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Entanglement is essential for quantum information processing, but is limited by noise. We address this by developing high-yield entanglement distillation protocols with several advancements. (1) We extend the 2-to-1 recurrence entanglement distillation protocol to higher-rate n-to-(n−1) protocols that can correct any single-qubit errors. These protocols are evaluated through numerical simulations focusing on fidelity and yield. We also outline a method to adapt any classical error-correcting code for entanglement distillation, where the code can correct both bit-flip and phase-flip errors by incorporating Hadamard gates. (2) We propose a constant-depth decoder for stabilizer codes that transforms logical states into physical ones using single-qubit measurements. This decoder is applied to entanglement distillation protocols, reducing circuit depth and enabling protocols derived from high-performance quantum error-correcting codes. We demonstrate this by evaluating the circuit complexity for entanglement distillation protocols based on surface codes and quantum convolutional codes. (3) Our stabilizer entanglement distillation techniques advance quantum computing. We propose a fault-tolerant protocol for constant-depth encoding and decoding of arbitrary states in surface codes, with potential extensions to more general quantum low-density parity-check codes. This protocol is feasible with state-of-the-art reconfigurable atom arrays and surpasses the limits of conventional logarithmic depth encoders. Overall, our study integrates stabilizer formalism, measurement-based quantum computing, and entanglement distillation, advancing both quantum communication and computing.
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This content will become publicly available on January 1, 2026
On Fault Tolerant Single-Shot Logical State Preparation and Robust Long-Range Entanglement
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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- Award ID(s):
- 2311733
- PAR ID:
- 10639259
- Editor(s):
- Meka, Raghu
- Publisher / Repository:
- Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- Date Published:
- Volume:
- 325
- ISSN:
- 1868-8969
- Page Range / eLocation ID:
- 16:1-16:9
- Subject(s) / Keyword(s):
- Quantum error correction fault tolerance single-shot error correction logical state preparation Theory of computation → Quantum computation theory
- Format(s):
- Medium: X Size: 9 pages; 881532 bytes Other: application/pdf
- Size(s):
- 9 pages 881532 bytes
- Location:
- https://drops.dagstuhl.de/storage/00lipics/lipics-vol325-itcs2025/LIPIcs.ITCS.2025.16/LIPIcs.ITCS.2025.16.pdf
- Sponsoring Org:
- National Science Foundation
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