Approximate quantum error correcting codes from conformal field theory

• URL: http://arxiv.org/abs/2406.09555v2
• Date: Wed, 7 Aug 2024 20:14:10 GMT
• Title: Approximate quantum error correcting codes from conformal field theory
• Authors: Shengqi Sang, Timothy H. Hsieh, Yijian Zou,
• Abstract summary: We consider generic 1+1D CFT codes under extensive local dephasing channels. We show that a CFT code with continuous symmetry saturates a bound on the recovery fidelity for covariant codes.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The low-energy subspace of a conformal field theory (CFT) can serve as a quantum error correcting code, with important consequences in holography and quantum gravity. We consider generic 1+1D CFT codes under extensive local dephasing channels and analyze their error correctability in the thermodynamic limit. We show that (i) there is a finite decoding threshold if and only if the minimal nonzero scaling dimension in the fusion algebra generated by the jump operator of the channel is larger than $1/2$ and (ii) the number of protected logical qubits $k \geq \Omega( \log \log n)$, where $n$ is the number of physical qubits. As an application, we show that the one-dimensional quantum critical Ising model has a finite threshold for certain types of dephasing noise. Our general results also imply that a CFT code with continuous symmetry saturates a bound on the recovery fidelity for covariant codes.

Related papers

• Exploring the quantum capacity of a Gaussian random displacement channel using Gottesman-Kitaev-Preskill codes and maximum likelihood decoding [0.9208007322096532]
  We analyze the error-correction performance of several families of multi-mode Gottesman-Kitaev-Preskill codes. We find that the error threshold of the surface-square GKP code is remarkably close to $sigma=1/sqrtesimeq 0.6065$. By focusing on multi-mode GKP codes that encode just one logical qubit over multiple bosonic modes, we show that GKP codes can achieve non-zero quantum state transmission rates.
  arXiv  Detail & Related papers  (2024-11-06T21:47:20Z)
• 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)
• Achieving metrological limits using ancilla-free quantum error-correcting codes [1.9265037496741413]
  Existing quantum error-correcting codes generally exploit entanglement between one probe and one noiseless ancilla of the same dimension. Here we construct two types of multi-probe quantum error-correcting codes, where the first one utilizes a negligible amount of ancillas and the second one is ancilla-free.
  arXiv  Detail & Related papers  (2023-03-02T00:51:02Z)
• 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)
• Asymptotically isometric codes for holography [3.6320742399728645]
  The holographic principle suggests that the low energy effective field theory of gravity has far too many states. It is then natural that any quantum error correcting code with such a quantum field theory as the code subspace is not isometric. We show that an isometric code can be recovered in the $N rightarrow infty$ limit when acting on fixed states in the code Hilbert space.
  arXiv  Detail & Related papers  (2022-11-22T17:46:58Z)
• Quantum Error Correction with Gauge Symmetries [69.02115180674885]
  Quantum simulations of Lattice Gauge Theories (LGTs) are often formulated on an enlarged Hilbert space containing both physical and unphysical sectors. We provide simple fault-tolerant procedures that exploit such redundancy by combining a phase flip error correction code with the Gauss' law constraint.
  arXiv  Detail & Related papers  (2021-12-09T19:29:34Z)
• 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)
• Exponential suppression of bit or phase flip errors with repetitive error correction [56.362599585843085]
  State-of-the-art quantum platforms typically have physical error rates near $10-3$. Quantum error correction (QEC) promises to bridge this divide by distributing quantum logical information across many physical qubits. We implement 1D repetition codes embedded in a 2D grid of superconducting qubits which demonstrate exponential suppression of bit or phase-flip errors.
  arXiv  Detail & Related papers  (2021-02-11T17:11:20Z)
• Error correction of a logical grid state qubit by dissipative pumping [0.0]
  We introduce and implement a dissipative map designed for physically realistic finite GKP codes. We demonstrate the extension of logical coherence using both square and hexagonal GKP codes.
  arXiv  Detail & Related papers  (2020-10-19T17:19:20Z)
• Fault-tolerant Coding for Quantum Communication [71.206200318454]
  encode and decode circuits to reliably send messages over many uses of a noisy channel. For every quantum channel $T$ and every $eps>0$ there exists a threshold $p(epsilon,T)$ for the gate error probability below which rates larger than $C-epsilon$ are fault-tolerantly achievable. Our results are relevant in communication over large distances, and also on-chip, where distant parts of a quantum computer might need to communicate under higher levels of noise.
  arXiv  Detail & Related papers  (2020-09-15T15:10:50Z)
• Quantum Error Source and Channel Coding [0.0]
  We prove conditions on the set of correctable error patterns allowing for unambiguous decoding based on a lookup table. We argue that quantum error correction is more aptly viewed as source compression in the sense of Shannon.
  arXiv  Detail & Related papers  (2020-04-20T17:55:21Z)

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.