Quantum circuits with classical channels and the principle of deferred measurements

07/17/2021

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by   Yuri Gurevich, et al.

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We define syntax and semantics of quantum circuits, allowing measurement gates and classical channels. We define circuit-based quantum algorithms and prove that, semantically, any such algorithm is equivalent to a single measurement that depends only on the underlying quantum circuit. Finally, we use our formalization of quantum circuits to state precisely and prove the principle of deferred measurements.