# Quantum circuits with classical channels and the principle of deferred measurements

arXiv: https://arxiv.org/abs/2107.08324 · HTML: https://mlsanity.com/paper/2107.08324/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Jul 2021.

## Built on by (most cited first, 2 of 2)

- [QKSAN: A Quantum Kernel Self-Attention Network](https://mlsanity.com/paper/2308.13422/) (2023)
- [Layerwise Federated Learning for Heterogeneous Quantum Clients using Quorus](https://mlsanity.com/paper/2510.06228/) (2025)

## Abstract (arXiv)

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.