Noise-adapted qudit codes for amplitude-damping noise

• URL: http://arxiv.org/abs/2406.02444v1
• Date: Tue, 4 Jun 2024 16:07:26 GMT
• Title: Noise-adapted qudit codes for amplitude-damping noise
• Authors: Sourav Dutta, Debjyoti Biswas, Prabha Mandayam,
• Abstract summary: We propose a class of qudit error correcting codes tailored to protect against amplitude-damping noise. Specifically, we construct a class of four-qudit codes that satisfies the error correction conditions for all single-qudit and a few two-qudit damping errors. For the $d=2$ case, our QEC scheme is identical to the known example of the $4$-qubit code and the associated syndrome-based recovery.
• Score: 6.320926638892934
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum error correction (QEC) plays a critical role in preventing information loss in quantum systems and provides a framework for reliable quantum computation. Identifying quantum codes with nice code parameters for physically motivated noise models remains an interesting challenge. Going beyond qubit codes, here we propose a class of qudit error correcting codes tailored to protect against amplitude-damping noise. Specifically, we construct a class of four-qudit codes that satisfies the error correction conditions for all single-qudit and a few two-qudit damping errors up to the leading order in the damping parameter $\gamma$. We devise a protocol to extract syndromes that identify this set of errors unambiguously, leading to a noise-adapted recovery scheme that achieves a fidelity loss of $\cO(\gamma^{2})$. For the $d=2$ case, our QEC scheme is identical to the known example of the $4$-qubit code and the associated syndrome-based recovery. We also assess the performance of our class of codes using the Petz recovery map and note some interesting deviations from the qubit case.

Related papers

• Variational Graphical Quantum Error Correction Codes: adjustable codes from topological insights [1.3999481573773074]
  We develop a new class of quantum error-correcting codes termed Variational Graphical Quantum Error Correction(VGQEC) codes. The VGQEC codes feature adjustable configuration parameters that play a pivotal role in determining the error-correcting capability of the codes.
  arXiv  Detail & Related papers  (2024-10-03T15:47:48Z)
• 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)
• Fault-tolerant noise guessing decoding of quantum random codes [0.0]
  We present a new decoder for quantum random linear codes (QRLCs) capable of dealing with imperfect decoding operations. We analyze the fault-tolerant characteristics of QRLCs with a new noise-guessing decoding technique.
  arXiv  Detail & Related papers  (2024-07-01T17:54:23Z)
• Bit-flipping Decoder Failure Rate Estimation for (v,w)-regular Codes [84.0257274213152]
  We propose a new technique to provide accurate estimates of the DFR of a two-iterations (parallel) bit flipping decoder. We validate our results, providing comparisons of the modeled and simulated weight of the syndrome, incorrectly-guessed error bit distribution at the end of the first iteration, and two-itcrypteration Decoding Failure Rates (DFR)
  arXiv  Detail & Related papers  (2024-01-30T11:40:24Z)
• Fault-tolerant quantum architectures based on erasure qubits [49.227671756557946]
  We exploit the idea of erasure qubits, relying on an efficient conversion of the dominant noise into erasures at known locations. We propose and optimize QEC schemes based on erasure qubits and the recently-introduced Floquet codes. Our results demonstrate that, despite being slightly more complex, QEC schemes based on erasure qubits can significantly outperform standard approaches.
  arXiv  Detail & Related papers  (2023-12-21T17:40:18Z)
• The END: An Equivariant Neural Decoder for Quantum Error Correction [73.4384623973809]
  We introduce a data efficient neural decoder that exploits the symmetries of the problem. We propose a novel equivariant architecture that achieves state of the art accuracy compared to previous neural decoders.
  arXiv  Detail & Related papers  (2023-04-14T19:46:39Z)
• 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)
• Tailored XZZX codes for biased noise [60.12487959001671]
  We study a family of codes having XZZX-type stabilizer generators. We show that these XZZX codes are highly qubit efficient if tailored to biased noise.
  arXiv  Detail & Related papers  (2022-03-30T17:26:31Z)
• Adaptive quantum codes: constructions, applications and fault tolerance [0.0]
  A perfect quantum code requires atleast five physical qubits to observe a noticeable improvement over the no-QEC scenario. We propose an adaptive QEC protocol that allows transmission of quantum information from one site to the other over a 1-d spin chain with high fidelity.
  arXiv  Detail & Related papers  (2022-03-07T10:06:16Z)
• Performance of teleportation-based error correction circuits for bosonic codes with noisy measurements [58.720142291102135]
  We analyze the error-correction capabilities of rotation-symmetric codes using a teleportation-based error-correction circuit. We find that with the currently achievable measurement efficiencies in microwave optics, bosonic rotation codes undergo a substantial decrease in their break-even potential.
  arXiv  Detail & Related papers  (2021-08-02T16:12:13Z)
• Efficiently computing logical noise in quantum error correcting codes [0.0]
  We show that measurement errors on readout qubits manifest as a renormalization on the effective logical noise. We derive general methods for reducing the computational complexity of the exact effective logical noise by many orders of magnitude.
  arXiv  Detail & Related papers  (2020-03-23T19:40:56Z)

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.