Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes

• URL: http://arxiv.org/abs/2609.11457v1
• Date: Thu, 10 Sep 2026 12:29:05 GMT
• Title: Local decoders for fault-tolerant quantum computation and translation-invariant stabilizer codes
• Abstract summary: We construct the first fully spatially local fault-tolerant quantum computer based on topological codes in fewer than four dimensions.<n>Our construction is a two-dimensional architecture that uses only geometrically local quantum and classical operations.
• Score: 0.45880283710344066
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We construct the first fully spatially local fault-tolerant quantum computer based on topological codes in fewer than four spatial dimensions. Our construction is a two-dimensional architecture that uses only geometrically local quantum and classical operations, bounded-speed classical communication and computation, and a constant density of quantum and classical resources. The core component is a new time-translation-invariant cellular-automaton decoder for the surface code. This decoder preserves logical information for a time stretched-exponential in the code distance and operates continuously during state injection, stabilizer-state preparation, lattice surgery, and transversal readout. We also prove that every translation-invariant topological Pauli stabilizer code is locally decodable under phenomenological noise.

Related papers

• Surface code logical operations on a superconducting quantum processor [66.1042398805403]
  We experimentally realize key elements of patch-based surface-code logical processing on a 107-qubit superconducting quantum processor.<n>Our results advance superconducting surface-code experiments from protected logical memory to active, patch-based fault-tolerant logical operations.
  arXiv  Detail & Related papers  (2026-07-01T21:07:02Z)
• Quantum Dynamic Time Warping for Multivariate Time Series Classification [41.99844472131922]
  We propose a hybrid Quantum Dynamic Time Warping architecture, replacing the classical distance metric with the parameterized geometry of a quantum Hilbert space.<n>We demonstrate this architecture allows untrained quantum kernels to act as highly expressive baselines, while parameterized training effectively untangles deeply overlapping hyper-dimensional data.
  arXiv  Detail & Related papers  (2026-06-26T07:58:37Z)
• Courant: a State-Adaptive Perceiver-Based Neural Surrogate with Local Support and Interpretable Field Decomposition [41.11599978669432]
  "Courant" is a Perceiver-based encoder-processor-decoder surrogate model.<n>It has latent features exhibiting adaptive specialization and local support in the physical space.<n>We demonstrate that Courant's inductive biases yield latents that are interpretable by design.
  arXiv  Detail & Related papers  (2026-05-24T14:55:12Z)
• Local decoder for the toric code with a high pseudo-threshold [0.0]
  Local decoders provide a promising approach to real-time quantum error-correction.<n>We propose a new local decoder for Kitaev's toric code: the 2D signal-rule.<n>We present numerical evidence of exponential logical error suppression with system size below some critical error rate.
  arXiv  Detail & Related papers  (2026-03-02T19:00:24Z)
• Quantum Memory and Autonomous Computation in Two Dimensions [0.0]
  We present a simple method for autonomous quantum error correction in two spatial dimensions.<n>The construction uses hierarchical, self-simulating control elements based on the classical schemes from the seminal results of Gcs (1986, 1989)
  arXiv  Detail & Related papers  (2026-01-28T18:13:06Z)
• A Mixture of Experts Vision Transformer for High-Fidelity Surface Code Decoding [12.998419492098462]
  Topological stabilizer codes are particularly appealing due to their geometric locality and practical relevance.<n>We propose QuantumSMoE, a quantum vision transformer based decoder that incorporates code structure through plus shaped embeddings.<n> Experiments on the toric code demonstrate that QuantumSMoE outperforms state-of-the-art machine learning decoders.
  arXiv  Detail & Related papers  (2026-01-18T16:49:59Z)
• Exploiting Movable Logical Qubits for Lattice Surgery Compilation [43.290156259065554]
  We introduce a paradigm shift by exploiting movable logical qubits via teleportation during the logical lattice surgery CNOT gate.<n> Numerical simulations show that the proposed approach can substantially reduce the routed circuit depth.<n>An open-source implementation of our method is available on GitHub.
  arXiv  Detail & Related papers  (2025-12-03T19:00:04Z)
• Efficient and Universal Neural-Network Decoder for Stabilizer-Based Quantum Error Correction [44.698141103370546]
  GraphQEC is a code-agnostic decoder leveraging machine-learning on the graph structure of stabilizer codes with linear time complexity.<n>Our approach represents the first universal solution for real-time quantum error correction across arbitrary stabilizer codes.
  arXiv  Detail & Related papers  (2025-02-27T10:56:53Z)
• A local automaton for the 2D toric code [0.0]
  We construct a local decoder for the 2D toric code using ideas from the hierarchical classical cellular automata of Tsirelson and G'acs.<n>Our decoder is a circuit of strictly local quantum operations preserving a logical state for exponential time in the presence of circuit-level noise.
  arXiv  Detail & Related papers  (2024-12-27T18:59:57Z)
• An Efficient Quantum Binary-Neuron Algorithm for Accurate Multi-Story Floor Localization [4.415197030186768]
  We propose a quantum algorithm for accurate multi-story localization. We implement the proposed algorithm on a real IBM quantum machine and evaluate it on three real indoor testbeds.
  arXiv  Detail & Related papers  (2024-09-01T18:09:38Z)
• Deep Quantum Error Correction [73.54643419792453]
  Quantum error correction codes (QECC) are a key component for realizing the potential of quantum computing. In this work, we efficiently train novel emphend-to-end deep quantum error decoders. The proposed method demonstrates the power of neural decoders for QECC by achieving state-of-the-art accuracy.
  arXiv  Detail & Related papers  (2023-01-27T08:16:26Z)
• A quantum processor based on coherent transport of entangled atom arrays [44.62475518267084]
  We show a quantum processor with dynamic, nonlocal connectivity, in which entangled qubits are coherently transported in a highly parallel manner. We use this architecture to realize programmable generation of entangled graph states such as cluster states and a 7-qubit Steane code state.
  arXiv  Detail & Related papers  (2021-12-07T19:00:00Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.