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On Fault Tolerant Single-Shot Logical State Preparation and Robust Long-Range Entanglement

Authors Thiago Bergamaschi , Yunchao Liu

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Author Details

Thiago Bergamaschi
  • University of California Berkeley, CA, USA
Yunchao Liu
  • University of California Berkeley, CA, USA
  • Harvard University, Cambridge, MA, USA

Funding

T.B. acknowledges support by the National Science Foundation under Grant No. DGE 2146752. Y.L. is supported by DOE Grant No. DE-SC0024124, NSF Grant No. 2311733, and DOE Quantum Systems Accelerator.

Acknowledgements

We thank Zhiyang He (Sunny) for helpful discussions. We thank Jong Yeon Lee for helpful discussions and for informing us about an upcoming work with Isaac Kim on single-shot error correction and cluster states. This work was done in part while the authors were visiting the Simons Institute for the Theory of Computing.

Cite As Get BibTex

Thiago Bergamaschi and Yunchao Liu. On Fault Tolerant Single-Shot Logical State Preparation and Robust Long-Range Entanglement. In 16th Innovations in Theoretical Computer Science Conference (ITCS 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 325, pp. 16:1-16:9, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ITCS.2025.16

Abstract

Preparing encoded logical states is the first step in a fault-tolerant quantum computation. Standard approaches based on concatenation or repeated measurement incur a significant time overhead. The Raussendorf-Bravyi-Harrington cluster state [Raussendorf et al., 2005] offers an alternative: a single-shot preparation of encoded states of the surface code, by means of a constant depth quantum circuit, followed by a single round of measurement and classical feedforward [Bravyi et al., 2020]. In this work we generalize this approach and prove that single-shot logical state preparation can be achieved for arbitrary quantum LDPC codes. Our proof relies on a minimum-weight decoder and is based on a generalization of Gottesman’s clustering-of-errors argument [Gottesman, 2014]. As an application, we also prove single-shot preparation of the encoded GHZ state in arbitrary quantum LDPC codes. This shows that adaptive noisy constant depth quantum circuits are capable of generating generic robust long-range entanglement.

Subject Classification

ACM Subject Classification
  • Theory of computation → Quantum computation theory
Keywords
  • Quantum error correction
  • fault tolerance
  • single-shot error correction
  • logical state preparation

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