MODULE – 1 : Math Prelims (Linear Vectors Spaces)

Module Duration:

3 hours of recorded videos and 4 live online interactive sessions.

Faculty:

Prof. Prabha Mandayam, IIT Madras

Topics covered:

A brief review of the concepts from linear algebra that will be used in the course. This includes the concept of inner product, orthogonal states, eigenstates, eigenvalues and basis vectors.This module will also introduce the bra-ket notation that will be flowed throughout the course.

Learning Outcomes:

Evaluate inner products between two vectors, identify orthonormal bases, evaluate eigenstates and eigenvalues, ability to work with bra-ket notation.

Applications of the Module

Introduce the basic math concepts and notation required for understanding quantum bits and quantum computing.

MODULE – 2 : Quantum Mechanics Fundamentals (States, Operators and Measurement)

Module Duration :

3 hours of recorded video and 4 live online interactive sessions.

Faculty:

Prof. Prabha Mandayam, IIT Madras

Topics covered:

A quick introduction to quantum theory via two-level quantum systems. This module will discuss the postulates of quantum mechanics and describe quantum states, operators (unitary and Hermitian) and discuss the concept of measurement in quantum theory.

Learning Outcomes:

Superposition Principle, action of Hermitian operators and unitary operators, Z-basis and X-basis measurements

Applications of the Module:

Gain comfort with the basic concepts of quantum theory required for quantum computing.

MODULE 3 : Intro to qubits: Bloch sphere, basic single-qubit gates

Module Duration:

3 hours of recorded videos and 5 live online interactive sessions.

Faculty:

Prof. Prabha Mandayam, IIT Madras

Topics covered:

This module will introduce the idea of a quantum bit or qubit, geometric visualization of the qubit via the Bloch sphere and also discuss some of the logical operations on single qubits (X and Z gates and Hadamard gate )

Learning Outcomes:

Identify states on the Bloch sphere, construct single-qubit quantum circuits and evaluate their outputs.

Applications of the Module :

Design simple quantum circuits

MODULE 4: Two-qubit gates, Bell state circuit, No-cloning theorem and teleportation.

Module Duration:

3 hours of recorded videos and 4 live online interactive sessions.

Faculty:

Prof. Prabha Mandayam, IIT Madras

Topics covered:

This module will introduce multi-qubit systems and the concept of entanglement. It will describe the no-cloning theorem and the quantum teleportation protocol.

Learning Outcomes

Tensor-product notation to describe multi-qubit states, understand why quantum states cannot be copied,understand the difference between product states and entangled states.

Applications of the Module

The concept of entanglement, Bell-state circuits are widely used in quantum computation and quantum communication.

MODULE 5: Physical realizations of qubits, Introduction to IBM Q and Qiskit

Module Duration:

3 hours of recorded videos and 4 live online interactive sessions.

Faculty:

Dr. Chandrashekar Radhakrishnan, IIT Madras

Topics covered:

Discussion on different physical architectures for implementing qubits, with a special focus on superconducting qubits. This module will also introduce the IBMQ platform and the qiskit simulator.

Learning Outcomes: 

Ability to create simple quantum circuits and run them on qiskit simulator as well as quantum hardware.

Applications of the Module: 

Introduction to quantum software and hardware via IBM Q

MODULE 6: Quantum speed-up: Deutsch and DJ algorithm + Demo on Qiskit + Intro to Computational complexity

Module Duration : 

3 hours of recorded videos and 4 live online interactive sessions.

Faculty: 

Prof. Prabha Mandayam, IIT Madras

Dr. Chandrashekar Radhakrishnan, IIT Madras

Topics covered:

Introduce ideas of computational hardness (classical and quantum). Discussion of a simple quantum algorithm to demonstrate quantum speed-up.

Learning Outcomes:

Understand query complexity, implement Deutsch and Deutsch-Jozsa algorithms on qiskit

Applications of the Module :

The techniques learnt in the Deutsch algorithm will be applied in many quantum algorithms.

MODULE 7: Quantum Fourier Transform (QFT) and Phase estimation

Module Duration:

3 hours of recorded videos and 4 live online interactive sessions.

Faculty:

Prof. Prabha Mandayam, IIT Madras

Topics covered:

Discuss the circuit for implementing quantum Fourier transform and show the polynomial scaling. Also discuss the phase estimation algorithm as a simple application of QFT.

