Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits

Alexis De Vos, Stijn De Baerdemacker, Yvan Van Rentergem

• Publisher: Springer
• Year: 2022
• Print ISBN:
  9783031798948
  9783031798962
• eBook ISBN:
  9783031798955
• Topic: Technology & Engineering
• Subtopic: Hardware
• Index: Technology & Engineering

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.

Table of contents

• Cover
• Copyright Page
• Title Page
• Contents
• Acknowledgments
• Introduction
• Bottom
• Bottom-Up
• Top
• Top-Down
• Conclusion
• Polar Decomposition
• Bibliography
• Authors' Biographies
• Index