August challenge (#43)

* Add August challenge * Update README

Author: amirebrahimi

README.md

@@ -1,38 +1,40 @@
 # QOSF Monthly Challenges
 
-Repository containing monthly challenges in quantum computing.
+A repository containing monthly challenges in quantum computing.
 
 ## Current Challenge
 
-**Link to Problem Notebook**: [July 2021 Challenge](challenge-2021.07-jul/challenge-2021.07-jul.ipynb) - Quantum State Tomography
+**Link to Challenge Notebook**: [August 2021 Challenge](challenge-2021.07-aug/challenge-2021.07-aug.ipynb) - W states
 
-**Release date**: July 21st, 2021
+**Release date**: August 19th, 2021 
+**Submission deadline (optional):** September 16, 2021
 
-**Submission deadline (optional):** August 18th, 2021
+You can see previous challenges [here](#previous-challenges).
 
 ## How it Works
 
-These challenges will help you hone your general quantum computing skills by tackling some problems.
+These challenges will help you hone your quantum computing skills by being exposed to a variety of problems in different areas.
 
-We release a new question every month. These are open to everybody and you're welcome to try your hand at solving them either individually or as a team. 
-- You are free to use any framework that you like, and submit your solutions in any format. Just make sure they're easy to evaluate.
+We release a new challenge every month that are open to anyone and everyone. You're welcome to try your hand at solving them individually or as a team. 
 
-**You're also welcome to *contribute* challenge questions! Open an issue on this repo and describe the question, we'll take a look at it!** 
+You are free to use any framework that you like and submit your solutions in any format. Just make sure that they're easy to evaluate.
+
+**You're also welcome to *contribute* challenges! Open an issue on this repo and describe your idea and we'll be happy to take a look at it!** 
 
 ## Tentative Timeline
 
-- We will try and release each challenge on the same date every month.
-- You get a month's time to solve each question, but if you wish to have your solution reviewed please aim to submit your solution within the first 2 or 3 weeks (to allow for sufficient time for reviews).
+- We try and release each challenge on the same date every month, but some times this varies (hey, we're all volunteers).
+- You get a month's time to solve each challenge, but if you wish to have your solution reviewed please aim to submit your solution within the first 2 or 3 weeks (to allow for sufficient time for reviews).
 
 ## Submission
 
 - Please fork this repository and use that to work on your solutions to the challenges. 
-- Follow the folder structure that you see here. For each challenge, create a directory in your repo called `challenge-xx`, where xx is the challenge number.
-- Under this directory, create a folder with your github username (all lowercase, separated-by-hyphens). Your solution goes into this directory.
+- Under the challenge directory you wish to attempt to solve, create a folder with your github username (all lowercase, separated-by-hyphens). Your solution goes into this directory. Look at prior submissions for examples if you are not clear on this.
+- Do not delete or modify any of the original challenge files since this will show up when you submit your solution.
 - If you complete a challenge and want to "submit" your solution, raise a Pull Request (PR) from your repo to ours. 
-- If your solutions works, we'll merge it to our repo.
-- The best ones will be given a shout-out! 😃
-- Note that if you're working as a team, it is sufficient to submit just one PR.
+- **After you submit your PR, you must find at least one other reviewer to review your work**. Your reviewer could be a fellow challenge submitter (trade off reviews!), reach out individually to another community member on Slack, or post in the [#monthly-challenges](https://qosf.slack.com/archives/C01D2GB1DMM) channel asking for a review.
+- We will give shout-outs to the best submissions! 😃
+- Note that if you're working as a team, it is sufficient to submit just one PR. Please make sure to have all of your teammates properly credited in your solution.
 
 ## Evaluation
 
@@ -42,7 +44,7 @@ We release a new question every month. These are open to everybody and you're we
 
 ## Communication
 
-- Please join the Slack channel for the challenge, where you can ask any questions you might have: [#monthly-challenges](https://qosf.slack.com/archives/C01D2GB1DMM)
+- Please join the [#monthly-challenges](https://qosf.slack.com/archives/C01D2GB1DMM) Slack channel for the challenge where you can share ideas with others and ask any questions you might have.
 