Learning Outcomes:

Understand how QFT can be performed using Hadamard and controlled rotation gates; implementation on qiskit.

Applications of the Module:

QFT and phase estimation are the basic steps in the quantum factoring algorithm

MODULE 8: Order Finding and Factoring

Module Duration:

3 hours of recorded videos and 5 live online interactive sessions.

Faculty:

Prof. Prabha Mandayam, IIT Madras

Topics Covered

Discuss the order finding algorithm using phase estimation. Discuss Shor’s factoring algorithm via order finding.

Learning Outcomes

Implement quantum factoring algorithm on qiskit.

Applications of the Module

Integer factorization is used in public key cryptography

Module 9 – Simons, Bernstein-Vazirani + Demo on Qiskit

Module Duration:

3 hours of recorded videos and 4 live online interactive sessions.

Faculty:

Prof. Prabha Mandayam, IIT Madras

Topics Covered

Discuss a few related quantum algorithms such as Simons and Bernstein-Vazirani

Learning Outcomes

Implement Simons and B-V algorithms on qiskit.

Applications of the Module

Quantum algorithms for oracle-based problems, exmaple, hidden string problem.

Module 10 – Grover Search + Demo on Qiskit

Module Duration:

3 hours of recorded videos and 4 live online interactive sessions.

Faculty:

Prof. Prabha Mandayam, IIT Madras

Topics Covered

Explain the quantum search algorithm, the Grover iterate and demonstrate quadratic speed-up.

Learning Outcomes

Implement Grover search on qiskit.

Applications of the Module

Quantum search over an unstructured database.

Module 11 – Amplitude amplification, HHL algorithm + Demo on Qiskit

Module Duration:

3 hours of recorded videos and 4 live online interactive sessions.

Faculty:

Mr. Dhiraj Madan (IBM)

Topics Covered

Explain amplitude amplification and use it to discuss the HHL algorithm for solving a system of linear equations.

Learning Outcomes

Implement HHL on qiskit.

Applications of the Module

Quantum algorithm for solving linear systems of equations.

Module 12 – Public key cryptography + Quantum Key Distribution (BB84)

Module Duration:

3 hours of recorded videos and 4 live online interactive sessions.

Faculty:

Dr. Chandrashekar Radhakrishnan, IIT Madras

Topics Covered

Discuss the concept of (classical) public key cryptography and the RSA protocol. Introduce quantum key distribution (QKD ) and discuss the BB84 protocol.

Learning Outcomes

Understand how quantum concepts like the uncertainty principle lead to unconditional security of publick key cryptography using quantum states.

Applications of the Module

QKD protocols are at the heart of quantum communication networks.

MODULE – 1 : Quantum Machine Learning I : Introduction

About the Module:

After a brief introduction to classical machine learning, this module will discuss quantum machine learning (QML) techniques such as variational quantum classifier (VQC) and Quantum Support Vector Machines (QSVM)

Faculty:

Dr. Anupama Ray (IBM Research, India)

Learning Outcomes:

Understand and apply QML techniques like VQC, QSVM and quantum clustering.

Applications of the Module

VQC and QSVM are essential QML tools for several data/image classification applications.

MODULE – 2 : Quantum Machine Learning II : Theory

About the Module:

After a brief introduction to classical machine learning, this module will discuss quantum machine learning (QML) techniques such as variational quantum classifier (VQC) and Quantum Support Vector Machines (QSVM).

Faculty:

Dr. Anupama Ray (IBM Research, India)

Learning Outcomes:

Understand and apply QML techniques like VQC, QSVM and quantum clustering.

Applications of the Module:

VQC and QSVM are essential QML tools for several data/image classification applications

MODULE 3 : Quantum Machine Learning III : Applications

About the Module:

After a brief introduction to classical machine learning, this module will discuss quantum machine learning (QML) techniques such as variational quantum classifier (VQC) and Quantum Support Vector Machines (QSVM).

Faculty:

Dr. Anupama Ray (IBM Research, India)

Learning Outcomes:

Understand and apply QML techniques like VQC, QSVM and quantum clustering.

Applications of the Module :

VQC and QSVM are essential QML tools for several data/image classification applications.

