Scouring Parrondo's Paradox in Discrete-Time Quantum Walks
- URL: http://arxiv.org/abs/2401.08983v1
- Date: Wed, 17 Jan 2024 05:31:02 GMT
- Title: Scouring Parrondo's Paradox in Discrete-Time Quantum Walks
- Authors: Gururaj Kadiri
- Abstract summary: Parrondo's paradox is a phenomenon where a combination of losing strategies becomes a winning strategy.
Unlike traditional quantum steps that allow for equal magnitude forward and backward strides based on the outcome of the coin-toss, the steps employed here permit the strides to be of unequal magnitude.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We propose a quantum game based on coin-based quantum walks. Given a quantum
walk and a Hermitian operator on the coin-position composite space, winning
this game involves choosing an initial coin state such that the given quantum
walk leads to a composite state in which the expectation value of the given
Hermitian operator is greater than a certain value. Parrondo's paradox is a
phenomenon where a combination of losing strategies becomes a winning strategy.
We give a deterministic scheme for identifying Parrondo's paradox in our game,
in the sense that, given a collection of distinct quantum steps, we identify
initial coin states which happen to be losing states for all quantum walks
comprising solely of these steps individually, but turn out to be winning
states for a quantum walk comprising of all the given steps taken in a
sequence. Unlike traditional quantum steps that allow for equal magnitude
forward and backward strides based on the outcome of the coin-toss, the steps
of the quantum walks employed here, though still contingent upon coin-toss,
permit the strides to be of unequal magnitude, and not necessarily in opposite
directions. We believe the results presented here will contribute to a deeper
understanding of evolution of expectation values of observables in quantum
walks, and facilitate the development of novel quantum algorithms.
Related papers
- Parrondo's paradox in quantum walks with inhomogeneous coins [0.0]
Parrondo's paradox is a counterintuitive phenomenon where two losing strategies combine to produce a winning outcome.
In this study, we investigate the manifestation of Parrondo's paradox in discrete-time quantum walks.
arXiv Detail & Related papers (2024-07-23T15:14:12Z) - Realizing fracton order from long-range quantum entanglement in programmable Rydberg atom arrays [45.19832622389592]
Storing quantum information requires battling quantum decoherence, which results in a loss of information over time.
To achieve error-resistant quantum memory, one would like to store the information in a quantum superposition of degenerate states engineered in such a way that local sources of noise cannot change one state into another.
We show that this platform also allows to detect and correct certain types of errors en route to the goal of true error-resistant quantum memory.
arXiv Detail & Related papers (2024-07-08T12:46:08Z) - A computational test of quantum contextuality, and even simpler proofs of quantumness [43.25018099464869]
We show that an arbitrary contextuality game can be compiled into an operational "test of contextuality" involving a single quantum device.
Our work can be seen as using cryptography to enforce spatial separation within subsystems of a single quantum device.
arXiv Detail & Related papers (2024-05-10T19:30:23Z) - Polyander visualization of quantum walks [0.0]
We investigate quantum walks which play an important role in the modelling of many phenomena.
The detailed and thorough description is given to the discrete quantum walks on a line, where the total quantum state consists of quantum states of the walker and the coin.
arXiv Detail & Related papers (2023-11-01T10:01:08Z) - A vertical gate-defined double quantum dot in a strained germanium
double quantum well [48.7576911714538]
Gate-defined quantum dots in silicon-germanium heterostructures have become a compelling platform for quantum computation and simulation.
We demonstrate the operation of a gate-defined vertical double quantum dot in a strained germanium double quantum well.
We discuss challenges and opportunities and outline potential applications in quantum computing and quantum simulation.
arXiv Detail & Related papers (2023-05-23T13:42:36Z) - Simple Tests of Quantumness Also Certify Qubits [69.96668065491183]
A test of quantumness is a protocol that allows a classical verifier to certify (only) that a prover is not classical.
We show that tests of quantumness that follow a certain template, which captures recent proposals such as (Kalai et al., 2022) can in fact do much more.
Namely, the same protocols can be used for certifying a qubit, a building-block that stands at the heart of applications such as certifiable randomness and classical delegation of quantum computation.
arXiv Detail & Related papers (2023-03-02T14:18:17Z) - Maximal entanglement between a quantum walker and her quantum coin for
the third step and beyond regardless of the initial state [0.0]
We study maximal entanglement generation between a walker and her coin via a discrete-time quantum walk.
We solve maximal-entanglement generation as an optimization problem with quantum process fidelity as the cost function.
We demonstrate a ten-step quantum walk with such coin sequences and thereby show the desired high-dimensional bipartite entanglement.
arXiv Detail & Related papers (2022-09-05T02:24:29Z) - Steered discrete-time quantum walks for engineering of quantum states [0.0]
We analyze the strengths and limitations of steered discrete time quantum walks in generating quantum states of bipartite quantum systems.
We show that not all quantum states in the composite space are accessible through quantum walks, even under the most generalized definition of a quantum step.
arXiv Detail & Related papers (2022-05-10T13:14:25Z) - Quantum walk processes in quantum devices [55.41644538483948]
We study how to represent quantum walk on a graph as a quantum circuit.
Our approach paves way for the efficient implementation of quantum walks algorithms on quantum computers.
arXiv Detail & Related papers (2020-12-28T18:04:16Z) - Demonstration of quantum brachistochrones between distant states of an
atom [0.0]
We show fast coherent transport of an atomic wave packet over a distance of 15 times its size.
Results shed light upon a fundamental limit of quantum state dynamics and are expected to find relevant applications in quantum sensing and quantum computing.
arXiv Detail & Related papers (2020-09-04T15:00:11Z) - Jumptime unraveling of Markovian open quantum systems [68.8204255655161]
We introduce jumptime unraveling as a distinct description of open quantum systems.
quantum jump trajectories emerge, physically, from continuous quantum measurements.
We demonstrate that quantum trajectories can also be ensemble-averaged at specific jump counts.
arXiv Detail & Related papers (2020-01-24T09:35:32Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.