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 ...
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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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Add this copy of Synthesis of Quantum Circuits Vs. Synthesis of to cart. $292.68, very good condition, Sold by Orbiting Books rated 3.0 out of 5 stars, ships from Hereford, HEREFORDSHIRE, UNITED KINGDOM, published 2018 by Morgan & Claypool Publishers.
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