Synthesis of Quantum Circuits Vs. Synthesis of Classical Reversible Circuits (Synthesis Lectures on Digital Circuits and Systems)

Alexis De Vos, Stijn de Baerdemacker, Yvan Van Rentergem

  • 出版商: Morgan & Claypool
  • 出版日期: 2018-07-03
  • 售價: $2,060
  • 貴賓價: 9.5$1,957
  • 語言: 英文
  • 頁數: 125
  • 裝訂: Paperback
  • ISBN: 168173379X
  • ISBN-13: 9781681733791
  • 相關分類: 量子 Quantum
  • 海外代購書籍(需單獨結帳)

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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.