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DOI: 10.4230/LIPIcs.ITCS.2025.16

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

Authors: Thiago Bergamaschi and Yunchao Liu

Published in: LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025)

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.

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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)

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@InProceedings{bergamaschi_et_al:LIPIcs.ITCS.2025.16,
  author =	{Bergamaschi, Thiago and Liu, Yunchao},
  title =	{{On Fault Tolerant Single-Shot Logical State Preparation and Robust Long-Range Entanglement}},
  booktitle =	{16th Innovations in Theoretical Computer Science Conference (ITCS 2025)},
  pages =	{16:1--16:9},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-361-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{325},
  editor =	{Meka, Raghu},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.16},
  URN =		{urn:nbn:de:0030-drops-226444},
  doi =		{10.4230/LIPIcs.ITCS.2025.16},
  annote =	{Keywords: Quantum error correction, fault tolerance, single-shot error correction, logical state preparation}
}

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

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