Optimized Clifford Noise Reduction: Theory, Simulations and Experiments

Edwin Tham; Nicolas Delfosse

doi:10.22331/q-2025-08-27-1829

Optimized Clifford Noise Reduction: Theory, Simulations and Experiments

Edwin Tham and Nicolas Delfosse

IonQ Inc.

Published:	2025-08-27, volume 9, page 1829
Editor:	Alioscia Hamma
Eprint:	arXiv:2504.13356v2
Doi:	https://doi.org/10.22331/q-2025-08-27-1829
Citation:	Quantum 9, 1829 (2025).

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Abstract

We propose several optimizations of the CliNR partial error correction scheme which implements Clifford circuits by consuming a resource state. Errors are corrected by measuring a sequence of Pauli operators that we refer to as the verification sequence. We first propose a global optimization algorithm searching for a verification sequence resulting in a low logical error rate using tabu search. Then, we introduce a proxy for the logical error rate which is easier to evaluate and we design a two-step optimization algorithm. First, a verification sequence minimizing the proxy is computed, then this sequence is refined by reintroducing the logical error rate. Finally, we identify a large group of automorphisms of the search space which preserve the proxy and we use this symmetry to reduce the size of the search space. This results in a 168 $\times$ (respectively 20,160 $\times$) reduction of the size of the search space for the optimization of verification sequences with three (respectively four) Pauli operators. Our numerical simulations for 20-qubit Clifford circuits with size 400 under the ion chain model show that our optimization algorithms improve the performance of CliNR by 25% and that the two-step optimization achieves the same results as the global optimization with 64% fewer evaluations of the logical error rate. Finally, we perform experiments on a 36-qubit trapped ion quantum computer, without mid-circuit measurements, showing that the CZNR variant of CliNR is at breakeven.

Featured image: Comparing performance of optimized vs unoptimized CliNR and direct non-CliNR circuit implementations.

► BibTeX data

@article{Tham2025optimizedclifford,
  doi = {10.22331/q-2025-08-27-1829},
  url = {https://doi.org/10.22331/q-2025-08-27-1829},
  title = {Optimized {C}lifford {N}oise {R}eduction: {T}heory, {S}imulations and {E}xperiments},
  author = {Tham, Edwin and Delfosse, Nicolas},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {9},
  pages = {1829},
  month = aug,
  year = {2025}
}

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Cited by

[1] Victor V. Albert and Philippe Faist, "Handbook of Error-Correcting Codes", arXiv:2606.11484, (2026).

[2] James Brown, Jason Iaconis, Yuri Alexeev, Linta Joseph, Spencer Churchill, Kenny Heitritter, William Aguilar-Calvo, Martin Roetteler, and Martin Suchara, "Mid-Circuit Measurements for Clifford Noise Reduction in Hamiltonian Simulations", arXiv:2605.06792, (2026).

[3] Aharon Brodutch, Gregory Baimetov, Edwin Tham, and Nicolas Delfosse, "Recursive Clifford noise reduction", arXiv:2511.22624, (2025).

The above citations are from SAO/NASA ADS (last updated successfully 2026-07-15 12:27:25). The list may be incomplete as not all publishers provide suitable and complete citation data.

On Crossref's cited-by service no data on citing works was found (last attempt 2026-07-15 12:27:24).

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