Course

Unit 1

Introduction to computability theory, Turing machine, Church-Turing thesis, theory of computation, Computational complexity classes, P vs NP, Probabilistic complexity classes, BQP vs BPP. Quantum computational complexity advantages.

Unit 2

Quantum Fourier transform, quantum phase estimation, Shor’s algorithm, Quantum Searching and Grover’s Algorithm, Linear equation solver (HHL) algorithm, Quantum optimization, verifications using IBM Qiskit simulations.

Unit 3

Noisy quantum theory: Pure and mixed states, density operators, expectation values and measurements, partial trace and reduced density operator, density operator on a Bloch sphere. Noisy quantum evolution, quantum channels, Kraus and Choi representations, examples of quantum channels.

Unit 4

Entanglement manipulation, LOCC, quantum entropy, entanglement assisted classical communication.

Unit 5

Introduction to quantum cryptography: basics of encoding, RSA encryption basics, basics of quantum cryptography, BB84 protocol, B91 protocol, Device independent cryptography; demonstration of BB84 and B91 using IBM qiskit simulations.

Suggested lab exercises

1. Quantum Fourier transform
2. Quantum Phase estimation
3. Grovers algorithm – quantum searching
4. HHL algorithm – linear equation solver
5. Quantum cryptography: BB84 and B91 protocols

Course Description

This course focuses on advanced quantum algorithms and cryptographic protocols. Students will implement the Quantum Fourier Transform, Phase Estimation, Grover’s algorithm, the HHL algorithm, and quantum cryptography using IBM Qiskit for hands-on learning.

Course Outcomes

On successful completion of the course, students shall be able to

1. Understand, analyse, and describe classical and quantum complexity classes (P, NP, BQP, BPP) to assess quantum computational complexity advantages.
2. Apply and simulate quantum algorithms, including the quantum Fourier transform, Shor’s, Grover’s, and HHL algorithms, using IBM Qiskit for computational problem-solving.
3. Apply concepts of mixed quantum states and density operators, and perform calculations for noisy quantum evolution and quantum channels.
4. Perform calculations in entanglement manipulation techniques and demonstrate entanglement-assisted communication (LOCC, quantum entropy) in quantum information tasks.
5. Demonstrate quantum cryptographic protocols (BB84, B91) and explain quantum cryptography principles, including device-independent cryptography, using IBM Qiskit simulations.

1. David McMahon, Quantum Computing Explained, Wiley India.
2. Quantum Computation and Quantum Information: M.A. Nielsen and I.L. Chuang (2011), CUP.
3. P. Kaye, R. Laflamme, and M. Mosca, An Introduction to Quantum Computing, OUP, 2007
4. Peter Y Lee, Huiwen Ji, Ran Cheng, Quantum Computing and Information: A Scaffolding Approach, Polaris QCI (2024)
5. Eleanor Rieffel and Wolfgang Polak, Quantum Computing: A Gentle Introduction
6. Ray LaPierre, Introduction to Quantum Computing
7. S.M. Girvin, Introduction to Quantum Information, Computation and Communication, Lecture Notes, Yale, 2021-2024