2026-07-23T20:08:45Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:22644 2026-04-17T05:31:46Z ddc:004 open_access

On Fault Tolerant Single-Shot Logical State Preparation and Robust Long-Range Entanglement Bergamaschi, Thiago Liu, Yunchao Quantum error correction fault tolerance single-shot error correction logical state preparation 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Thiago Bergamaschi and Yunchao Liu 2025 Is Part Of LIPIcs, Volume 325, 16th Innovations in Theoretical Computer Science Conference (ITCS 2025) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ITCS.2025.16 urn:nbn:de:0030-drops-226444 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2025.16 eng https://creativecommons.org/licenses/by/4.0/legalcode