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Communications in Theoretical Physics

Second Quantization Representation of Quantum Logic Gate Transformations

Лей Ма, Zhang Yong-De

Published Jul 15, 2001• 0 citations
Publisher

Abstract

By using the theory of multimode linear transformation in Fock space, we offer an effective method to study the quantum logic gates based on fermion states. The forms of some basic quantum logic operations are also obtained.
DOI
10.1088/0253-6102/36/1/119

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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 essential component of the simulation of quantum systems is the mapping of the fermionic Fock space into qubits and the mapping of the creation and annihilation operators into qubit operators. This work covers the notions of the many-body problem, Slater determinants, second quantization as well as different mapping from the Fock space to the Hilbert space where qubits exist. Finally, this work also contains the development of a Mathematica code that performs two of the mappings mentioned above.