An Efficient quantum circuit analyser on qubits and qudits

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. Program summary: Program title: CUGates.m Catalogue identifier: AEJM-v1-0 Program summary: URL: http://cpc.cs.qub.ac.uk/summaries/AEJM-v1-0.html Program obtainable from: CPC Program Library, Queens University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/ licence.html No. of lines in distributed program, including test data, etc.: 8168 No. of bytes in distributed program, including test data, etc.: 173 899 Distribution format: tar.gz Programming language: Mathematica Computer: Any computer installed with Mathematica 6.0 or higher. Operating system: Any system with a copy of Mathematica 6.0 or higher installed. Classification: 4.15 Nature of problem: The CUGates notebook simulates arbitrarily complex quantum circuits comprised of single/multiple qubit and qudit quantum gates. Solution method: It utilizes an irreducible form of matrix decomposition for a general controlled gate with multiple conditionals and is highly efficient in simulating complex quantum circuits. Running time: Details of CPU time usage for various example runs are given in Section 4.