Related Experiment Videos
Recurrence and Pólya number of quantum walks
1Department of Physics, FJFI CVUT v Praze, Brehová 7, 115 19 Praha 1 - Staré Mesto, Czech Republic.
Physical Review Letters
|February 1, 2008
Summary
Quantum walks can be recurrent or transient, unlike classical walks. Their recurrence probability depends on topology, coin, and initial state, allowing control over walk behavior.
Area of Science:
- Quantum Physics
- Complex Systems
Background:
- Classical random walks exhibit recurrence probabilities characteristic of their dimension.
- Quantum walks introduce unique behaviors due to superposition and interference.
Purpose of the Study:
- Analyze recurrence probability (Pólya number) for d-dimensional unbiased quantum walks.
- Derive conditions for quantum walk recurrence and localization.
- Investigate factors influencing quantum walk recurrence.
Main Methods:
- Mathematical analysis of quantum walk dynamics.
- Derivation of a sufficient condition for recurrence.
- Exploration of the Pólya number in quantum walks.
Main Results:
- A sufficient condition for quantum walk recurrence is established.
- A criterion for quantum walk localization is identified.
- Quantum walk recurrence depends on topology, coin, and initial state, unlike classical walks.
Conclusions:
- Quantum walk recurrence is tunable via initial state, coin choice, and topology.
- This tunability allows switching between recurrent and transient behaviors.
- Findings offer new insights into quantum walk dynamics and localization phenomena.
Related Concept Videos
02:32The de Broglie Wavelength
In the macroscopic world, objects that are large enough to be seen by the naked eye follow the rules of classical physics. A billiard ball moving on a table will behave like a particle; it will continue traveling in a straight line unless it collides with another ball, or it is acted on by some other force, such as friction. The ball has a well-defined position and velocity or well-defined momentum, p = mv, which is defined by mass m and velocity v at any given moment. This is the typical...
02:43Quantum Numbers
It is said that the energy of an electron in an atom is quantized; that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels.
01:17Wald-Wolfowitz Runs Test I
The Wald-Wolfowitz test, also known as the runs test, is a nonparametric statistical test used to assess the randomness of a sequence of two different types of elements (e.g., positive/negative values, successes/failures). It examines whether the order of the elements in a sequence is random or if there is a pattern or trend present. This nonparametric test applies to any ordered data despite the population and sample data distribution, even if a higher sample size is available.
The test works...
The test works...
01:15Binomial Probability Distribution
A binomial distribution is a probability distribution for a procedure with a fixed number of trials, where each trial can have only two outcomes.
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
The outcomes of a binomial experiment fit a binomial probability distribution. A statistical experiment can be classified as a binomial experiment if the following conditions are met:
There are a fixed number of trials. Think of trials as repetitions of an experiment. The letter n denotes the number of trials.
There are only two possible outcomes,...
02:45The Quantum-Mechanical Model of an Atom
Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
01:09Poisson Probability Distribution
A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.
The...
The...