Non-Uniform Noise Rates and Griffiths Phases in Topological Quantum Error Correction

• URL: http://arxiv.org/abs/2409.03325v1
• Date: Thu, 5 Sep 2024 07:54:23 GMT
• Title: Non-Uniform Noise Rates and Griffiths Phases in Topological Quantum Error Correction
• Authors: Adithya Sriram, Nicholas O'Dea, Yaodong Li, Tibor Rakovszky, Vedika Khemani,
• Abstract summary: We study effects non-uniform error rates in the representative examples of the 1D repetition code and the 2D toric code. Rare events may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch.
• Score: 0.025206105035672277
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The performance of quantum error correcting (QEC) codes are often studied under the assumption of spatio-temporally uniform error rates. On the other hand, experimental implementations almost always produce heterogeneous error rates, in either space or time, as a result of effects such as imperfect fabrication and/or cosmic rays. It is therefore important to understand if and how their presence can affect the performance of QEC in qualitative ways. In this work, we study effects of non-uniform error rates in the representative examples of the 1D repetition code and the 2D toric code, focusing on when they have extended spatio-temporal correlations; these may arise, for instance, from rare events (such as cosmic rays) that temporarily elevate error rates over the entire code patch. These effects can be described in the corresponding statistical mechanics models for decoding, where long-range correlations in the error rates lead to extended rare regions of weaker coupling. For the 1D repetition code where the rare regions are linear, we find two distinct decodable phases: a conventional ordered phase in which logical failure rates decay exponentially with the code distance, and a rare-region dominated Griffiths phase in which failure rates are parametrically larger and decay as a stretched exponential. In particular, the latter phase is present when the error rates in the rare regions are above the bulk threshold. For the 2D toric code where the rare regions are planar, we find no decodable Griffiths phase: rare events which boost error rates above the bulk threshold lead to an asymptotic loss of threshold and failure to decode. Unpacking the failure mechanism implies that techniques for suppressing extended sequences of repeated rare events (which, without intervention, will be statistically present with high probability) will be crucial for QEC with the toric code.

Related papers

• Fault-Tolerant Belief Propagation for Practical Quantum Memory [6.322831694506286]
  A fault-tolerant approach to reliable quantum memory is essential for scalable quantum computing. We propose a decoder that utilizes a space-time Tanner graph across multiple rounds of syndrome extraction with mixed-alphabet error variables. Our simulations demonstrate high error thresholds of 0.4%-0.87% and strong error-floor performance for topological code families.
  arXiv  Detail & Related papers  (2024-09-27T12:21:45Z)
• Perturbative stability and error correction thresholds of quantum codes [0.029541734875307393]
  Topologically-ordered phases are stable to local perturbations, and topological quantum error-correcting codes enjoy thresholds to local errors. We construct classical statistical mechanics models for decoding general CSS codes and classical linear codes. For CSS codes satisfying the LDPC condition and with a sufficiently large code distance, we prove the existence of a low temperature ordered phase.
  arXiv  Detail & Related papers  (2024-06-22T06:46:41Z)
• Subsystem surface and compass code sensitivities to non-identical infidelity distributions on heavy-hex lattice [0.0]
  We investigate how the logical error rate depends on parameters of the noise distribution for the subsystem surface code and the compass code. The average logical error rate depends on the average of the physical qubit infidelity distribution without sensitivity to higher moments. A decoder that is aware of location specific error rates modestly improves the logical error rate.
  arXiv  Detail & Related papers  (2024-02-13T04:05:50Z)
• Graph Spatiotemporal Process for Multivariate Time Series Anomaly Detection with Missing Values [67.76168547245237]
  We introduce a novel framework called GST-Pro, which utilizes a graphtemporal process and anomaly scorer to detect anomalies. Our experimental results show that the GST-Pro method can effectively detect anomalies in time series data and outperforms state-of-the-art methods.
  arXiv  Detail & Related papers  (2024-01-11T10:10:16Z)
• A U-turn on Double Descent: Rethinking Parameter Counting in Statistical Learning [68.76846801719095]
  We show that double descent appears exactly when and where it occurs, and that its location is not inherently tied to the threshold p=n. This provides a resolution to tensions between double descent and statistical intuition.
  arXiv  Detail & Related papers  (2023-10-29T12:05:39Z)
• Bounds on Autonomous Quantum Error Correction [3.9119979887528125]
  We analyze Markovian autonomous decoders that can be implemented with a wide range of qubit and bosonic error-correcting codes. For many-body quantum codes, we show that, to achieve error suppression comparable to active error correction, autonomous decoders generally require correction rates that grow with code size.
  arXiv  Detail & Related papers  (2023-08-30T18:00:07Z)
• Holographic Codes from Hyperinvariant Tensor Networks [70.31754291849292]
  We show that a new class of exact holographic codes, extending the previously proposed hyperinvariant tensor networks into quantum codes, produce the correct boundary correlation functions. This approach yields a dictionary between logical states in the bulk and the critical renormalization group flow of boundary states.
  arXiv  Detail & Related papers  (2023-04-05T20:28:04Z)
• Lattice gauge theory and topological quantum error correction with quantum deviations in the state preparation and error detection [0.0]
  We focus on the topological surface code, and study the case when the code suffers from both noise and coherent noise on the multi-qubit entanglement gates. We conclude that this type of unavoidable coherent errors could have a fatal impact on the error correction performance.
  arXiv  Detail & Related papers  (2023-01-30T13:12:41Z)
• 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)
• Are we certain it's anomalous? [57.729669157989235]
  Anomaly detection in time series is a complex task since anomalies are rare due to highly non-linear temporal correlations. Here we propose the novel use of Hyperbolic uncertainty for Anomaly Detection (HypAD) HypAD learns self-supervisedly to reconstruct the input signal.
  arXiv  Detail & Related papers  (2022-11-16T21:31:39Z)
• Crosstalk Suppression for Fault-tolerant Quantum Error Correction with Trapped Ions [62.997667081978825]
  We present a study of crosstalk errors in a quantum-computing architecture based on a single string of ions confined by a radio-frequency trap, and manipulated by individually-addressed laser beams. This type of errors affects spectator qubits that, ideally, should remain unaltered during the application of single- and two-qubit quantum gates addressed at a different set of active qubits. We microscopically model crosstalk errors from first principles and present a detailed study showing the importance of using a coherent vs incoherent error modelling and, moreover, discuss strategies to actively suppress this crosstalk at the gate level.
  arXiv  Detail & Related papers  (2020-12-21T14:20:40Z)

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.