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Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits, Hardback Book

Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits Hardback

Part of the Synthesis Lectures on Digital Circuits and Systems series

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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 w qubits, is described by an n x n unitary matrix with n=2w, a reversible classical circuit, acting on w bits, is described by a 2w x 2w permutation matrix.

The permutation matrices are studied in group theory of finite groups (in particular the symmetric group Sn); the unitary matrices are discussed in group theory of continuous groups (a.k.a.

Lie groups, in particular the unitary group U(n). 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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