add k mwms paper (#5)

Author: maolinml

README.md

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 This package contains lattice algorithms that were used in the paper [Closest lattice point decoding for multimode Gottesman-Kitaev-Preskill codes](https://journals.aps.org/prxquantum/abstract/10.1103/PRXQuantum.4.040334). The package contains several [lattice reduction algorithms](https://www.ant.uni-bremen.de/sixcms/media.php/102/10740/SPM_2011_Wuebben.pdf), such as [Lenstra-Lenstra-Lovász](https://en.wikipedia.org/wiki/Lenstra%E2%80%93Lenstra%E2%80%93Lov%C3%A1sz_lattice_basis_reduction_algorithm) and [Korkine-Zolotarev](https://en.wikipedia.org/wiki/Korkine%E2%80%93Zolotarev_lattice_basis_reduction_algorithm) algorithms, and a [search algorithm](https://publications.lib.chalmers.se/records/fulltext/14990/local_14990.pdf) for solving the [closest point problem](https://en.wikipedia.org/wiki/Lattice_problem#Closest_vector_problem_(CVP)) and the [shortest vector problem](https://en.wikipedia.org/wiki/Lattice_problem#Shortest_vector_problem_(SVP)). For the Gottesman-Kitaev-Preskill (GKP) codes, the package includes  the $D_n$ lattice and two types of repetition-GKP codes, which can be decoded efficiently from a lattice perspective. The data and code for the paper can be found in the folder `examples/papers/Closest_lattice_point_decoding_for_multimode_GKP_codes`.
 
 This package also contains several algorithms that were used in the paper [Exploring the quantum capacity of a Gaussian random displacement channel using
-Gottesman-Kitaev-Preskill codes and maximum likelihood decoding](tbd), including an efficient and exact maximum likelihood decoder (MLD) for surface-square GKP codes, and a tensor-network decoder to approximate the MLD for generic concatenated-GKP codes. The latter is built on top of the decoder in [SweepContractor.jl](https://github.com/chubbc/SweepContractor.jl). The data and code for the paper can be found in the folder `examples/papers/Exploring_the_quantum_capacity_of_a_Gaussian_random_displacement_channel_using_GKP_codes_and_maximum_likelihood_decoding`. 
+Gottesman-Kitaev-Preskill codes and maximum likelihood decoding](https://arxiv.org/abs/2411.04277), including an efficient and exact maximum likelihood decoder (MLD) for surface-square GKP codes, and a tensor-network decoder to approximate the MLD for generic concatenated-GKP codes. The latter is built on top of the decoder in [SweepContractor.jl](https://github.com/chubbc/SweepContractor.jl). The data and code for the paper can be found in the folder `examples/papers/Exploring_the_quantum_capacity_of_a_Gaussian_random_displacement_channel_using_GKP_codes_and_maximum_likelihood_decoding`. 
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+This package also contains several algorithms that were used in the paper *Approximate maximum likelihood decoding with $K$ minimum weight matchings*  (to appear soon). In this paper, we introduce a novel algorithm to approximate the optimal maximum likelihood decoding strategey via finding $K$ minimum weight matchings from the decoding graph. The data and plots for the paper can be found in the folder `examples/papers/Approximate_maximum_likelihood_decoding_with_K_minimum_weight_matchings`. 
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 ## Security
 

examples/papers/Approximate_maximum_likelihood_decoding_with_K_minimum_weight_matchings/Fig_qubit_surface.ipynb

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+In this folder, we provide the code to reproduce the plots from the paper *Approximate maximum likelihood decoding with $K$ minimum weight matchings* (To appear soon). 
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+1. The data used in the paper can be found in the `data/` folder.
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+2. The plots used in the paper can be found in the `plots/` folder.
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+3. To reproduce the figures in the paper with existing data, simply run "Figs_*.ipynb"