Quantum Locally Recoverable Codes

• URL: http://arxiv.org/abs/2311.08653v1
• Date: Wed, 15 Nov 2023 02:27:01 GMT
• Title: Quantum Locally Recoverable Codes
• Authors: Louis Golowich and Venkatesan Guruswami
• Abstract summary: In the long term, like their classical counterparts, quantum locally recoverable codes may be used for large-scale quantum data storage. We show that even the weakest form of a stronger locality property called local correctability, which permits more robust local recovery, is impossible quantumly.
• Score: 27.438045041448248
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Classical locally recoverable codes, which permit highly efficient recovery from localized errors as well as global recovery from larger errors, provide some of the most useful codes for distributed data storage in practice. In this paper, we initiate the study of quantum locally recoverable codes (qLRCs). In the long term, like their classical counterparts, such qLRCs may be used for large-scale quantum data storage. Our results also have concrete implications for quantum LDPC codes, which are applicable to near-term quantum error-correction. After defining quantum local recoverability, we provide an explicit construction of qLRCs based on the classical LRCs of Tamo and Barg (2014), which we show have (1) a close-to-optimal rate-distance tradeoff (i.e. near the Singleton bound), (2) an efficient decoder, and (3) permit good spatial locality in a physical implementation. Although the analysis is significantly more involved than in the classical case, we obtain close-to-optimal parameters by introducing a "folded" version of our quantum Tamo-Barg (qTB) codes, which we then analyze using a combination of algebraic techniques. We furthermore present and analyze two additional constructions using more basic techniques, namely random qLRCs, and qLRCs from AEL distance amplification. Each of these constructions has some advantages, but neither achieves all 3 properties of our folded qTB codes described above. We complement these constructions with Singleton-like bounds that show our qLRC constructions achieve close-to-optimal parameters. We also apply these results to obtain Singleton-like bounds for qLDPC codes, which to the best of our knowledge are novel. We then show that even the weakest form of a stronger locality property called local correctability, which permits more robust local recovery and is achieved by certain classical codes, is impossible quantumly.

Related papers

• List Decodable Quantum LDPC Codes [49.2205789216734]
  We give a construction of Quantum Low-Density Parity Check (QLDPC) codes with near-optimal rate-distance tradeoff. We get efficiently list decodable QLDPC codes with unique decoders.
  arXiv  Detail & Related papers  (2024-11-06T23:08:55Z)
• Toward a 2D Local Implementation of Quantum LDPC Codes [1.1936126505067601]
  Geometric locality is an important theoretical and practical factor for quantum low-density parity-check (qLDPC) codes. We present an error correction protocol built on a bilayer architecture that aims to reduce operational overheads when restricted to 2D local gates.
  arXiv  Detail & Related papers  (2024-04-26T19:48:07Z)
• Tradeoff Constructions for Quantum Locally Testable Codes [11.640839589988788]
  We present three constructions that can make new quantum locally testable codes (qLTCs) from old. These constructions can be used on as-yet undiscovered qLTCs to obtain new parameters. We find a number of present applications to prove the existence of codes in previously unknown parameter regimes.
  arXiv  Detail & Related papers  (2023-09-11T15:25:15Z)
• Quantum Gate Optimization for Rydberg Architectures in the Weak-Coupling Limit [55.05109484230879]
  We demonstrate machine learning assisted design of a two-qubit gate in a Rydberg tweezer system. We generate optimal pulse sequences that implement a CNOT gate with high fidelity. We show that local control of single qubit operations is sufficient for performing quantum computation on a large array of atoms.
  arXiv  Detail & Related papers  (2023-06-14T18:24:51Z)
• Classical-to-Quantum Transfer Learning Facilitates Machine Learning with Variational Quantum Circuit [62.55763504085508]
  We prove that a classical-to-quantum transfer learning architecture using a Variational Quantum Circuit (VQC) improves the representation and generalization (estimation error) capabilities of the VQC model. We show that the architecture of classical-to-quantum transfer learning leverages pre-trained classical generative AI models, making it easier to find the optimal parameters for the VQC in the training stage.
  arXiv  Detail & Related papers  (2023-05-18T03:08:18Z)
• General Distance Balancing for Quantum Locally Testable Codes [12.547444644243544]
  We prove a lower bound on the soundness of quantum locally testable codes under the distance balancing construction of Evra et al. arXiv:2004.07935 [quant-ph] Our technical contribution is that the new soundness of the quantum code is at least the old soundness divided by the classical code length (up to a constant factor) By using a good classical LDPC code, we are able to grow the dimension of the hypersphere product codes arXiv:1608.05089 [quant-ph] and the hemicubic codes arXiv:1911.03069 [
  arXiv  Detail & Related papers  (2023-05-01T07:03:10Z)
• 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)
• Gaussian conversion protocol for heralded generation of qunaught states [66.81715281131143]
  bosonic codes map qubit-type quantum information onto the larger bosonic Hilbert space. We convert between two instances of these codes GKP qunaught states and four-foldsymmetric binomial states corresponding to a zero-logical encoded qubit. We obtain GKP qunaught states with a fidelity of over 98% and a probability of approximately 3.14%.
  arXiv  Detail & Related papers  (2023-01-24T14:17:07Z)
• Quantum Error Correction via Noise Guessing Decoding [0.0]
  Quantum error correction codes (QECCs) play a central role in both quantum communications and quantum computation. This paper shows that it is possible to both construct and decode QECCs that can attain the maximum performance of the finite blocklength regime.
  arXiv  Detail & Related papers  (2022-08-04T16:18:20Z)
• Realization of arbitrary doubly-controlled quantum phase gates [62.997667081978825]
  We introduce a high-fidelity gate set inspired by a proposal for near-term quantum advantage in optimization problems. By orchestrating coherent, multi-level control over three transmon qutrits, we synthesize a family of deterministic, continuous-angle quantum phase gates acting in the natural three-qubit computational basis.
  arXiv  Detail & Related papers  (2021-08-03T17:49:09Z)
• Constructing quantum codes from any classical code and their embedding in ground space of local Hamiltonians [6.85316573653194]
  We give an algorithm that explicitly constructs quantum codes with linear distance and constant rate. Motivated by quantum LDPC codes and the use of physics to protect quantum information, we introduce a new 2-local frustration free quantum spin chain Hamiltonian.
  arXiv  Detail & Related papers  (2020-12-02T19:00:19Z)

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.