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

Logics of Quantum Computation with Quantum Simulable Operators

Martinvaldo Konig

Published Jan 1, 2008• 0 citations
OpenAlex

Abstract

Abstract In quantum computational logics meaning of sentences are repre-sented by quantum information quantities. Any n-qubit sequence is identified with a unit vector of the tensor product of the complex Hilbert space ⊗nC2. Let us split the set of the vectors of its computational basis in the two sets: Bn1: = {i: ‖ i À= | x1,.., xn 〉 and xn = 1}; Bn0: = {i: ‖ i À= | x1,.., xn 〉 and xn = 0}. Any unit vector | ψ 〉 can be expressed in the form: | ψ 〉 = ∑i∈B0 ai ‖ iÀ +∑j∈B1 bj ‖ j À where by the Born rule,∑ i∈B0 | ai |2 + j∈B1 | bj |2 = 1 A key role in the definition of semantics is played by the probability-value of | ψ〉, defined as follows: p( | ψ〉): = ∑j∈B1 | bj |2 Moreover a function g: [0, 1]2 7 → [0, 1] is said quantum simulable iff ∃n ≥ 1, a unitary operator Ug: ⊗n+2C2 7 → ⊗n+2C2 and a quregister | χ 〉 ∈ ⊗nC2 such

Related papers

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

QUANTUM COMPUTATIONAL LOGICS AND FOCK SPACE SEMANTICS

María Luisa Dalla Chiara, Roberto Giuntini, 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 α is identified with a quantum information quantity, represented by a density operator of a Hilbert space, whose dimension depends on the logical complexity of α. At the same time, the logical connectives of the language are interpreted as operations defined in terms of quantum logical gates. Standard quantum computational models can be described as special cases of Fock space models, where the meaning of any sentence is localized in a precise sector of a Fock space ℱ. From an intuitive point of view, the increasing number of particles described in the different sectors of ℱ can be interpreted as increasing information.

International Journal of Quantum Information•Dec 17, 2004•7 citations

LOGICS FROM QUANTUM COMPUTATION

María Luisa Dalla Chiara, Roberto Giuntini, 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) or, more generally, with a mixture of quregisters (called qumix). In this framework, any sentence α of the language gives rise to a quantum tree: a kind of quantum circuit that transforms the quregister (qumix) associated to the atomic subformulas of α into the quregister (qumix) associated to α. A variant of the quantum computational semantics is represented by the quantum holistic semantics, which permits us to represent entangled meanings. Physical models of quantum computational logics can be built by means of Mach–Zehnder interferometers.

International Journal of Quantum Information•May 31, 2005•55 citations

An axiomatization of quantum computational Logic

Vladimir L. Vasyukov

One of the logical proposals that arise from quantum computation is the idea to use the quantum theoretical formalism to represent parallel reasoning. To this aim a quantum computation is considered by means of convenient unitary operators assuming arguments and values in particular sets of qubit systems. Isolating some important unitary operators that have a special role in quantum computation (logical gates or quregisters) we obtain an opportunity to yield the language of Quantum Computational Logic (QCL) (cf. [Cattaneo et al., 2003; Cattaneo et al., 2004; Dalla Chiara et al., 2004]). The basic concept of the semantics of this language is the notion of quantum computational realization such that the meaning associated to any sentence is a quregister. Unlike the semantic of a standard quantum logic QCL-conjunction and QCL-disjunction do not correspond to lattice operations since they are not generally idempotent. Moreover, in QCL the weak distributivity principle breaks down and both the excluded middle and the non contradiction principles are violated. Finally, the axiomatizability of QCL is still an open problem. In the paper an axiomatization of QCL is proposed construing it as a kind of so-called Goldblatt’s binary logic. Some metalogical theorems (paraconsistency and completeness) are proved.

Logical Investigations•Jan 1, 2023•0 citations

A holistic quantum computational semantics

María Luisa Dalla Chiara, Roberto Giuntini, Roberto Leporini

Does quantum holism give rise to new forms of abstract holistic semantics? This question can be discussed in the framework of quantum computational logics, non-standard versions of quantum logic that have been suggested by the theory of logical gates in quantum computation. The basic idea of the quantum computational semantics is the following: meanings of sentences are identified with quantum information quantities, represented by pure or mixed states of special quantum systems. In particular cases, the meaning of a sentence may correspond to an entangled state. On this basis, one can formally describe some typical holistic semantic situations, where the meaning of the whole determines the meanings of its parts, but generally not vice versa.

