Update README and docs

README.md

@@ -57,7 +57,7 @@ When using PyMatching for research, please cite:
 ```
 @misc{higgott2020pymatching,
   author = {Higgott, Oscar},
-  title = {{PyMatching}: A library for decoding quantum error correcting codes using minimum-weight perfect matching},
+  title = {{PyMatching}: A Python package for decoding quantum error correcting codes using minimum-weight perfect matching},
   year = {2020},
   publisher = {GitHub},
   journal = {GitHub repository},

docs/index.rst

@@ -6,46 +6,43 @@
 PyMatching
 ==========
 
-PyMatching is a Python library for decoding quantum codes with the 
+PyMatching is a Python package for decoding quantum codes with the 
 minimum-weight perfect matching (MWPM) decoder, and is designed to 
 be fast and easy to use. 
 
-While a Python library such as NetworkX can also be used to 
+While a Python package such as NetworkX can also be used to 
 implement MWPM, it is far too slow to be used for large 
 fault-tolerance simulations, which often require 
 matching graphs with many thousands of nodes. On the other hand, 
-the widly used C++ BlossomV library is fast, but using it to decode 
+the widely used C++ BlossomV library is fast, but using it to decode 
 quantum codes also requires path-finding algorithms, which must 
 also be implemented in C++ for a fast implementation. Furthermore, 
 attempting to solve the full matching problem even with BlossomV 
 can become prohibitively expensive for matching graphs with more 
-than a few thousand nodes, since the average complexity is 
-empirically roughly quadratic in the number of nodes. BlossomV 
-is also not open-source since it does not have a permissive license.
+than a few thousand nodes, since the complexity is worse than 
+quadratic in the number of nodes. BlossomV is also not 
+open-source since it does not have a permissive license.
 
-PyMatching is intended to provide the best of both 
-worlds: all the 
-core functionality of PyMatching is useable via the Python 
-bindings, making it easy to use 
-in conjunction with numpy, scipy and NetworkX. However the 
-core algorithms and data structures are implemented 
-in C++ for good performance (with the help of the open-source 
-Lemon and the Boost Graph libraries), 
-using a local variant of the matching decoder given in the 
-Appendix of https://arxiv.org/abs/2010.09626, which empirically 
-has an average runtime roughly linear in the number of nodes 
+PyMatching is typically faster than a BlossomV/C++ implementation 
+of the full matching problem, while being easy to use in conjunction 
+with numpy, scipy and NetworkX using the Python bindings. 
+The core algorithms and data structures are implemented in C++ 
+for good performance (with the help of the open-source Lemon 
+and Boost Graph libraries), using a local variant of the matching 
+decoder given in the Appendix of https://arxiv.org/abs/2010.09626, 
+which empirically has an average runtime roughly linear in the number of nodes 
 and gives the same output as full matching in practice. Since 
-PyMatching uses the open-source Lemon C++ library for matching,
-which has similar performance to BlossomV, both PyMatching and 
+PyMatching uses the open-source Lemon C++ library for the Blossom algorithm,
+which has similar performance to Kolmogorov's BlossomV library, both PyMatching and 
 its dependencies have permissive licenses. PyMatching can be 
 applied to any quantum code for which 
 defects come in pairs (or in isolation at a boundary), 
-and does not require knowledge of the specific geometry 
+and it does not require knowledge of the specific geometry 
 used.
 
 Compared to a pure Python NetworkX implementation of MWPM, PyMatching 
 can be orders of magnitude faster, as shown here for the 
-toric code under an independent noise model at :math:`p=0.5`:
+toric code under an independent noise model at :math:`p=0.05`:
 
 .. figure::  _static/pymatching_vs_networkx.png
    :width: 300