A Conceptual Technology-Dependent Framework of Ternary Quantum Gates

TL;DR

This paper proposes a conceptual framework for technology-dependent ternary quantum gates designed for future superconducting and photonic quantum systems operating with qutrits.

Contribution

It introduces a set of specific ternary quantum gates and circuits tailored for future implementation in quantum computing hardware.

Findings

Defines a set of ternary quantum gates including Chrestenson and Z3.

Proposes a cost-effective Toffoli gate for ternary systems.

Lays out a framework for implementing ternary quantum operations in future hardware.

Abstract

This paper introduces a conceptual framework of technology-dependent ternary quantum gates that could be implemented and fabricated into future superconducting and photonic quantum systems for operating 3-valued quantum bits (qutrits). The "technology-dependent" means that such ternary quantum gates are on-purpose designed analogy to the contemporary binary quantum gates. Conceptually, the final built technology-dependent one-, two-, and three-qutrit gates are Chrestenson, Z3, 01, 02, 12, +1, +2 (including their corresponding inverse and controlled gates), a non-phase relative SWAP gate, and a cost-effective Toffoli gate, which is a generic ternary Galois Field (GF3) multiplication and addition circuit.