Parrondo's paradox in quantum walks with deterministic aperiodic sequence of coins
Zbigniew Walczak, Jarosław H. Bauer
Abstract
Parrondo's effect is a well-known apparent paradox where a combination of biased random walks displays a counterintuitive reversal of the bias direction. We show that Parrondo's effect can occur not only in the case of one-dimensional discrete quantum walks with random or deterministic periodic sequence of two- or multistate quantum coins but also in the case of one-dimensional discrete quantum walks with deterministic aperiodic sequence of two-state quantum coins. Moreover, we show how Parrondo's effect affects the time evolution of the walker-coin quantum entanglement.
Topics & Concepts
Quantum walkAperiodic graphSequence (biology)CounterintuitiveMathematicsQuantumRandom walkStatistical physicsQuantum algorithmDiscrete mathematicsQuantum operationDiscrete time and continuous timeQuantum channelQuantum computerQuantum systemSimple (philosophy)Random sequenceCombinatoricsQuantum mechanicsQuantum discordQuantum phase estimation algorithmQuantum processQuantum Computing Algorithms and ArchitectureQuantum-Dot Cellular AutomataQuantum Mechanics and Applications