Title :
Exact synthesis of 3-qubit quantum circuits from non-binary quantum gates using multiple-valued logic and group theory
Author :
Yang, Guowu ; Hung, William N N ; Song, Xiaoyu ; Perkowski, Marek
Author_Institution :
Dept. of Electr. & Comput. Eng., Portland State Univ., OR, USA
Abstract :
We propose an approach to optimally synthesize quantum circuits from non-permutative quantum gates such as controlled-square-root-of-not (i.e., controlled-V). Our approach reduces the synthesis problem to multiple-valued optimization and uses group theory. We devise a novel technique that transforms the quantum logic synthesis problem from a multi-valued constrained optimization problem to a group permutation problem. The transformation enables us to utilize group theory to exploit the properties of the synthesis problem. Assuming a cost of one for each two-qubit gate, we find all reversible circuits with quantum costs of 4, 5, 6, etc, and give another algorithm to realize these reversible circuits with quantum gates.
Keywords :
group theory; logic design; multivalued logic circuits; quantum gates; 3-qubit quantum circuits; controlled-V gates; controlled-square-root-of-not gates; group permutation problem; group theory; multiple-valued logic; multiple-valued optimization; nonbinary quantum gates; nonpermutative quantum gates; optimal synthesis; reversible circuits; Circuit synthesis; Circuit testing; Constraint optimization; Costs; Logic circuits; Logic gates; Multivalued logic; Optimal control; Quantum mechanics; Writing;
Conference_Titel :
Design, Automation and Test in Europe, 2005. Proceedings
Print_ISBN :
0-7695-2288-2
DOI :
10.1109/DATE.2005.145