Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits |
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| Author:
| De Baerdemacker, Stijn
Van Rentergem, Yvan
De Vos, Alexis |
| Series title: | Synthesis Lectures on Digital Circuits and Systems Ser. |
| ISBN: | 978-3-031-79894-8 |
| Publication Date: | Jul 2018 |
| Publisher: | Springer International Publishing AG
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| Imprint: | Springer |
| Book Format: | Paperback |
| List Price: | USD $74.99USD $64.99 |
Book Description:
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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...
More DescriptionAt 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.