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

Applied Mathematics & Information Sciences

Irreversibility in Quantum Computational Logics

Giuseppe Sergioli, Roberto Giuntini, Francesco Paoli

Published Jan 1, 2011• 6 citations
OpenAlex

Abstract

In this paper we discuss an approach to quantum computation where the basic information units (qubits and quregisters) are replaced by density operators and the restriction to unitary operators as logical gates is lifted through the introduction of the more general concept of quantum operation ( [17], [1]). This perspective is especially suited to provide a physical description of open systems. In particular, we illustrate the advantages of this approach over the standard one and show that it can account for two importantirreversibletransformationsalreadyconsideredintheliterature: theirreversible conjunction IAND and the fuzzy-like Łukasiewicz disjunction⊕.

Related papers

Quantum Computational Fuzzy Logics

Cesarino Bertini, Roberto Leporini

The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincaré algebra. Such a system allows to establish a completeness theorem for the treatment of quantum information.

•Jan 1, 2007•0 citations

Stone-Weierstrass Style Theorem for Quantum Operations

Héctor Freytes, Antonio Ledda

In the usual representation of quantum computational processes, a quantum circuit is identified with an appropriate composition of quantum gates, i.e. unitary operators acting on pure states (qubits or quregisters) of a convenient (n-fold tensor product) Hilbert space ⊗nC2 (where C2 is the bidimensional complex Hilbert space). Consequently, quantum gates represent reversible time evolution of the system. According to [1] however, such a representation is unduly restrictive insomuch it does not encompass open systems where coupling with environment and measurement processes may occur. In this case, time evolution is no longer reversible. In [1] the authors formulate a more general model of quantum computational processes, where pure states and unitary operators are replaced by density operators and quantum operations, respectively. Let H be a Hilbert space, L(H) the vector space of all linear operators of H and D(H) the set of density operators in H. A quantum operation [2] is a linear and completely positive operator O: L(H1) → L(H2). By [2], for every quantum operation O: L(H1) → L(H2), there exists a set of operators {Ai} such that iA iAi = I and ∀ρ ∈ D(H1): E(ρ) = iAiρA

•Dec 26, 2014•0 citations

An Axiomatic System Suggested by Quantum Computation

Cesarino Bertini, Roberto Leporini

The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincaré algebra. Such a system allows to establish a completeness theorem.

Journal of Logic and Computation•Feb 27, 2009•0 citations

QUANTUM COMPUTATIONAL FINITE-VALUED LOGICS

Cesarino Bertini, Roberto Leporini

The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quantum information quantity, represented by a quregister (a system of qudits) or, more generally, by a mixture of quregisters (called qumix), whose dimension depends on the logical complexity of the sentence. At the same time, the logical connectives are interpreted as logical operations defined in terms of quantum logical gates. Physical models of quantum computational logics can be built by means of Mach-Zehnder interferometers.

International Journal of Quantum Information•Oct 1, 2007•6 citations

Fuzzy Propositional Logic Associated with Quantum Computational Gates

Domenech, G, Freytes, H

We apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincare structure.

•Dec 26, 2006•16 citations

Insights into classical irreversible computation using quantum information concepts

Berry Groisman

The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been successfully tested on two computational tasks. Several basic logic gates have been analyzed and the nonlocal content of the associate quantum transformations have been calculated. The results provide us with new interesting insight into the notion of complexity of logic operations.

arXiv:0810.3710•Oct 21, 2008•0 citations
In this paper we discuss an approach to quantum computation where the basic information units (qubits and quregisters) are replaced by density operators and the restriction to unitary operators as logical gates is lifted through the introduction of the more general concept of quantum operation ( [17], [1]). This perspective is especially suited to provide a physical description of open systems. In particular, we illustrate the advantages of this approach over the standard one and show that it can account for two importantirreversibletransformationsalreadyconsideredintheliterature: theirreversible conjunction IAND and the fuzzy-like Łukasiewicz disjunction⊕.
The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincaré algebra. Such a system allows to establish a completeness theorem for the treatment of quantum information.
In the usual representation of quantum computational processes, a quantum circuit is identified with an appropriate composition of quantum gates, i.e. unitary operators acting on pure states (qubits or quregisters) of a convenient (n-fold tensor product) Hilbert space ⊗nC2 (where C2 is the bidimensional complex Hilbert space). Consequently, quantum gates represent reversible time evolution of the system. According to [1] however, such a representation is unduly restrictive insomuch it does not encompass open systems where coupling with environment and measurement processes may occur. In this case, time evolution is no longer reversible. In [1] the authors formulate a more general model of quantum computational processes, where pure states and unitary operators are replaced by density operators and quantum operations, respectively. Let H be a Hilbert space, L(H) the vector space of all linear operators of H and D(H) the set of density operators in H. A quantum operation [2] is a linear and completely positive operator O: L(H1) → L(H2). By [2], for every quantum operation O: L(H1) → L(H2), there exists a set of operators {Ai} such that iA iAi = I and ∀ρ ∈ D(H1): E(ρ) = iAiρA
The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quregister (a system of qubits in a pure state) or, more generally, with a mixture of quregisters (called qumix). Following an approach proposed by Domenech and Freytes, we apply residuated structures associated with fuzzy logic to develop certain aspects of information processing in quantum computing from a logical perspective. For this purpose, we introduce an axiomatic system whose natural interpretation is the irreversible quantum Poincaré algebra. Such a system allows to establish a completeness theorem.
The theory of logical gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics. The basic semantic idea is the following: the meaning of a sentence is identified with a quantum information quantity, represented by a quregister (a system of qudits) or, more generally, by a mixture of quregisters (called qumix), whose dimension depends on the logical complexity of the sentence. At the same time, the logical connectives are interpreted as logical operations defined in terms of quantum logical gates. Physical models of quantum computational logics can be built by means of Mach-Zehnder interferometers.
The method of using concepts and insight from quantum information theory in order to solve problems in reversible classical computing (introduced in Ref. [1]) have been generalized to irreversible classical computing. The method have been successfully tested on two computational tasks. Several basic logic gates have been analyzed and the nonlocal content of the associate quantum transformations have been calculated. The results provide us with new interesting insight into the notion of complexity of logic operations.