Realizing Ternary Quantum Switching Networks without Ancilla Bits

Abstract

This paper investigates the synthesis of quantum networks built to realize ternary switching circuits in the absence of ancilla bits. The results we established are twofold. The first shows that ternary Swap, ternary Not and ternary Toffoli gates are universal for the realization of arbitrary $n\times n$ ternary quantum switching networks without ancilla bits. The second result proves that all $n\times n$ quantum ternary networks can be generated by Not, Controlled-Not, Multiply-Two, and Toffoli gates. Our approach is constructive. key words: ternary quantum logic synthesis, quantum circuit optimization, group theory.

10 pages, Latex. in press, J. Phys. A: Math. Gen. (2005)

References in corpus (7)

• Quantum cryptography with 3-state systems
• Multi-valued Logic Gates for Quantum Computation
• Quantum Encodings in Spin Systems and Harmonic Oscillators
• Quantum computation based on d-level cluster states
• Asymptotically Optimal Quantum Circuits for d-level Systems
• Quantum gates on hybrid qudits
• The Controlled-U and Unitary Transformation in Two-Qudit

Cited by in corpus (3)

• Quantum Ternary Circuit Synthesis Using Projection Operations
• On the Complexity of the Cycles based Synthesis of Ternary Reversible Circuits
• Finite generating sets for reversible gate sets under general conservation laws