An efficient quantum circuit analyser on qubits and qudits

TL;DR

This paper introduces a highly efficient quantum circuit analysis method that simplifies complex circuits with qubits and qudits, significantly reducing computational effort and including the first implementation for qudit gates.

Contribution

It presents a novel decomposition scheme and Mathematica implementation for analyzing complex quantum circuits with qubits and qudits, reducing computational complexity.

Findings

Reduces multiple unitary operations to two matrix additions

Includes the first efficient analysis for qudit quantum gates

Enhances classical simulation capabilities for quantum circuits

Abstract

This paper presents a highly efficient decomposition scheme and its associated Mathematica notebook for the analysis of complicated quantum circuits comprised of single/multiple qubit and qudit quantum gates. In particular, this scheme reduces the evaluation of multiple unitary gate operations with many conditionals to just two matrix additions, regardless of the number of conditionals or gate dimensions. This improves significantly the capability of a quantum circuit analyser implemented in a classical computer. This is also the first efficient quantum circuit analyser to include qudit quantum logic gates.