add summary table to README.md (#140)

README.md

@@ -4,10 +4,45 @@
 The Braket Algorithm Library provides Amazon Braket customers with pre-built implementations of prominent quantum algorithms and experimental workloads as ready-to-run example notebooks.
 
 ---
+### Braket algorithms
+
 Currently, Braket algorithms are tested on Linux, Windows, and Mac.
 
 Running notebooks locally requires additional dependencies located in [notebooks/textbook/requirements.txt](https://github.com/amazon-braket/amazon-braket-algorithm-library/blob/main/notebooks/textbook/requirements.txt). See notebooks/textbook/README.md for more information.
 
+| Textbook algorithms | Notebook | References | 
+| ----- | ----- | ----- |
+| Bell's Inequality     | [Bells_Inequality.ipynb](notebooks/textbook/Bells_Inequality.ipynb)     | [Bell1964](https://journals.aps.org/ppf/abstract/10.1103/PhysicsPhysiqueFizika.1.195), [Greenberger1990](https://doi.org/10.1119/1.16243)     |
+| Bernstein–Vazirani | [Bernstein_Vazirani_Algorithm.ipynb](notebooks/textbook/Bernstein_Vazirani_Algorithm.ipynb) | [Bernstein1997](https://epubs.siam.org/doi/10.1137/S0097539796300921) |
+| CHSH Inequality | [CHSH_Inequality.ipynb](notebooks/textbook/CHSH_Inequality.ipynb) | [Clauser1970](https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.23.880) |
+| Deutsch-Jozsa | [Deutsch_Jozsa_Algorithm.ipynb](notebooks/textbook/Deutsch_Jozsa_Algorithm.ipynb) | [Deutsch1992](https://royalsocietypublishing.org/doi/10.1098/rspa.1992.0167) |
+| Grover's Search | [Grovers_Search.ipynb](notebooks/textbook/Grovers_Search.ipynb) | [Figgatt2017](https://www.nature.com/articles/s41467-017-01904-7), [Baker2019](https://arxiv.org/abs/1904.01671) |
+| QAOA | [Quantum_Approximate_Optimization_Algorithm.ipynb](notebooks/textbook/Quantum_Approximate_Optimization_Algorithm.ipynb) | [Farhi2014](https://arxiv.org/abs/1411.4028) |
+| Quantum Circuit Born Machine | [Quantum_Circuit_Born_Machine.ipynb](notebooks/textbook/Quantum_Circuit_Born_Machine.ipynb) | [Benedetti2019](https://www.nature.com/articles/s41534-019-0157-8),  [Liu2018](https://journals.aps.org/pra/abstract/10.1103/PhysRevA.98.062324) | 
+| QFT | [Quantum_Fourier_Transform.ipynb](notebooks/textbook/Quantum_Fourier_Transform.ipynb) | [Coppersmith2002](https://arxiv.org/abs/quant-ph/0201067) | 
+| QPE | [Quantum_Phase_Estimation_Algorithm.ipynb](notebooks/textbook/Quantum_Phase_Estimation_Algorithm.ipynb) | [Kitaev1995](https://arxiv.org/abs/quant-ph/9511026) |
+| Quantum Walk | [Quantum_Walk.ipynb](notebooks/textbook/Quantum_Walk.ipynb) | [Childs2002](https://arxiv.org/abs/quant-ph/0209131) |
+|Shor's| [Shors_Algorithm.ipynb](notebooks/textbook/Shors_Algorithm.ipynb) | [Shor1998](https://arxiv.org/abs/quant-ph/9508027) |
+| Simon's | [Simons_Algorithm.ipynb](notebooks/textbook/Simons_Algorithm.ipynb) | [Simon1997](https://epubs.siam.org/doi/10.1137/S0097539796298637) |
+
+
+| Advanced algorithms | Notebook | References |
+| ----- | ----- | ----- |
+| Quantum PCA | [Quantum_Principal_Component_Analysis.ipynb](notebooks/advanced_algorithms/Quantum_Principal_Component_Analysis.ipynb) | [He2022](https://ieeexplore.ieee.org/document/9669030) |
+| QMC | [Quantum_Computing_Quantum_Monte_Carlo.ipynb](notebooks/advanced_algorithms/Quantum_Computing_Quantum_Monte_Carlo.ipynb) | [Motta2018](https://wires.onlinelibrary.wiley.com/doi/10.1002/wcms.1364), [Peruzzo2014](https://www.nature.com/articles/ncomms5213) |
+
+---
+### Community repos
+
+> :warning: **The following includes projects that are not provided by AWS. You are solely responsible for your use of those projects (including compliance with any applicable licenses and fitness of the project for your particular purpose).**
+
+Quantum algorithm implementations using Braket in other repos:
+
+| Algorithm | Repo | References | Additional dependencies |
+| ----- | ----- | ----- | ----- |
+
+[comment]: <> (If you wish to highlight your implementation,  append the following content in a new line to the table above : | <Name> | <link to github repo> | <published reference> | <list of required packages on top of what is listed in amazon-braket-algorithm-library setup.py> |)
+
 ---
 ## <a name="install">Installing the Amazon Braket Algorithm Library</a>
 The Amazon Braket Algorithm Library can be installed from source by cloning this repository and running a pip install command in the root directory of the repository.