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Paper 1
A simple decoder for topological codes
James R. Wootton
- Year
- 2013
- Journal
- arXiv preprint
- DOI
- arXiv:1310.2393
- arXiv
- 1310.2393
Here we study an efficient algorithm for decoding the topological codes. It is based on a simple principle, which should allow straightforward generalization to complex decoding problems. It is benchmarked with the planar code for both i.i.d. and spatially correlated errors and is found to compare well with existing methods.
Open paperPaper 2
QKAN: Quantum Kolmogorov-Arnold Networks
Petr Ivashkov, Po-Wei Huang, Kelvin Koor, Lirandë Pira, Patrick Rebentrost
- Year
- 2024
- Journal
- arXiv preprint
- DOI
- arXiv:2410.04435
- arXiv
- 2410.04435
The potential of learning models in quantum hardware remains an open question. Yet, the field of quantum machine learning persistently explores how these models can take advantage of quantum implementations. Recently, a new neural network architecture, called Kolmogorov-Arnold Networks (KAN), has emerged, inspired by the compositional structure of the Kolmogorov-Arnold representation theorem. In this work, we design a quantum version of KAN called QKAN. Our QKAN exploits powerful quantum linear algebra tools, including quantum singular value transformation, to apply parameterized activation functions on the edges of the network. QKAN is based on block-encodings, making it inherently suitable for direct quantum input. Furthermore, we analyze its asymptotic complexity, building recursively from a single layer to an end-to-end neural architecture. The gate complexity of QKAN scales linearly with the cost of constructing block-encodings for input and weights, suggesting broad applicability in tasks with high-dimensional input. QKAN serves as a trainable quantum machine learning model by combining parameterized quantum circuits with established quantum subroutines. Lastly, we propose a multivariate state preparation strategy based on the construction of the QKAN architecture.
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