# Simulation of discrete quantum random walk

## Week - 1: Classical Random Walk
### Resources
- [Classical Random Walks](https://en.wikipedia.org/wiki/Random_walk) - Wiki Page (Overall Idea)
- [Thesis Paper (Main Focus)](https://bayesianbrad.github.io/assets/publications/2014_thesis/paper.pdf) - contains all the main topics.
- [Blog on One Dimensional Random Walk](https://galileo.phys.virginia.edu/classes/152.mf1i.spring02/RandomWalk.htm)
- [Central Limit Theorem](https://youtu.be/zeJD6dqJ5lo?si=GzLH5Cepca7NMcR4)

### Task


- Code the above tasks in jupyter notebook and also include the information regarding the emergence of symmetery and also learn about the central limit theorem

## Week - 2: Quantum Computing Basics

### Resources
- Quantum Computation and Information - Nielsen and Chuang.
(Ch - 1 & 2)
- [QISKIT Global Summer School](https://youtube.com/playlist?list=PLOFEBzvs-VvrXTMy5Y2IqmSaUjfnhvBHR&si=FTyDUcvV8iOPIqzc) - Upto 6th Lecture. (For understanding Grover's Algorithm and Qiskit Library)

### Task
- Go through the above resources and understand the qiskit library and quantum computing basics properly

## Week - 3: Quantum Random Walk
### Resources
- [Original Quantum RW Paper](https://arxiv.org/abs/quant-ph/0303081) - Just for fun.
- [Thesis Paper (Main Focus - contains discrete and continuous quantum RW)](https://bayesianbrad.github.io/assets/publications/2014_thesis/paper.pdf) - contains all the main topics.
- [YQIS Tutorial](https://youtu.be/Gk3GuG-tUgQ?si=Xwv2OHgjhFjcBsp_)
- [QRW using Cirq](https://quantumai.google/cirq/experiments/quantum_walks)
- [QRW using Qiskit](https://github.com/qiskit-community/qiskit-community-tutorials/blob/master/terra/qis_adv/quantum_walk.ipynb)

### Task
Implement a discrete as well as continuous quantum random walk using any of the quantum computing library, preferably Qiskit.

## Week - 4: Grover's search algorithm
### Resources
- [Grover's Algorithm - Qiskit Texbook](https://github.com/Qiskit/textbook/blob/main/notebooks/ch-algorithms/grover.ipynb)
- [Youtube Tutorial](https://youtu.be/EoH3JeqA55A?si=0og2vyIPPnUb9XR1)
- [Wikipedia Page for brief overview](https://en.wikipedia.org/wiki/Grover's_algorithm)
- [Application of Grover's Search on Boolean SAT Problem](https://github.com/Qiskit/textbook/blob/main/notebooks/ch-applications/satisfiability-grover.ipynb)

### Task
Implement the grover's search algorithm for the boolean SAT problem, and understand the amplitude amplification part in the algorithm properly.