14,713 research outputs found
Neural Decoder for Topological Codes using Pseudo-Inverse of Parity Check Matrix
Recent developments in the field of deep learning have motivated many
researchers to apply these methods to problems in quantum information. Torlai
and Melko first proposed a decoder for surface codes based on neural networks.
Since then, many other researchers have applied neural networks to study a
variety of problems in the context of decoding. An important development in
this regard was due to Varsamopoulos et al. who proposed a two-step decoder
using neural networks. Subsequent work of Maskara et al. used the same concept
for decoding for various noise models. We propose a similar two-step neural
decoder using inverse parity-check matrix for topological color codes. We show
that it outperforms the state-of-the-art performance of non-neural decoders for
independent Pauli errors noise model on a 2D hexagonal color code. Our final
decoder is independent of the noise model and achieves a threshold of .
Our result is comparable to the recent work on neural decoder for quantum error
correction by Maskara et al.. It appears that our decoder has significant
advantages with respect to training cost and complexity of the network for
higher lengths when compared to that of Maskara et al.. Our proposed method can
also be extended to arbitrary dimension and other stabilizer codes.Comment: 12 pages, 12 figures, 2 tables, submitted to the 2019 IEEE
International Symposium on Information Theor
Scalable Neural Network Decoders for Higher Dimensional Quantum Codes
Machine learning has the potential to become an important tool in quantum
error correction as it allows the decoder to adapt to the error distribution of
a quantum chip. An additional motivation for using neural networks is the fact
that they can be evaluated by dedicated hardware which is very fast and
consumes little power. Machine learning has been previously applied to decode
the surface code. However, these approaches are not scalable as the training
has to be redone for every system size which becomes increasingly difficult. In
this work the existence of local decoders for higher dimensional codes leads us
to use a low-depth convolutional neural network to locally assign a likelihood
of error on each qubit. For noiseless syndrome measurements, numerical
simulations show that the decoder has a threshold of around when
applied to the 4D toric code. When the syndrome measurements are noisy, the
decoder performs better for larger code sizes when the error probability is
low. We also give theoretical and numerical analysis to show how a
convolutional neural network is different from the 1-nearest neighbor
algorithm, which is a baseline machine learning method
Inviwo -- A Visualization System with Usage Abstraction Levels
The complexity of today's visualization applications demands specific
visualization systems tailored for the development of these applications.
Frequently, such systems utilize levels of abstraction to improve the
application development process, for instance by providing a data flow network
editor. Unfortunately, these abstractions result in several issues, which need
to be circumvented through an abstraction-centered system design. Often, a high
level of abstraction hides low level details, which makes it difficult to
directly access the underlying computing platform, which would be important to
achieve an optimal performance. Therefore, we propose a layer structure
developed for modern and sustainable visualization systems allowing developers
to interact with all contained abstraction levels. We refer to this interaction
capabilities as usage abstraction levels, since we target application
developers with various levels of experience. We formulate the requirements for
such a system, derive the desired architecture, and present how the concepts
have been exemplary realized within the Inviwo visualization system.
Furthermore, we address several specific challenges that arise during the
realization of such a layered architecture, such as communication between
different computing platforms, performance centered encapsulation, as well as
layer-independent development by supporting cross layer documentation and
debugging capabilities
Tricolored Lattice Gauge Theory with Randomness: Fault-Tolerance in Topological Color Codes
We compute the error threshold of color codes, a class of topological quantum
codes that allow a direct implementation of quantum Clifford gates, when both
qubit and measurement errors are present. By mapping the problem onto a
statistical-mechanical three-dimensional disordered Ising lattice gauge theory,
we estimate via large-scale Monte Carlo simulations that color codes are stable
against 4.5(2)% errors. Furthermore, by evaluating the skewness of the Wilson
loop distributions, we introduce a very sensitive probe to locate first-order
phase transitions in lattice gauge theories.Comment: 12 pages, 5 figures, 1 tabl
Analysing correlated noise on the surface code using adaptive decoding algorithms
Laboratory hardware is rapidly progressing towards a state where quantum
error-correcting codes can be realised. As such, we must learn how to deal with
the complex nature of the noise that may occur in real physical systems. Single
qubit Pauli errors are commonly used to study the behaviour of error-correcting
codes, but in general we might expect the environment to introduce correlated
errors to a system. Given some knowledge of structures that errors commonly
take, it may be possible to adapt the error-correction procedure to compensate
for this noise, but performing full state tomography on a physical system to
analyse this structure quickly becomes impossible as the size increases beyond
a few qubits. Here we develop and test new methods to analyse blue a particular
class of spatially correlated errors by making use of parametrised families of
decoding algorithms. We demonstrate our method numerically using a diffusive
noise model. We show that information can be learnt about the parameters of the
noise model, and additionally that the logical error rates can be improved. We
conclude by discussing how our method could be utilised in a practical setting
blue and propose extensions of our work to study more general error models.Comment: 19 pages, 8 figures, comments welcome; v2 - minor typos corrected
some references added; v3 - accepted to Quantu
Topological color codes on Union Jack lattices: A stable implementation of the whole Clifford group
We study the error threshold of topological color codes on Union Jack
lattices that allow for the full implementation of the whole Clifford group of
quantum gates. After mapping the error-correction process onto a statistical
mechanical random 3-body Ising model on a Union Jack lattice, we compute its
phase diagram in the temperature-disorder plane using Monte Carlo simulations.
Surprisingly, topological color codes on Union Jack lattices have similar error
stability than color codes on triangular lattices, as well as the Kitaev toric
code. The enhanced computational capabilities of the topological color codes on
Union Jack lattices with respect to triangular lattices and the toric code
demonstrate the inherent robustness of this implementation.Comment: 8 pages, 4 figures, 1 tabl
Benchmarking and Error Diagnosis in Multi-Instance Pose Estimation
We propose a new method to analyze the impact of errors in algorithms for
multi-instance pose estimation and a principled benchmark that can be used to
compare them. We define and characterize three classes of errors -
localization, scoring, and background - study how they are influenced by
instance attributes and their impact on an algorithm's performance. Our
technique is applied to compare the two leading methods for human pose
estimation on the COCO Dataset, measure the sensitivity of pose estimation with
respect to instance size, type and number of visible keypoints, clutter due to
multiple instances, and the relative score of instances. The performance of
algorithms, and the types of error they make, are highly dependent on all these
variables, but mostly on the number of keypoints and the clutter. The analysis
and software tools we propose offer a novel and insightful approach for
understanding the behavior of pose estimation algorithms and an effective
method for measuring their strengths and weaknesses.Comment: Project page available at
http://www.vision.caltech.edu/~mronchi/projects/PoseErrorDiagnosis/; Code
available at https://github.com/matteorr/coco-analyze; published at ICCV 1
- …