Elementary gates for ternary quantum logic circuit

TL;DR

This paper introduces elementary gates for ternary quantum logic circuits, including controlled X and Z gates, and discusses their synthesis, implementation, and extension to qudit systems, providing a unified framework for multi-valued quantum circuits.

Contribution

It proposes new elementary gates for ternary quantum circuits and extends the framework to general qudit systems, enhancing synthesis and implementation methods.

Findings

Proposed ternary controlled X and Z gates as universal two-qutrit gates.

Provided synthesis schemes for important ternary gates.

Discussed physical implementation and extension to qudit systems.

Abstract

In this article the elementary gates for ternary quantum logic circuit are studied. We propose the ternary controlled X (TCX) gate or ternary controlled Z (TCZ) gate as two-qutrit elementary gate, which is universal when assisted by arbitrary one-qutrit gates. It is primitive, efficient and easy to implement. Based on Cartan decomposition, we also give the one-qutrit elementary gates. Then the synthesis of some important ternary gates is investigated and the scheme of physical implementation for these ternary gates is discussed. Finally we extend these elementary gates to more general qudit case, so it provides a unified description for the synthesis of the binary and multi-valued quantum circuits.