Measurement and feedforward circuits from quantum error correcting codes
Abstract
Measurements and feedforward enhance the power of shallow quantum circuits, enabling the deterministic implementation of global unitary operations and the preparation of long-range entangled states. We establish a general correspondence between all such protocols and quantum error-correcting codes: the circuit preceding the measurements acts as an encoder, and unitary feedforward can eliminate post-selection if and only if the measurement projectors are detectable errors on the codespace. This correspondence provides a common framework for state preparation and implementation of global unitaries with measurements and feedforward, turning both into a code-design problem. For stabilizer codes with Pauli measurements, although the resulting operation can be non-Clifford, we show that its nonstabilizerness originates entirely from the encoder. We overcome this restriction using non-Pauli measurements or non-additive codes, constructing protocols that generate long-range nonstabilizerness while requiring only single-qubit unitary corrections.
Related
- Rare Event Simulation of Quantum Error-Correcting Circuits
- One generation of the Standard Model as a quantum error-correcting code
- Topological Quantum Error-Correcting Thresholds of a Symmetry-Enriched Toric Code
- Self-testing of logical subspaces of quantum error-correcting codes
- Quantum error-correcting code parameters, checkable by a certificate of provable size
BibTeX
@misc{styliaris2026measurement,
title = {{Measurement and feedforward circuits from quantum error correcting codes}},
author = {Georgios Styliaris and Rahul Trivedi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39764},
eprint = {2609.39764},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39764},
}
RIS
TY - UNPB
TI - Measurement and feedforward circuits from quantum error correcting codes
AU - Georgios Styliaris
AU - Rahul Trivedi
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39764
UR - https://arxiv.org/abs/2609.39764
AB - Measurements and feedforward enhance the power of shallow quantum circuits, enabling the deterministic implementation of global unitary operations and the preparation of long-range entangled states. We establish a general correspondence between all such protocols and quantum error-correcting codes: the circuit preceding the measurements acts as an encoder, and unitary feedforward can eliminate post-selection if and only if the measurement projectors are detectable errors on the codespace. This correspondence provides a common framework for state preparation and implementation of global unitaries with measurements and feedforward, turning both into a code-design problem. For stabilizer codes with Pauli measurements, although the resulting operation can be non-Clifford, we show that its nonstabilizerness originates entirely from the encoder. We overcome this restriction using non-Pauli measurements or non-additive codes, constructing protocols that generate long-range nonstabilizerness while requiring only single-qubit unitary corrections.
ER -