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

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

・ISBN 978-3-031-79894-8 paper EUR 59.99

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お気に入り
著者・編者Vos, Alexis De / Baerdemacker, Stijn De / Rentergem, Yvan Van,
シリーズ (Synthesis Lectures on Digital Circuits & Systems)
出版社 (Springer International Publishing AG, SZ)
出版年月2018
ページ数109 pp.
言語ENG
ニュース番号<A02-83514>

解説

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 ?? x ?? unitary matrix with ??=2??, a reversible classical circuit, acting on ?? bits, is described by a 2?? x 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.