•Jan 1, 2006•2 citations

LOGICS FROM QUANTUM COMPUTATION WITH BOUNDED ADDITIVE OPERATORS

Cesarino Bertini, Roberto Leporini

The theory of gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics, where the meaning of a sentence is identified with a system of qubits in a pure or, more generally, mixed state. In this framework, any formula of the language gives rise to a quantum circuit that transforms the state associated to the atomic subformulas into the state associated to the formula and vice versa. On this basis, some holistic semantic situations can be described, where the meaning of whole determines the meaning of the parts, by non-linear and anti-unitary operators. We prove that the semantics with such operators and the semantics with unitary operators turn out to characterize the same logic.

International Journal of Quantum Information•Apr 1, 2012•3 citations
Abstract In quantum computational logics meaning of sentences are repre-sented by quantum information quantities. Any n-qubit sequence is identified with a unit vector of the tensor product of the complex Hilbert space ⊗nC2. Let us split the set of the vectors of its computational basis in the two sets: Bn1: = {i: ‖ i À= | x1,.., xn 〉 and xn = 1}; Bn0: = {i: ‖ i À= | x1,.., xn 〉 and xn = 0}. Any unit vector | ψ 〉 can be expressed in the form: | ψ 〉 = ∑i∈B0 ai ‖ iÀ +∑j∈B1 bj ‖ j À where by the Born rule,∑ i∈B0 | ai |2 + j∈B1 | bj |2 = 1 A key role in the definition of semantics is played by the probability-value of | ψ〉, defined as follows: p( | ψ〉): = ∑j∈B1 | bj |2 Moreover a function g: [0, 1]2 7 → [0, 1] is said quantum simulable iff ∃n ≥ 1, a unitary operator Ug: ⊗n+2C2 7 → ⊗n+2C2 and a quregister | χ 〉 ∈ ⊗nC2 such
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 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 α is identified with a quantum information quantity, represented by a density operator of a Hilbert space, whose dimension depends on the logical complexity of α. At the same time, the logical connectives of the language are interpreted as operations defined in terms of quantum logical gates. Standard quantum computational models can be described as special cases of Fock space models, where the meaning of any sentence is localized in a precise sector of a Fock space ℱ. From an intuitive point of view, the increasing number of particles described in the different sectors of ℱ can be interpreted as increasing information.
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) or, more generally, with a mixture of quregisters (called qumix). In this framework, any sentence α of the language gives rise to a quantum tree: a kind of quantum circuit that transforms the quregister (qumix) associated to the atomic subformulas of α into the quregister (qumix) associated to α. A variant of the quantum computational semantics is represented by the quantum holistic semantics, which permits us to represent entangled meanings. Physical models of quantum computational logics can be built by means of Mach–Zehnder interferometers.
One of the logical proposals that arise from quantum computation is the idea to use the quantum theoretical formalism to represent parallel reasoning. To this aim a quantum computation is considered by means of convenient unitary operators assuming arguments and values in particular sets of qubit systems. Isolating some important unitary operators that have a special role in quantum computation (logical gates or quregisters) we obtain an opportunity to yield the language of Quantum Computational Logic (QCL) (cf. [Cattaneo et al., 2003; Cattaneo et al., 2004; Dalla Chiara et al., 2004]). The basic concept of the semantics of this language is the notion of quantum computational realization such that the meaning associated to any sentence is a quregister. Unlike the semantic of a standard quantum logic QCL-conjunction and QCL-disjunction do not correspond to lattice operations since they are not generally idempotent. Moreover, in QCL the weak distributivity principle breaks down and both the excluded middle and the non contradiction principles are violated. Finally, the axiomatizability of QCL is still an open problem. In the paper an axiomatization of QCL is proposed construing it as a kind of so-called Goldblatt’s binary logic. Some metalogical theorems (paraconsistency and completeness) are proved.
Does quantum holism give rise to new forms of abstract holistic semantics? This question can be discussed in the framework of quantum computational logics, non-standard versions of quantum logic that have been suggested by the theory of logical gates in quantum computation. The basic idea of the quantum computational semantics is the following: meanings of sentences are identified with quantum information quantities, represented by pure or mixed states of special quantum systems. In particular cases, the meaning of a sentence may correspond to an entangled state. On this basis, one can formally describe some typical holistic semantic situations, where the meaning of the whole determines the meanings of its parts, but generally not vice versa.
The theory of gates in quantum computation has suggested new forms of quantum logic, called quantum computational logics, where the meaning of a sentence is identified with a system of qubits in a pure or, more generally, mixed state. In this framework, any formula of the language gives rise to a quantum circuit that transforms the state associated to the atomic subformulas into the state associated to the formula and vice versa. On this basis, some holistic semantic situations can be described, where the meaning of whole determines the meaning of the parts, by non-linear and anti-unitary operators. We prove that the semantics with such operators and the semantics with unitary operators turn out to characterize the same logic.