We went through the basics of quantum mechanics using the notation of linear algebra. Studied the unitary time evolution under the Hamiltonion. Learnt about the Hermitan operators and importance of their eigenvlaues and eigenvectors. Learnt about the effects of measurement on Quantum systems. Also understood the idea of measurement in terms of projection operators.
- We started with the fundamental concept of quantum computation and quantum information, the quantum bit.
- We then studied the basic single qubit gates like identity gates, pauli gates, hadamard transform and rotations.
- We then studied that any one qubit gate can be built using just rotation gates.
- Studied the CNOT gate and understood the proof of how any multiple qubit logic gate maybe composed from CNOT and single qubit gates.
- Studied the no-cloning theroem.
- Understood the technique of Quantum teleportaion and Superdense coding.
- Prepared Bell gates in Qiskit and extended it to construct GHZ gate.
- Constructed basic gates like swap gate and incrementation mod 8 gate.
- Studied how quantum computers can do any classical computation.
- Studied quantum parallelism.
- Studied Deutsch and Deutsch-Josha algorithms.
- Implemented Deutsch-Josha algorithm on qiskit.
- Studied discrete Fourier Transform and it's inverse.
- Studied the phase finding algorithm for finding the phase of eigenvalues. Also studied the number of qubits needed to set the precision of the phase value.
- Understood the order finding and factoring algorithms using phase estimation algorithm.
- Then implemented QFT, Phase estimation algorithm, shor's algorithm and grovers algorithm on Qiskit.
- Learnt the concept of Linear and Logistic regression and how to implement them using python.
- Learnt how the clustering technique forms clusters of the points having similarities.
- Learnt how SVM's create lines or hyperplanes to form separate classes.
- Learnt how different kernal methods project the input data to a higher dimensional space.
- Learnt how to implement stochastic gradient decsent learning algorithm for feed-forward neural network.
- Implemented linear regression, clustering and SVM classifications using SkLearn library.
- Implemented a neural network to classify images from MNIST dataset into 10 categories using TensorFlow library.
- Then studied some quantum machine learning models and learned how using quantum circuits can reduce the computations involved to get a certain level of accuracy, when compared to a similar classical machine learning mode
- Then finally, implemented a paper introducing Quanvolutional Neural Network, utilizing quantum features to preprocess the dataset.