Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits

Name: Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits
Brand: Springer Nature
SKU: 9783031798948
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Springer Nature

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9783031798948

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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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