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Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits (in English)
Alexis de Vos
(Author)
·
Stijn de Baerdemacker
(Author)
·
Yvan Van Rentergem
(Author)
·
Springer
· Paperback
Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits (in English) - Vos, Alexis de ; Baerdemacker, Stijn de ; Rentergem, Yvan Van
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Synopsis "Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits (in English)"
At first sight, quantum computing is completely different from classical computing. Nevertheless, a link is provided by reversible computation. Whereas an arbitrary quantum circuit, acting on qubits, is described by an × unitary matrix with =2, a reversible classical circuit, acting on bits, is described by a 2 × 2 permutation matrix. The permutation matrices are studied in group theory of finite groups (in particular the symmetric group ); the unitary matrices are discussed in group theory of continuous groups (a.k.a. Lie groups, in particular the unitary group U( )). Both the synthesis of a reversible logic circuit and the synthesis of a quantum logic circuit take advantage of the decomposition of a matrix: the former of a permutation matrix, the latter of a unitary matrix. In both cases the decomposition is into three matrices. In both cases the decomposition is not unique.
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