Engineering Commons^™

Synthesis Of Linear Reversible Circuits And Exor-And-Based Circuits For Incompletely Specified Multi-Output Functions, Ben Schaeffer

Dissertations and Theses

At this time the synthesis of reversible circuits for quantum computing is an active area of research. In the most restrictive quantum computing models there are no ancilla lines and the quantum cost, or latency, of performing a reversible form of the AND gate, or Toffoli gate, increases exponentially with the number of input variables. In contrast, the quantum cost of performing any combination of reversible EXOR gates, or CNOT gates, on n input variables requires at most O(n^₂/log₂n) gates. It was under these conditions that EXOR-AND-EXOR, or EPOE, synthesis was developed.

In this …

Minimization Of Quantum Circuits Using Quantum Operator Forms, Martin Lukac, Michitaka Kameyama, Marek Perkowski, Pawel Kerntopf

Electrical and Computer Engineering Faculty Publications and Presentations

In this paper we present a method for minimizing reversible quantum circuits using the Quantum Operator Form (QOF); a new representation of quantum circuit and of quantum-realized reversible circuits based on the CNOT, CV and CV† quantum gates. The proposed form is a quantum extension to the well known Reed-Muller but unlike the Reed-Muller form, the QOF allows the usage of different quantum gates. Therefore QOF permits minimization of quantum circuits by using properties of different gates than only the multi-control Toffoli gates. We introduce a set of minimization rules and a pseudo-algorithm that can be used to design circuits …