Synthesis of Quantum Circuits vs. Synthesis of Classical Reversible Circuits
Author | : Alexis De Vos |
Publisher | : Morgan & Claypool Publishers |
Total Pages | : 127 |
Release | : 2018-07-03 |
ISBN-10 | : 9781681733807 |
ISBN-13 | : 1681733803 |
Rating | : 4/5 (07 Downloads) |
Book excerpt: 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.