MODULE 4 : Quantum Machine Learning IV : Applications

About the Module:

After a brief introduction to classical machine learning, this module will discuss quantum machine learning (QML) techniques such as variational quantum classifier (VQC) and Quantum Support Vector Machines (QSVM).

Faculty:

Dr. Anupama Ray (IBM Research, India)

Learning Outcomes:

Understand and apply QML techniques like VQC, QSVM and quantum clustering.

Applications of the Module :

VQC and QSVM are essential QML tools for several data/image classification applications.

MODULE 5: Variational Quantum Algorithms

About the Module:

This module will discuss the class of variational quantum algorithms, with special focus on the variational quantum eigensolver (VQE).

Faculty:

Dr. Anupama Ray (IBM Research, India)

Learning Outcomes

Understand and implement VQE on qiskit.

Applications of the Module

VQE is widely applied in quantum chemistry.

MODULE 6: Noise and Quantum Error Correction

About the Module:

Describe the theory of noise in quantum devices and introduce ideas of quantum error correction.

Faculty:

Prof. Prabha Mandayam, IIT Madras

Learning Outcomes: 

Understand different noise models like bit-flip, phase-flip, depolarizing and T1/T2 processes. Implement a basic QEC code on IBM Qiskit.

Applications of the Module: 

A basic understanding of noise and QEC is essential for working with today’s noisy quantum hardware.

MODULE 7: Error mitigation for NISQ devices

About the Module:

Introduce error mitigation techniques such as Zero Noise Interpolation and Probabilistic Error Cancellation

Faculty:

Dr. Ritajit Majumdar (IBM Research, India)

Learning Outcomes:

Incorporating error mitigation while programming NISQ hardware like IBM Q.

Applications of the Module:

Quantum error mitigation is widely used to reduce the effects of noise on quantum algorithms in current generation NISQ hardware.

MODULE 8: Qiskit runtime, Transpling, Circuit Cutting

About the Module:

Discuss quantum software techniques such as Qiskit Runtime and Transpling on IBM Q

Faculty:

Dr. Dhinakaran Vinayagamurthy (IBM Research, India)

Learning Outcomes

Ability to transpile quantum circuits on IBM Q and understand the use of qiskit runtime

Applications of the Module

Transpling and Qiskit Runtime are important tools in the IBMQ software stack.

MODULE 9: Quantum communication Protocols

About the Module:

This module will introduce two important quantum communication protocols: quantum teleportation and super-dense coding.

Faculty:

Dr. Chandrashekar Radhakrishnan, IIT Madras

Learning Outcomes

Understand the teleportation circuit and super-dense coding protocol; implement them on IBM Qiskit

Applications of the Module

Teleportation and super-dense coding are two important applications of quantum entanglement. These are widely used in quantum communication theory.

MODULE 10: Introduction to Pulse Programming

About the Module:

Introduce the idea of Pulse Programming with a simple example on IBMQ hardware.

Faculty:

Dr. Chandrashekar Radhakrishnan, IIT Madras

Learning Outcomes

Understand the concept of programming quantum hardware via pulse programming routines.

Applications of the Module

Pulse programming is used to optimize the performance of quantum hardware, and make it more resilient to the effects of noise.

MODULE 11: Solving optimization problems on a quantum computer – Part 1

About the Module:

Introduce techniques such as Quantum Integer Programming (QuIP) to solve optimization problems efficiently on quantum devices.

Faculty:

Dr. Anil Prabhakar (IIT Madras)

Learning Outcomes

Solve quadratic unconstrained binary optimisation (QUBO) problems on IBMQ and quantum annealers like D Wave.

Applications of the Module

QUBOs are widely used for practical problems such as bin-packing, optimal routing including traveling salesman problems.

MODULE 12: Solving optimization problems on a quantum computer – Part 2

About the Module:

Introduce techniques such as Quantum Integer Programming (QuIP) to solve optimization problems efficiently on quantum devices.

Faculty:

Dr. Anil Prabhakar (IIT Madras)

Learning Outcomes

Solve quadratic unconstrained binary optimization (QUBO) problems on IBMQ and quantum annealers like D Wave.

Applications of the Module

QUBOs are widely used for practical problems such as bin-packing, optimal routing including traveling salesman problems.