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