Synthesis of Ternary Quantum Logic Circuits by Decomposition.pdfVIP

Synthesis of Ternary Quantum Logic Circuits by Decomposition Faisal Shah Khan† and Marek M. Perkowski∗ † Department of Mathematic and Statistics Portland State University, PO Box 751, Portland, Oregon 97207-0751; ∗ Department of Electrical and Computer Engineering Portland State University, PO Box 751, Portland, Oregon 97207-0751 5 0 ABSTRACT 0 2 Recent research in multi-valued logic for quantum computing has shown practical advantages for scaling up a quantum computer. [1, 12] Multivalued quantum systems have also been used in the framework of quantum cryp- v tography, [4] and the concept of a qudit cluster state has been proposed by generalizing the qubit cluster state. [5] o N An evolutionary algorithm based synthesizer for ternary quantum circuits has recently been presented, [2] as well as a synthesis method based on matrix factorization [3].In this paper, a recursive synthesis method for ternary 4 quantum circuits based on the Cosine-Sine unitary matrix decomposition is presented. 1 Keywords: Quantum Logic Synthesis, Cosine-Sine Decomposition, Ternary Quantum Logic v 1 PACS numbers: 03.67.Lx, 03.65.Fd 03.65.Ud 4 0 1. INTRODUCTION 1 1 A collection of controlled three state quantum systems (qutrits) perturbed by a classical force can result in the 5 state of one system controlling the evolution of a second; this is called a quantum circuit. Qutrits replace classical 0 ternary bits as information units in ternary quantum computing. They a