A report on Quantum Computing for Algorithm Analysis and Design course duing Monsoon'20
For our project, we chose to explore the field of Quantum Computing and it's application in the world right now, and what they could be in the future.
We began by studying the prerequisites like Linear Algebra and basic understanding of quantum mechanics. After that, we went on to study quantum computing through various lectures series and books/notes.
Finally, after we had a good understanding on how things work in quantum world and the basic advantages it provides in computing, we further went on to study and understand a couple of research papers for our presentations.
Our report included a brief introduction to quantum mechanics and how it gave rise to quantum computing. It introduced and explained some of the basic fundamentals of quantum computing, the Principle of Delayed Measurement and Quantum Erasure which can be considered as an advancement to the double slit experiment.
- In this experiment scietists tried to get the interference pattern(position) and the knowledge of the slit from which it passed(momentum) but the photon prevented it by making sure that the information remains hidden and the particle follows the uncertainty principle.
- One of the major observation that can be made from the experiment was photons predicting the measurement(position or momentum measurement) of their entangled counterparts done in future, explanation of such behaviour comes down to the time depedence of the measurment and the behaviour of entangled quantum particles.
We then went on to explain the 3 cornerstone algorithms of computing computing in detail:
- Simon's Algorithm: One of the first algorithm which exploited the use of the quantum particles and the information they store, gave an exponential speed up to the simon's problem of finding period of an unknown boolean black box function. Paved way for other algorithms such as the shor's algorithm and other period finding algorithms.
- Shor's Factoring Algorithm: Shor's algorithm is one of the algorithms that shows how quantum computers can give exponential speedups over classical algorithms. This factoring algorithm has the potential to break the RSA encryption which is considered as the standard and most secure among the encryption methods.
- Grover's Search Algorithm: Does not gives exponential speedups as given by simon's and shor's algorithms, but a polynomial time improvement over classical computing.
Our presentation also included a talk about some of the interesting applications of quantum computing which we came across from research papers. These included
- A Simple Proof that Toffoli and Hadamard are Quantum Universal by Dorit Aharonov
- Prediction by linear regression on a quantum computer by Maria Schuld et all
- Solution to 0/1 Knapsack Problem Based on Improved Ant Colony Algorithm by Hanxiao SHI
- Ryan O'Donnel's lectures on QC at CMU [link]
- Ronald de Wolf's notes on Quantum Computing [link]
- Quantum Computing and Quantum Information by Nelson and Chuang [link]
- Quantum Mechanics and Quantum Computing by Umesh Vazirani [link]
- Qiskit community [link]
- QC - Quantum Computing Series by Jonathan Hui [link]
The team comprised of Kunal Jain, Samay Kothari and Naman Ahuja