Quantum Implementation of Parrondo's Paradox

Quantum game theory [1–3] is a new field of science having its roots in both game theory and quantum information theory. For about a decade quantum computer scientists have been searching for new methods of quantum algorithm design. Thorough investigation of different quantum games may bring new insight into the development of quantum algorithms. It was shown that Grover’s algorithm [4] can be treated as an example of a quantum Parrondo’s paradox [5, 6]. Operators used in Grover’s algorithm can be treated as Parrondo games having separately zero expected values, however, if they are interwired, the expected value fluctuates. This effect is well known in Grover’s algorithm. Implementation of a quantum Parrondo’s paradox has been described in papers [7–10]. In this paper we present a new implementation scheme of a capitaldependent Parrondo’s paradoxical games on a relatively small number of qubits.