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Despite the rapid development of quantum computing these years,state-of-the-art quantum devices still contain only a very limited number ofqubits. One possible way to execute more realistic algorithms in near-termquantum devices is to employ dynamic quantum circuits, in which measurementscan happen during the circuit and their outcomes are used to control otherparts of the circuit. This technique can help to significantly reduce theresources required to achieve a given accuracy of a quantum algorithm. However,since this type of quantum circuits are more flexible, their verification ismuch more challenging. In this paper, we give a formal definition of dynamicquantum circuits and then propose to characterise their functionality in termsof ensembles of linear operators. Based on this novel semantics, two dynamicquantum circuits are equivalent if they have the same functionality. We furtherpropose and implement two decision diagram-based algorithms for checking theequivalence of dynamic quantum circuits. Experiments show that embeddingclassical logic into conventional quantum circuits does not incur significanttime and space burden.

Equivalence Checking of Dynamic Quantum Circuits