arXiv:quant-ph/0203043

Parrondo Games and Quantum Algorithms

Chiu Fan Lee, Neil F. Johnson

Published Mar 10, 2002• 14 citations

Abstract

We pursue the possible connections between classical games and quantum computation. The Parrondo game is one in which a random combination of two losing games produces a winning game. We introduce novel realizations of this Parrondo effect in which the player can `win' via random reflections and rotations of the state-vector, and connect these to known quantum algorithms.

DOI: 10.48550/arxiv.quant-ph/0203043

Related papers

Quantum models of Parrondo's games

Adrian P. Flitney, Derek Abbott

It is possible to have two games that are losing when played in isolation but that, because of some form of feedback, produce a winning game when played alternately or even in a random mixture. This effect is known as Parrondo's paradox. Quantum mechanics provides novel methods of combining two games through interference and entanglement. Two models of quantum Parrondo's games have been published and these are reviewed here. We speculate on a model of a quantum Parrondo's game using entanglement. Such games could find a use in the development of algorithms for quantum computers.

Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIENov 1, 20020 citations

Study of Parrondo's paradox regions in one-dimensional quantum walks

Munsif Jan, Xiao-Ye Xu, Wang Qin Qin +4 more

The well-known counterintuitive phenomenon, where the combination of unfavorable situations can establish favorable ones, is called Parrondo's paradox. Here, we study one-dimensional discrete-time quantum walks, manipulating two different coins (two-state) operators representing two losing games A and B, respectively, to create the Parrondo effect in the quantum domain. We exhibit that games A and B are losing games when played individually but could produce a winning expectation when played alternatively for a particular sequence of the different periods. Moreover, we also analyze the relationships between Parrondo's games and quantum entanglement in our scheme. Along with the applications of different kinds of quantum walks, our outcomes potentially encourage the development of new quantum algorithms.

Jun 30, 20202 citations

Territories of Parrondo's paradox and its relation with entanglement in quantum walks

Munsif Jan, Khan, Niaz Ali, Gao Xianlong

Parrondo's paradox is a well-known counterintuitive phenomenon, where the combination of unfavorable situations can establish favorable ones. In this paper, we study one-dimensional discrete-time quantum walks, manipulating two different coins (two-state) operators representing two losing games A and B, respectively, to create the Parrondo effect in the quantum domain. We exhibit that games A and B are losing games when played individually but could produce a winning expectation when played alternatively for a particular sequence of different periods for distinct choices of the relative phase. Furthermore, we investigate the regimes of the relative phase of the initial state of coins where Parrondo games exist. Moreover, we also analyze the relationships between Parrondo's game and quantum entanglement and show regimes where the Parrondo sequence may generate a maximal entangler state in our scheme. Along with the applications of different kinds of quantum walks, our outcomes potentially encourage the development of new quantum algorithms.

arXiv:2006.16585Jun 30, 20200 citations

Quantum Parrondo's game with random strategies¶

J. Košík, Jarosław Adam Miszczak, V. Bužek∥

We present a quantum implementation of Parrondo's game with randomly switched strategies using (1) a quantum walk as a source of ‘randomness’ and (2) a completely positive (CP) map as a randomized evolution. The game exhibits the same paradox as in the classical setting where a combination of two losing strategies might result in a winning strategy. We show that the CP-map scheme leads to significantly lower net gain than the quantum-walk scheme.

arXiv:0704.2937Journal of Modern OpticsSep 10, 200721 citations

Parrondo effect in quantum coin-toss simulations

Joel Weijia Lai, Kang Hao Cheong

Game A + Game B = Game C. Parrondo's games follow this basic structure where A and B are losing games and C is a winning game-a phenomenon called Parrondo's paradox. These games can take on a wider class of definitions and exhibit these paradoxical results. In this paper, we show three paradoxical cases. (i) The successive "tossing" of a single fair quantum coin gives a biased result, a previously known result. (ii) The random tossing of two quantum coins, each with successive biased expectations, gives an average random walk position of approximately zero. (iii) The sequential periodic tossing of two quantum coins, each with successive negative biased expectations, gives an average random walk with positive expectation. Using these results, we then propose a protocol for identifying and classifying quantum operations that span the same Hilbert space for a two-level quantum system.

Physical review. EMay 18, 202035 citations

QUANTUM PARRONDO'S GAMES CONSTRUCTED BY QUANTUM RANDOM WALKS

Min Li, Yong-Sheng Zhang, Guang‐Can Guo

We construct a Parrondo's game using discrete-time quantum walks (DTQWs). Two losing games are represented by two different coin operators. By mixing the two coin operators UA(αA, βA, γA) and UB(αB, βB, γB), we may win the game. Here, we mix the two games in position instead of time. With a number of selections of the parameters, we can win the game with sequences ABB, ABBB, etc. If we set βA = 45°, γA = 0, αB = 0, βB = 88°, we find game 1 with [Formula: see text], [Formula: see text] will win and get the most profit. If we set αA = 0, βA = 45°, αB = 0, βB = 88° and game 2 with [Formula: see text], [Formula: see text] will win most. Game 1 is equivalent to game 2 with changes in sequences and steps. But at large enough steps, the game will lose at last. Parrondo's paradox does not exist in classical situation with our model.

Fluctuation and Noise LettersOct 22, 201319 citations