Bias-tailored quantum LDPC codes
- URL: http://arxiv.org/abs/2202.01702v3
- Date: Fri, 5 May 2023 15:09:11 GMT
- Title: Bias-tailored quantum LDPC codes
- Authors: Joschka Roffe, Lawrence Z. Cohen, Armanda O. Quintavalle, Daryus
Chandra, Earl T. Campbell
- Abstract summary: We introduce a bias-tailored lifted product code construction that provides the framework to expand bias-tailoring methods.
We show that bias-tailored quantum low density parity check codes can be similarly bias-tailored.
Our Monte Carlo simulations, performed under asymmetric noise, show that bias-tailored codes achieve several orders of magnitude improvement in their error suppression.
- Score: 3.565124653091339
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Bias-tailoring allows quantum error correction codes to exploit qubit noise
asymmetry. Recently, it was shown that a modified form of the surface code, the
XZZX code, exhibits considerably improved performance under biased noise. In
this work, we demonstrate that quantum low density parity check codes can be
similarly bias-tailored. We introduce a bias-tailored lifted product code
construction that provides the framework to expand bias-tailoring methods
beyond the family of 2D topological codes. We present examples of bias-tailored
lifted product codes based on classical quasi-cyclic codes and numerically
assess their performance using a belief propagation plus ordered statistics
decoder. Our Monte Carlo simulations, performed under asymmetric noise, show
that bias-tailored codes achieve several orders of magnitude improvement in
their error suppression relative to depolarising noise.
Related papers
- Tailoring Dynamical Codes for Biased Noise: The X$^3$Z$^3$ Floquet Code [0.0]
We propose the X$3$Z$3$ Floquet code, a type of dynamical code with improved performance under biased noise.
Our work establishes the X$3$Z$3$ code as a prime quantum error-correcting code candidate.
arXiv Detail & Related papers (2024-11-07T18:49:16Z) - 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) - 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) - Neural Belief Propagation Decoding of Quantum LDPC Codes Using
Overcomplete Check Matrices [60.02503434201552]
We propose to decode QLDPC codes based on a check matrix with redundant rows, generated from linear combinations of the rows in the original check matrix.
This approach yields a significant improvement in decoding performance with the additional advantage of very low decoding latency.
arXiv Detail & Related papers (2022-12-20T13:41:27Z) - Correcting non-independent and non-identically distributed errors with
surface codes [0.8039067099377079]
We develop and investigate the properties of topological surface codes adapted to a known noise structure by Clifford conjugations.
We show that the surface code locally tailored to non-uniform single-qubit noise in conjunction with a scalable matching decoder yields an increase in error thresholds and exponential suppression of sub-threshold failure rates.
arXiv Detail & Related papers (2022-08-03T16:21:44Z) - 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) - Improved decoding of circuit noise and fragile boundaries of tailored
surface codes [61.411482146110984]
We introduce decoders that are both fast and accurate, and can be used with a wide class of quantum error correction codes.
Our decoders, named belief-matching and belief-find, exploit all noise information and thereby unlock higher accuracy demonstrations of QEC.
We find that the decoders led to a much higher threshold and lower qubit overhead in the tailored surface code with respect to the standard, square surface code.
arXiv Detail & Related papers (2022-03-09T18:48:54Z) - 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) - Optimal noise estimation from syndrome statistics of quantum codes [0.7264378254137809]
Quantum error correction allows to actively correct errors occurring in a quantum computation when the noise is weak enough.
Traditionally, this information is obtained by benchmarking the device before operation.
We address the question of what can be learned from only the measurements done during decoding.
arXiv Detail & Related papers (2020-10-05T18:00:26Z) - 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.