Quantum circuits with classical channels and the principle of deferred measurements

TL;DR

This paper formalizes quantum circuits with measurements and classical channels, proving that any such algorithm can be simplified to a single measurement at the end, thereby rigorously establishing the principle of deferred measurements.

Contribution

It introduces a formal syntax and semantics for quantum circuits with classical channels and proves the principle of deferred measurements within this framework.

Findings

Any quantum algorithm with measurements can be represented as a single measurement at the end.

The formalization allows precise statements and proofs of the principle of deferred measurements.

The work bridges the gap between abstract quantum algorithms and their circuit implementations.

Abstract

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.