Equivalence Checking of Dynamic Quantum Circuits

Despite the rapid development of quantum computing these years, state-of-the-art quantum devices still contain only a limited number of qubits. One possible way to execute more realistic algorithms in near-term quantum devices is to employ dynamic quantum circuits (DQCs). In DQCs, measurements can happen during the circuit, and their outcomes can be processed with classical computers and used to control other parts of the circuit. This technique can help significantly reduce the qubit resources required to implement a quantum algorithm. In this paper, we give a formal definition of DQCs and then characterise their functionality in terms of ensembles of linear operators, following the Kraus representation of superoperators. We further interpret DQCs as tensor networks, implement their functionality as tensor decision diagrams (TDDs), and reduce the equivalence of two DQCs to checking if they have the same TDD representation. Experiments show that embedding classical logic into conventional quantum circuits does not incur a significant time and space burden.