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 Probability elicitation using geostatistics in hydrocarbon exploration

2021 ◽  
Author(s):  
André Luís Morosov ◽  
Reidar Brumer Bratvold
Keyword(s):  
Value Creation ◽  
Decision Process ◽  
Conceptual Models ◽  
Joint Probability ◽  
Decision Makers ◽  
Hydrocarbon Exploration ◽  
Joint Probability Distribution ◽  
Proof Of Concept ◽  
Geological Information ◽  
Decision Supporting

AbstractThe exploratory phase of a hydrocarbon field is a period when decision-supporting information is scarce while the drilling stakes are high. Each new prospect drilled brings more knowledge about the area and might reveal reserves, hence choosing such prospect is essential for value creation. Drilling decisions must be made under uncertainty as the available geological information is limited and probability elicitation from geoscience experts is key in this process. This work proposes a novel use of geostatistics to help experts elicit geological probabilities more objectively, especially useful during the exploratory phase. The approach is simpler, more consistent with geologic knowledge, more comfortable for geoscientists to use and, more comprehensive for decision-makers to follow when compared to traditional methods. It is also flexible by working with any amount and type of information available. The workflow takes as input conceptual models describing the geology and uses geostatistics to generate spatial variability of geological properties in the vicinity of potential drilling prospects. The output is stochastic realizations which are processed into a joint probability distribution (JPD) containing all conditional probabilities of the process. Input models are interactively changed until the JPD satisfactory represents the expert’s beliefs. A 2D, yet realistic, implementation of the workflow is used as a proof of concept, demonstrating that even simple modeling might suffice for decision-making support. Derivative versions of the JPD are created and their effect on the decision process of selecting the drilling sequence is assessed. The findings from the method application suggest ways to define the input parameters by observing how they affect the JPD and the decision process.

scholarly journals Quantum sensing of noises in one and two dimensional quantum walks

2017 ◽  
Vol 7 (1) ◽  
Author(s):  
Tian Chen ◽  
Xiong Zhang ◽  
Xiangdong Zhang
Keyword(s):  
Quantum Walks ◽  
Two Dimensional ◽  
Quantum Sensing

scholarly journals A TWO-CLASS RETRIAL SYSTEM WITH COUPLED ORBIT QUEUES

2017 ◽  
Vol 31 (2) ◽  
pp. 139-179 ◽  
Author(s):  
Ioannis Dimitriou
Keyword(s):  
Performance Metrics ◽  
Kernel Method ◽  
Length Distribution ◽  
Probability Generating Function ◽  
Joint Probability ◽  
Joint Probability Distribution ◽  
Single Server ◽  
Method Performance ◽  
Service Station ◽  
Queue Length Distribution

We consider a single server system accepting two types of retrial customers, which arrive according to two independent Poisson streams. The service station can handle at most one customer, and in case of blocking, typeicustomer,i=1, 2, is routed to a separate typeiorbit queue of infinite capacity. Customers from the orbits try to access the server according to the constant retrial policy. We consider coupled orbit queues, and thus, when both orbit queues are non-empty, the orbit queueitries to re-dispatch a blocked customer of typeito the main service station after an exponentially distributed time with rate μi. If an orbit queue empties, the other orbit queue changes its re-dispatch rate from μito$\mu_{i}^{\ast}$. We consider both exponential and arbitrary distributed service requirements, and show that the probability generating function of the joint stationary orbit queue length distribution can be determined using the theory of Riemann (–Hilbert) boundary value problems. For exponential service requirements, we also investigate the exact tail asymptotic behavior of the stationary joint probability distribution of the two orbits with either an idle or a busy server by using the kernel method. Performance metrics are obtained, computational issues are discussed and a simple numerical example is presented.

scholarly journals Quantum walks and elliptic integrals

2010 ◽  
Vol 20 (6) ◽  
pp. 1091-1098 ◽  
Author(s):  
NORIO KONNO
Keyword(s):  
Random Walk ◽  
Generating Function ◽  
Elliptic Integral ◽  
Quantum Walk ◽  
Quantum Walks ◽  
Elliptic Integrals ◽  
Two Dimensional ◽  
One Dimensional ◽  
Similar Expression ◽  
Return Probability

Pólya showed in his 1921 paper that the generating function of the return probability for a two-dimensional random walk can be written in terms of an elliptic integral. In this paper we present a similar expression for a one-dimensional quantum walk.

Sign in / Sign up

Export Citation Format

Share Document