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Paper 1

Simplified circuit-level decoding using Knill error correction

Ewan Murphy, Subhayan Sahu, Michael Vasmer

Year

2026

Journal

arXiv preprint

DOI

arXiv:2603.05320

arXiv

2603.05320

Quantum error correction will likely be essential for building a large-scale quantum computer, but it comes with significant requirements at the level of classical control software. In particular, a quantum error-correcting code must be supplemented with a fast and accurate classical decoding algorithm. Standard techniques for measuring the parity-check operators of a quantum error-correcting code involve repeated measurements, which both increases the amount of data that needs to be processed by the decoder, and changes the nature of the decoding problem. Knill error correction is a technique that replaces repeated syndrome measurements with a single round of measurements, but requires an auxiliary logical Bell state. Here, we provide a theoretical and numerical investigation into Knill error correction from the perspective of decoding. We give a self-contained description of the protocol, prove its fault tolerance under locally decaying (circuit-level) noise, and numerically benchmark its performance for quantum low-density parity-check codes. We show analytically and numerically that the time-constrained decoding problem for Knill error correction can be solved using the same decoder used for the simpler code-capacity noise model, illustrating that Knill error correction may alleviate the stringent requirements on classical control required for building a large-scale quantum computer.

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Paper 2

Generic eigenstate preparation via measurement-based purification

Jia-shun Yan, Jun Jing

Year

2023

Journal

arXiv preprint

DOI

arXiv:2307.16496

arXiv

2307.16496

It is not a general opinion that that a quantum system could be purified into a target eigenstate via repeated measurements on a coupled qubit rather than direct transitions in the Hamiltonian. The projective measurement on the ancillary qubit gives rise to the positive operator-valued measures on the system that can filter out the unwanted states except the target one. In application, we discuss the measurement-based entanglement purification by which maximally entangled states (Bell states and Greenberger-Horne-Zeilinger states) can be distilled from the maximally mixed states or separable states. We also demonstrate the significant acceleration of a stimulated Raman adiabatic passage assisted by similar measurements. Our scheme allows arbitrary eigenstate preparation and reveals efficiency in multipartite systems for subspace purification. It offers a promising and generic quantum-control framework enriching the functionalities of quantum measurement.

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