 ## Git FAQ
 
@@ -119,4 +121,10 @@ Submission deadline (optional): May 30th, 2021
 
 [June 2021 Challenge](challenge-2021.06-jun/challenge-2021.06-jun.ipynb): k-Nearest Neighbors 
 Release date: June 19th, 2021 
-Submission deadline (optional): July 17th, 2021 
+Submission deadline (optional): July 17th, 2021 
+
+---
+
+[July 2021 Challenge](challenge-2021.07-jul/challenge-2021.07-jul.ipynb): Quantum State Tomography 
+Release date: July 21st, 2021 
+Submission deadline (optional): August 18th, 2021 

challenge-2021.08-aug/challenge-2021.08-aug.ipynb

@@ -0,0 +1,87 @@
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+ "# August 2021 Challenge: W states\n",
+ "\n",
+ "A [**W state**](https://en.wikipedia.org/wiki/W_state) is an entangled state of the form:\n",
+ "\n",
+ "$$ | \\text{W} \\rangle = \\sqrt{\\frac{1}{3}} \\left( | 001 \\rangle + | 010 \\rangle + | 100 \\rangle \\right ) $$\n",
+ "\n",
+ "If you're coming from a machine learning background, you might think it looks like a superposition of [one-hots](https://en.wikipedia.org/wiki/One-hot) where each one-hot is equally probable.\n",
+ "\n",
+ "If you're new to quantum computing, then it might look similar to the [**GHZ state**](https://en.wikipedia.org/wiki/Greenberger%E2%80%93Horne%E2%80%93Zeilinger_state), which you've probably been acquainted with:\n",
+ "\n",
+ "$$ | \\text{GHZ} \\rangle = \\frac{| 000 \\rangle + | 111 \\rangle}{\\sqrt{2}} $$\n",
+ "\n",
+ "which itself is a natural extension of the $|\\Phi^+\\rangle$ [**Bell state**](https://en.wikipedia.org/wiki/Bell_state):\n",
+ "\n",
+ "$$ | \\Phi^+ \\rangle = \\frac{| 00 \\rangle + | 11 \\rangle}{\\sqrt{2}} $$\n",
+ "\n",
+ "The original state was 3 qubits and has since been generalized to $n$ qubits:\n",
+ "\n",
+ "$$\n",
+ "| W_n \\rangle = \\frac{1}{\\sqrt{n}} \\left ( | 0\\dots 01 \\rangle + | 0\\dots 10 \\rangle + \\dots + | 1\\dots 00 \\rangle \\right ) \n",
+ "$$\n",
+ "\n",
+ "Where it differs from the $\\text{GHZ}$ state is in its robustness. After a single qubit is measured there is still remaining entanglement among the other qubits. This is not the case in a $\\text{GHZ}$ state. As such, it can be a valuable resource in the implementation of teleportation or quantum memories.\n",
+ "\n",
+ "If you're interested in a more detailed explanation, then please see Resource [A].\n",
+ "\n",
+ "For this challenge, we're going to put a slight spin on what's normally asked of you. If you Google \"W state preparation\" you're going to find many examples, such as those in Resource [B]. Instead of a straight-forward analytical approach to solving this challenge, we ask you to implement a solution using a [variational quantum algorithm (VQA)](https://www.mustythoughts.com/vqas-how-do-they-work). Which one? That is up to you.\n",
+ "\n",
+ "**Warm up:** If you're new to state preparation, then as a warm up start by creating the $|\\Phi^+\\rangle$ and $|\\text{GHZ}\\rangle$ states above without the use of a VQA.\n",
+ "\n",
+ "**Level 1:** Use a VQA to create a 4-qubit $\\text{W}$ state.\n",
+ "\n",
+ "**Level 2:** Generalize the program to create an $n$-qubit $\\text{W}$ state.\n",
+ "\n",
+ "**Level 3:** Adjust your VQA to have it not introduce any global phase (NOTE: this implies that we're using a simulator since you wouldn't be able to determine global phase on actual hardware).\n",
+ "\n",
+ "**Bonus:** If you're enjoying this challenge, then you may also like to try implementing the approach in Reference [1].\n",
+ "\n",
+ "**Resources**\n",
+ "\n",
+ "[A] IBM Quantum Composer Docs: Field Guide on Entaglement. https://quantum-computing.ibm.com/composer/docs/iqx/guide/entanglement#w-states-vs-ghz-states \n",
+ "[B] Stack Exchange: General construction of $\\text{W}_n$-state. https://quantumcomputing.stackexchange.com/questions/4350/general-construction-of-w-n-state \n",
+ "\n",
+ "**References**\n",
+ "\n",
+ "[1] Efficient quantum algorithms for GHZ and W states, and implementation on the IBM quantum computer. Diogo Cruz, et. al. https://arxiv.org/pdf/1807.05572.pdf \n",
+ "\n",
+ "\n",
+ "_Special thanks to Diego Emilio Serrano for the idea, who also credits Soham Pal_"
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