Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Physical Review A

Quantumlike bits and logic gates based on classical oscillators

Yuri F. Orlov

Published Nov 27, 2002• 3 citations
Publisher

Abstract

It is shown how a classical system can possess such quantum properties as indeterminism, interference of probabilities, unitary transformations, wave functions, and noncommuting operators, and be used in quantumlike computations.
DOI
10.1103/physreva.66.052324

Related papers

Quantum Computers

S. Rajasekar, R. Velusamy

In quantum computers a unitary transformation is applied to a given initial state of a set of qubits through several quantum gates. Tests were conducted using Grover's algorithm and implemented in a variety of different ways on the publically available IBM quantum computers. Essentially, quantum computers manipulate quantum states instead of classical bits. Quantum information can be represented by the elementary units called quantum bits abbreviated as qubits or qbits. This chapter discusses the fundamental properties of quantum systems that are relevant to information processing. Quantum computation needs something much more than that quantum parallelism to be useful. This is achieved in Deutsch's algorithm which combines quantum parallelism with interference. One can simulate a classical circuit using a quantum circuit. That is, it is possible to perform classical computations on quantum computers. But the advantage of quantum computing is that powerful functions may be computed by making use of quantum parallelism, the fundamental feature of many quantum algorithms.

CRC Press eBooks•Oct 5, 2022•0 citations

Comparison of Classical Logic Gates with Quantum Logic Gates

Liang Liu

In this article,we describe the differences between classical logic gates and quantum logic gates,and explain the characteristics of quantum computation,the strong power of the quantum algorithm,and the problem of the realization of quantum logic gates.

Computer Engineering and Science•Jan 1, 2005•0 citations

Quantumlike representation of extensive form games: Probabilistic aspects

Andrei Yu. Khrennikov

We consider an application of the mathematical formalism of quantum mechanics outside physics, namely, to game theory. We present a simple game between macroscopic players, say, Alice and Bob (or in a more complex form—Alice, Bob, and Cecilia), which can be represented in the quantumlike (QL) way—by using a complex probability amplitude (game’s “wave function”) and noncommutative operators. The crucial point is that games under consideration are so-called extensive form games. Here the order of actions of players is important; such a game can be represented by the tree of actions. The QL probabilistic behavior of players is a consequence of incomplete information (which is available to, e.g., Bob) about the previous action of Alice. In general one could not construct a classical probability space underlying a QL game. This can happen even in a QL game with two players. In a QL game with three players Bell’s inequality can be violated. The most natural probabilistic description is given by the so-called contextual probability theory completed by the frequency definition of probability.

arXiv:0705.1260•Journal of Mathematical Physics•Jul 1, 2007•6 citations

Quantum information with quantumlike bits

Graziano Amati, Gregory D. Scholes

In previous work we proposed a construction of quantum-like bits that could endow a large synchronizing classical system, for example, of oscillators, with quantum-like function that is not compromised by decoherence. In the present paper we investigate further this platform of quantum-like states. First, we discuss a general protocol on how to construct classical synchronizing networks that allow for emergent states. We then study how gates can be implemented on those states. This suggests the possibility of quantum-like information processing on a special class of many-body classical systems. Finally, we show that our approach allows for non-Kolmogorov interference, a feature that separates our model from a classical probabilistic system. This paper aims to explore the mathematical structure of quantum-like resources distilled from classical synchronizing systems and shows how arbitrary gates can be implemented by manipulating many-body correlations.

arXiv:2408.06485•Physical Review A•Jun 2, 2025•10 citations

Quantum logic as a consequence of realistic measurements on deterministic systems

H. D. Doebner, W. Lücke

It is shown why, from the deterministic point of view, quantum logic and not classical logic is the appropriate language for describing realistic measurements.

Journal of Mathematical Physics•Jan 1, 1991•4 citations

Qubits, Gates, and Circuits

Eduardo R. Mucciolo

Before we start to discuss quantum bits (“qubits” for short), let us spend some time reviewing classical bits, which we will simply call bits, and the types of operations one can perform with them.

CRC Press eBooks•Aug 6, 2025•0 citations
In quantum computers a unitary transformation is applied to a given initial state of a set of qubits through several quantum gates. Tests were conducted using Grover's algorithm and implemented in a variety of different ways on the publically available IBM quantum computers. Essentially, quantum computers manipulate quantum states instead of classical bits. Quantum information can be represented by the elementary units called quantum bits abbreviated as qubits or qbits. This chapter discusses the fundamental properties of quantum systems that are relevant to information processing. Quantum computation needs something much more than that quantum parallelism to be useful. This is achieved in Deutsch's algorithm which combines quantum parallelism with interference. One can simulate a classical circuit using a quantum circuit. That is, it is possible to perform classical computations on quantum computers. But the advantage of quantum computing is that powerful functions may be computed by making use of quantum parallelism, the fundamental feature of many quantum algorithms.
We consider an application of the mathematical formalism of quantum mechanics outside physics, namely, to game theory. We present a simple game between macroscopic players, say, Alice and Bob (or in a more complex form—Alice, Bob, and Cecilia), which can be represented in the quantumlike (QL) way—by using a complex probability amplitude (game’s “wave function”) and noncommutative operators. The crucial point is that games under consideration are so-called extensive form games. Here the order of actions of players is important; such a game can be represented by the tree of actions. The QL probabilistic behavior of players is a consequence of incomplete information (which is available to, e.g., Bob) about the previous action of Alice. In general one could not construct a classical probability space underlying a QL game. This can happen even in a QL game with two players. In a QL game with three players Bell’s inequality can be violated. The most natural probabilistic description is given by the so-called contextual probability theory completed by the frequency definition of probability.
In previous work we proposed a construction of quantum-like bits that could endow a large synchronizing classical system, for example, of oscillators, with quantum-like function that is not compromised by decoherence. In the present paper we investigate further this platform of quantum-like states. First, we discuss a general protocol on how to construct classical synchronizing networks that allow for emergent states. We then study how gates can be implemented on those states. This suggests the possibility of quantum-like information processing on a special class of many-body classical systems. Finally, we show that our approach allows for non-Kolmogorov interference, a feature that separates our model from a classical probabilistic system. This paper aims to explore the mathematical structure of quantum-like resources distilled from classical synchronizing systems and shows how arbitrary gates can be implemented by manipulating many-body correlations.