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Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits [electronic resource] / by Alexis De Vos, Stijn De Baerdemacker, Yvan Van Rentergem.

By: Vos, Alexis De [author.].
Contributor(s): Baerdemacker, Stijn De [author.] | Rentergem, Yvan Van [author.] | SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Synthesis Lectures on Digital Circuits & Systems: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2018Edition: 1st ed. 2018.Description: XV, 109 p. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783031798955.Subject(s): Engineering | Electronic circuits | Control engineering | Robotics | Automation | Computers | Technology and Engineering | Electronic Circuits and Systems | Control, Robotics, Automation | Computer HardwareAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 620 Online resources: Click here to access online
Contents:
Acknowledgments -- Introduction -- Bottom -- Bottom-Up -- Top -- Top-Down -- Conclusion -- Bibliography -- Authors' Biographies -- Index.
In: Springer Nature eBookSummary: 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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Acknowledgments -- Introduction -- Bottom -- Bottom-Up -- Top -- Top-Down -- Conclusion -- Bibliography -- Authors' Biographies -- Index.

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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