and their combinations). For the case of a single walker on a two-dimensional lattice, the simulator can also implement the Möbius strip. Furthermore, other topologies for the walker are also simulated by the proposed tool, like certain types of planar graphs with degree up to 4, by considering missing links over the lattice. The main purpose of the simulator is to study the genuinely quantum effects on the global properties of the two-particle joint probability distribution on the entanglement between the walkers/axis. For that purpose, the simulator is designed to compute various quantities such as: the entanglement and classical correlations, (classical and quantum) mutual information, the average distance between the two walkers, different hitting times and quantum discord. These quantities are of vital importance in designing possible algorithmic applications of quantum walks, namely in search, 3-SAT problems, etc. The simulator can also implement the static partial measurements of particle(s) positions and dynamic breaking of the links between certain nodes, both of which can be used to investigate the effects of decoherence on the walker(s). Finally, the simulator can be used to investigate the dynamic Anderson-like particle localization by varying the coin operators of certain nodes on the line/lattice. We also present some illustrative and relevant examples of one- and two-particle quantum walks in various scenarios. The tool was implemented in C and is available on-line at http://qwsim.weebly.com/ .

scholarly journals Hitting times of local and global optima in genetic algorithms with very high selection pressure

2017 ◽  
Vol 27 (3) ◽  
pp. 323-339 ◽  
Author(s):  
Anton Eremeev
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Selection Pressure ◽  
Upper Bounds ◽  
Hitting Times ◽  
Global Optima ◽  
High Selection ◽  
First Hitting Times ◽  
Very High

The paper is devoted to upper bounds on the expected first hitting times of the sets of local or global optima for non-elitist genetic algorithms with very high selection pressure. The results of this paper extend the range of situations where the upper bounds on the expected runtime are known for genetic algorithms and apply, in particular, to the Canonical Genetic Algorithm. The obtained bounds do not require the probability of fitness-decreasing mutation to be bounded by a constant which is less than one.

scholarly journals Hitting statistics from quantum jumps

Quantum ◽  
2017 ◽  
Vol 1 ◽  
pp. 19
Author(s):  
A. Chia ◽  
T. Paterek ◽  
L. C. Kwek
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Quantum Walks ◽  
Hitting Time ◽  
Hitting Times ◽  
Unitary Evolution ◽  
Quantum Jumps ◽  
Quantum Jump ◽  
Open Quantum ◽  
Starting Point

We define the hitting time for a model of continuous-time open quantum walks in terms of quantum jumps. Our starting point is a master equation in Lindblad form, which can be taken as the quantum analogue of the rate equation for a classical continuous-time Markov chain. The quantum jump method is well known in the quantum optics community and has also been applied to simulate open quantum walks in discrete time. This method however, is well-suited to continuous-time problems. It is shown here that a continuous-time hitting problem is amenable to analysis via quantum jumps: The hitting time can be defined as the time of the first jump. Using this fact, we derive the distribution of hitting times and explicit exressions for its statistical moments. Simple examples are considered to illustrate the final results. We then show that the hitting statistics obtained via quantum jumps is consistent with a previous definition for a measured walk in discrete time [Phys. Rev. A 73, 032341 (2006)] (when generalised to allow for non-unitary evolution and in the limit of small time steps). A caveat of the quantum-jump approach is that it relies on the final state (the state which we want to hit) to share only incoherent edges with other vertices in the graph. We propose a simple remedy to restore the applicability of quantum jumps when this is not the case and show that the hitting-time statistics will again converge to that obtained from the measured discrete walk in appropriate limits.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

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