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.
| Autorius: | Alexis De Vos, Yvan Van Rentergem, Stijn De Baerdemacker, |
| Serija: | Synthesis Lectures on Digital Circuits & Systems |
| Leidėjas: | Springer Nature Switzerland |
| Išleidimo metai: | 2018 |
| Knygos puslapių skaičius: | 128 |
| ISBN-10: | 3031798945 |
| ISBN-13: | 9783031798948 |
| Formatas: | Knyga minkštu viršeliu |
| Kalba: | Anglų |
| Žanras: | Electronics: circuits and components |
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