Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory

Guowu Yang (1) , William N. N. Hung (1) , Xiaoyu Song (1) , Marek Perkowski (1)

1 ECE - Department of Electrical and Computer Engineering [Portland]

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 found all reversible circuits with quantum costs of 4, 5, 6, etc, and give another algorithm to realize these reversible circuits with quantum gates.

Domaines: Architectures Matérielles [cs.AR]; Electronique

Guowu Yang, William N. N. Hung, Xiaoyu Song, Marek Perkowski. Exact Synthesis of 3-Qubit Quantum Circuits from Non-Binary Quantum Gates Using Multiple-Valued Logic and Group Theory. DATE'05, Mar 2005, Munich, Germany. pp.434-435. ⟨hal-00181552⟩