This is an introductory course about designing solutions for computation problems using the quantum computing models. It has been shown that these models allow us to solve certain problems more efficiently compared to classical platforms (like Digital circuits or Turing machines). On the other hand, there are certain scenarios where this model is siimlar or even worse than classical platforms. In this course a student will learn about the models and interesting solutions (circuits, algorithms) for some problems from the perspective of computer science. The first half of the course will introduce the postulates of quantum computing, operations and operators and basic structure of circuits and algorithms on the circuit model and the Turing machine model. We will also cover some simple but amazing solutions like quantum teleportation, super-dense coding and Deutsch-Jozsa algorithm. The second half of the course will cover important algorithmic tools like the quantum Fourier transformation, amplitude amplification and eigenvalue estimation and discuss important algorithms like Groverâ€™s search, Shor's factoring, BB84 protocol which bring significant efficiency compared to classical algorithms. Depending upon time and interest, some recent advances will be covered. Students may have to read a recent/classical research paper and/or simulate some of their algorithms and circuits on some quantum backend (e.g., IBM quantum computer) to gain a solid understanding about the system.

- Linear Algebra
- Probability
- Analysis and Design of Algorithms

You are expected to be comfortable with the following prior concepts:

If you are not familiar or comfortable with these concepts, then you__must__ do a self-study before joining the course (you are recommend to solve a few problems in those concepts from any textbook; mere reading of concepts may not provide sufficient depth); this book chapter explains the linear algebraic concepts suitable for quantum computation in one place.

- Complex numbers,
- Taylor expansion,
- Linear algebraic concepts like Vector space, Vectors and matrices over complex numbers, Basis, Change of basis, Inner product, norm, Eigenvector & eigenvalues,
- Conditional probability, Expectation of random variables
- Asymptotic analysis of algorithms

If you are not familiar or comfortable with these concepts, then you

- Understand the principles of quantum computing.
- Understand different quantum computing models used in different applications like search, numerical algorithms, cryptography, etc.
- Design and/or analyse quantum algorithms and circuits.
- Explain and/or implement simple algorithms and circuits from research papers.

Evaluation will be based on homeworks, closed-book proctored midsem and endsem exams, and project/survey.

- Midsem : 30%
- Endsem : 35%
- Homeworks : 4 (out of 5) x 5% = 20%
- Project/survey : 15%

All office hours will take place on the Meet Link given on Classroom.

**Debajyoti Bera -** dbera@ - TBA (email me if you want meet at some other time)

**Tharrmashastha** - tharrmashasthav@ - TBA

Lecture No. | Date | Theme | Topics |
---|---|---|---|

1 | 8 Jan 2024 | Single qubit system | Hilbert space, ket-bra notation, Hadamard gate, Superposition |

2 | 10 Jan 2024 | Single qubit system | Inner product, Linear operators, Spectral decomposition, Projective measurement, B92 protocol |

3 | 15 Jan 2024 | Single qubit system | Evolution, Operator function, Rotation gates, Important single qubit gates, identification of states |

4 | 17 Jan 2024 | Multiple qubits | Tensor product, Hadamard basis, CNOT gate, Bell states, Entanglement, No-cloning theorem |

5 | 22 Jan 2024 | Bell States | Partial evolution, Partial measurement, Teleportation |

6 | 24 Jan 2024 | Bell States | Measuring B11 in any basis, Time-invariance of B11, Remote state preparation |

Building blocks | Input representation in quantum circuits, Oracle/query model, Parameterized circuit model | ||

26 Jan 2024 | HW1 Due | ||

7 | 29 Jan 2024 | Building blocks | Amplitude & Basis encoding, single-qubit gates, multi-qubit & controlled-gates, phase kickback |

8 | 31 Jan 2024 | Simple algorithms | SWAP test, Hadamard test, H-U-H framework, Deutsch & Deutsch-Jozsa algorithm |

9 | 5 Feb 2024 | Simple algorithms | Algorithmic frameworks: Amplitude amplification, QPE, Hamiltonian simulation |

10 | 7 Feb 2024 | Quantum ML/Dhiraj Madan | Quantum variational algorithms, VQE |

12 Feb 2024 | NO CLASS (Friday timetable) | ||

11 | 14 Feb 2024 | Quantum ML/Dhiraj Madan | QSVM |

12 | 19 Feb 2024 | Amplitude Amplification | Review, Exact amplification, Amplification for unknown theta |

13 | 21 Feb 2024 | Amplitude Amplification | Exact amplification, Minimum finding, Finding all solutions, Finding top-K |

MIDSEM EXAM (syllabus: all of the above) | |||

14 | 11 Mar 2024 | Hamiltonian Simulation | Reducing MaxCut to ground state computation, QUBO, VQE, Simulation on gate-based QPUs |

15 | 13 Mar 2024 | Hamiltonian Simulation | Quantum annealing, Trotterization |

16 | 18 Mar 2024 | Hamiltonian Simulation | QAOA, Error analysis of Hamiltonian simulation for unordered search |

17 | 20 Mar 2024 | QFT | Review of DFT, QFT, QFT on periodic states, Reduction of factoring to order finding |

25 Mar 2024 | HOLI | ||

18 | 27 Mar 2024 | QFT | Shor's quantum algorithm for order finding |

19 | 1 Apr 2024 | QFT | Circuit for QFT, Watrous-Cleve optimized circuit |

20 | 3 Apr 2024 | QFT | QPE, Kitaev's algorithm, QFT-based algorithm |

21 | 8 Apr 2024 | Quantum complexity | Simon's algorithm, forrelation, query complexity |

22 | 10 Apr 2024 | QFT | Applications of QFT: Amplitude estimation |

23 | 15 Apr 2024 | Quantum Information Theory | Density matrix representation |

17 Apr 2024 | NO CLASS (Holiday) | ||

24 | 22 Apr 2024 | Quantum Information Theory | Density matrix representation |

25 | 24 Apr 2024 | Advanced topics | HHL algorithm (not in syllabus) |

26 | 29 Apr 2024 | Review | Review |