Vos, Alexis De.
Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits [electronic resource] / by Alexis De Vos, Stijn De Baerdemacker, Yvan Van Rentergem. - 1st ed. 2018. - XV, 109 p. online resource. - Synthesis Lectures on Digital Circuits & Systems, 1932-3174 . - Synthesis Lectures on Digital Circuits & Systems, .
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.
9783031798955
10.1007/978-3-031-79895-5 doi
Engineering.
Electronic circuits.
Control engineering.
Robotics.
Automation.
Computers.
Technology and Engineering.
Electronic Circuits and Systems.
Control, Robotics, Automation.
Computer Hardware.
T1-995
620
Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits [electronic resource] / by Alexis De Vos, Stijn De Baerdemacker, Yvan Van Rentergem. - 1st ed. 2018. - XV, 109 p. online resource. - Synthesis Lectures on Digital Circuits & Systems, 1932-3174 . - Synthesis Lectures on Digital Circuits & Systems, .
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.
9783031798955
10.1007/978-3-031-79895-5 doi
Engineering.
Electronic circuits.
Control engineering.
Robotics.
Automation.
Computers.
Technology and Engineering.
Electronic Circuits and Systems.
Control, Robotics, Automation.
Computer Hardware.
T1-995
620