Unified and Generalized Approach to Entanglement-Assisted Quantum Error Correction

• URL: http://arxiv.org/abs/2411.14389v1
• Date: Thu, 21 Nov 2024 18:24:03 GMT
• Title: Unified and Generalized Approach to Entanglement-Assisted Quantum Error Correction
• Authors: Priya J. Nadkarni, Serge Adonsou, Guillaume Dauphinais, David W. Kribs, Michael Vasmer,
• Abstract summary: We introduce a framework for entanglement-assisted quantum error correcting codes called EAQEC, EAOQEC, and EACQ under a single umbrella. The unification is arrived at by viewing entanglement-assisted codes from the operator algebra quantum error correction perspective. We show how EACQ codes form a proper subclass of the entanglement-assisted subspace codes defined by EAOAQEC.
• Score: 0.1398098625978622
• License:
• Abstract: We introduce a framework for entanglement-assisted quantum error correcting codes that unifies the three original frameworks for such codes called EAQEC, EAOQEC, and EACQ under a single umbrella. The unification is arrived at by viewing entanglement-assisted codes from the operator algebra quantum error correction perspective, and it is built upon a recently established extension of the stabilizer formalism to that setting. We denote the framework by EAOAQEC, and we prove a general error correction theorem for such codes, derived from the algebraic perspective, that generalizes each of the earlier results. This leads us to a natural notion of distance for such codes, and we derive a number of distance results for subclasses of the codes. We show how EACQ codes form a proper subclass of the entanglement-assisted subspace codes defined by EAOAQEC. We identify and construct new classes of entanglement-assisted subsystem codes and entanglement-assisted hybrid classical-quantum codes that are found outside of the earlier approaches.

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)
• Class of codes correcting absorptions and emissions [59.90381090395222]
  We construct a family of quantum codes that protect against all emission, absorption, dephasing, and raising/lowering errors up to an arbitrary fixed order. We derive simplified error correction conditions for a general AE code and show that any permutation-invariant code that corrects $le t$ errors can be mapped to an AE code.
  arXiv  Detail & Related papers  (2024-10-04T16:14:03Z)
• Smallest quantum codes for amplitude damping noise [6.58877386288094]
  We describe the smallest quantum error correcting (QEC) code to correct for amplitude-damping (AD) noise, namely, a 3-qubit code. We generalize this construction to create a family of codes that correct AD noise up to any fixed order.
  arXiv  Detail & Related papers  (2024-09-30T18:55:09Z)
• Testing the Accuracy of Surface Code Decoders [55.616364225463066]
  Large-scale, fault-tolerant quantum computations will be enabled by quantum error-correcting codes (QECC) This work presents the first systematic technique to test the accuracy and effectiveness of different QECC decoding schemes.
  arXiv  Detail & Related papers  (2023-11-21T10:22:08Z)
• Stabilizer Formalism for Operator Algebra Quantum Error Correction [0.0]
  We introduce a stabilizer formalism for the general quantum error correction framework called operator algebra quantum error correction (OAQEC) We formulate a theorem that fully characterizes the Pauli errors that are correctable for a given code. We show how some recent hybrid subspace code constructions are captured by the formalism.
  arXiv  Detail & Related papers  (2023-04-22T16:45:50Z)
• Quantum spherical codes [55.33545082776197]
  We introduce a framework for constructing quantum codes defined on spheres by recasting such codes as quantum analogues of the classical spherical codes. We apply this framework to bosonic coding, obtaining multimode extensions of the cat codes that can outperform previous constructions.
  arXiv  Detail & Related papers  (2023-02-22T19:00:11Z)
• Gottesman-Kitaev-Preskill codes: A lattice perspective [0.7734726150561088]
  We show how different decoding strategies are precisely related, propose new ways to obtain GKP codes by means of glued lattices and the product of lattices. We present general results that we illustrate through examples taken from different classes of codes, including scaled self-dual GKP codes and the tensord surface-GKP code.
  arXiv  Detail & Related papers  (2021-09-29T18:08:37Z)
• Modifying method of constructing quantum codes from highly entangled states [0.0]
  We provide explicit constructions for codewords, encoding procedure and stabilizer formalism of the QECCs. We modify the method to produce another set of stabilizer QECCs that encode a logical qudit into a subspace spanned by AME states.
  arXiv  Detail & Related papers  (2020-05-04T12:28:58Z)
• Using Quantum Metrological Bounds in Quantum Error Correction: A Simple Proof of the Approximate Eastin-Knill Theorem [77.34726150561087]
  We present a proof of the approximate Eastin-Knill theorem, which connects the quality of a quantum error-correcting code with its ability to achieve a universal set of logical gates. Our derivation employs powerful bounds on the quantum Fisher information in generic quantum metrological protocols.
  arXiv  Detail & Related papers  (2020-04-24T17:58:10Z)
• Cellular automaton decoders for topological quantum codes with noisy measurements and beyond [68.8204255655161]
  We propose an error correction procedure based on a cellular automaton, the sweep rule, which is applicable to a broad range of codes beyond topological quantum codes. For simplicity, we focus on the three-dimensional (3D) toric code on the rhombic dodecahedral lattice with boundaries and prove that the resulting local decoder has a non-zero error threshold. We find that this error correction procedure is remarkably robust against measurement errors and is also essentially insensitive to the details of the lattice and noise model.
  arXiv  Detail & Related papers  (2020-04-15T18:00:01Z)

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.