scholarly journals A many-valued approach to quantum computational logics

2018 ◽  
Vol 335 ◽  
pp. 94-111 ◽  
Author(s):  
M.L. Dalla Chiara ◽  
R. Giuntini ◽  
G. Sergioli ◽  
R. Leporini
Keyword(s):  
Quantum Computational Logics

scholarly journals Holistic logical arguments in quantum computation

2016 ◽  
Vol 66 (2) ◽  
Author(s):  
Maria Luisa Dalla Chiara ◽  
Roberto Giuntini ◽  
Roberto Leporini ◽  
Giuseppe Sergioli
Keyword(s):  
Quantum Information ◽  
Quantum Computation ◽  
Essential Role ◽  
Circuit Theory ◽  
Logical Connectives ◽  
Quantum Computational Logics

AbstractQuantum computational logics represent a logical abstraction from the circuit-theory in quantum computation. In these logics formulas are supposed to denote pieces of quantum information (qubits, quregisters or mixtures of quregisters), while logical connectives correspond to (quantum logical) gates that transform quantum information in a reversible way. The characteristic holistic features of the quantum theoretic formalism (which play an essential role in entanglement-phenomena) can be used in order to develop a

QUANTUM COMPUTATIONAL FINITE-VALUED LOGICS

2007 ◽  
Vol 05 (05) ◽  
pp. 641-665 ◽  
Author(s):  
CESARINO BERTINI ◽  
ROBERTO LEPORINI
Keyword(s):  
Quantum Information ◽  
Quantum Computation ◽  
Quantum Logic ◽  
Physical Models ◽  
Information Quantity ◽  
Logical Operations ◽  
Logical Connectives ◽  
Quantum Computational Logics ◽  
Basic Semantic

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.

scholarly journals Logical Structures Underlying Quantum Computing

Entropy ◽  
2019 ◽  
Vol 21 (1) ◽  
pp. 77 ◽  
Author(s):  
Federico Holik ◽  
Giuseppe Sergioli ◽  
Hector Freytes ◽  
Angel Plastino
Keyword(s):  
Quantum Computing ◽  
Quantum Algorithms ◽  
Quantum Computational Logics ◽  
Logical Structures

In this work we advance a generalization of quantum computational logics capable of dealing with some important examples of quantum algorithms. We outline an algebraic axiomatization of these structures.

Quantum Computational Logics and Possible Applications

2007 ◽  
Vol 47 (1) ◽  
pp. 44-60 ◽  
Author(s):  
Maria Luisa Dalla Chiara ◽  
Roberto Giuntini ◽  
Roberto Leporini ◽  
Giuliano Toraldo di Francia
Keyword(s):  
Quantum Computational Logics

LOGICS FROM QUANTUM COMPUTATION

2005 ◽  
Vol 03 (02) ◽  
pp. 293-337 ◽  
Author(s):  
MARIA LUISA DALLA CHIARA ◽  
ROBERTO GIUNTINI ◽  
ROBERTO LEPORINI
Keyword(s):  
Quantum Computation ◽  
Quantum Logic ◽  
Quantum Circuit ◽  
Physical Models ◽  
Computational Semantics ◽  
Quantum Computational Logics ◽  
Basic Semantic

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.

Towards Quantum Computational Logics

2010 ◽  
Vol 49 (12) ◽  
pp. 3158-3165 ◽  
Author(s):  
Antonio Ledda ◽  
Giuseppe Sergioli
Keyword(s):  
Quantum Computational Logics

LOGICS FROM QUANTUM COMPUTATION WITH BOUNDED ADDITIVE OPERATORS

2012 ◽  
Vol 10 (03) ◽  
pp. 1250036
Author(s):  
CESARINO BERTINI ◽  
ROBERTO LEPORINI
Keyword(s):  
Quantum Computation ◽  
Quantum Logic ◽  
Mixed State ◽  
Quantum Circuit ◽  
The State ◽  
Unitary Operators ◽  
Non Linear ◽  
Quantum Computational Logics

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.

QUANTUM COMPUTATIONAL LOGICS AND FOCK SPACE SEMANTICS

2005 ◽  
Vol 03 (01) ◽  
pp. 9-16 ◽  
Author(s):  
MARIA LUISA DALLA CHIARA ◽  
ROBERTO GIUNTINI ◽  
ROBERTO LEPORINI
Keyword(s):  
Computational Models ◽  
Fock Space ◽  
Point Of View ◽  
Information Quantity ◽  
Standard Quantum ◽  
Special Cases ◽  
Logical Connectives ◽  
Quantum Computational Logics ◽  
Basic Semantic ◽  
Number Of Particles

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.

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