Bounds on Autonomous Quantum Error Correction
- URL: http://arxiv.org/abs/2308.16233v1
- Date: Wed, 30 Aug 2023 18:00:07 GMT
- Title: Bounds on Autonomous Quantum Error Correction
- Authors: Oles Shtanko, Yu-Jie Liu, Simon Lieu, Alexey V. Gorshkov, Victor V.
Albert
- Abstract summary: 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.
- Score: 3.9119979887528125
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Autonomous quantum memories are a way to passively protect quantum
information using engineered dissipation that creates an "always-on'' decoder.
We analyze Markovian autonomous decoders that can be implemented with a wide
range of qubit and bosonic error-correcting codes, and derive several upper
bounds and a lower bound on the logical error rate in terms of correction and
noise rates. 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. For codes with a
threshold, we show that it is possible to achieve faster-than-polynomial decay
of the logical error rate with code size by using superlogarithmic scaling of
the correction rate. We illustrate our results with several examples. One
example is an exactly solvable global dissipative toric code model that can
achieve an effective logical error rate that decreases exponentially with the
linear lattice size, provided that the recovery rate grows proportionally with
the linear lattice size.
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) - Fault-tolerant quantum computation using large spin cat-codes [0.8640652806228457]
We construct a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code.
We show how to generate a universal gate set, including the rank-preserving CNOT gate, using quantum control and the Rydberg blockade.
These findings pave the way for encoding a qubit in a large spin with the potential to achieve fault tolerance, high threshold, and reduced resource overhead in quantum information processing.
arXiv Detail & Related papers (2024-01-08T22:56:05Z) - 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) - 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) - A Practical and Scalable Decoder for Topological Quantum Error
Correction with Digital Annealer [0.5658123802733283]
We propose an efficient and scalable decoder for quantum error correction using Fujitsu Digital Annealer (DA)
In particular, we implement the proposed DA decoder for the surface code and perform detailed numerical experiments for various code to see its performance and scalability.
It is also shown that the DA decoder has advantages over the Union-Find (UF) decoder from a variety of perspectives including hardware implementation.
arXiv Detail & Related papers (2022-03-29T07:48:51Z) - 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) - 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) - 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) - Correcting spanning errors with a fractal code [7.6146285961466]
We propose an efficient decoder for the Fibonacci code'; a two-dimensional classical code that mimics the fractal nature of the cubic code.
We perform numerical experiments that show our decoder is robust to one-dimensional, correlated errors.
arXiv Detail & Related papers (2020-02-26T19:00:06Z)
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.