CS 682: Quantum Computing

### Course description:

Quantum computation captured the imagination of computer scientists with the discovery of efficient quantum algorithms for factoring and fast algorithm for search. The aim of quantum computing is to do computation using the quantum meachanical effects. The study of quantum computation and information involves mathematics, physics and computer science. This course will primarily focus on the mathematics and computer science aspect of it. We will start the course by answering "why quantum computing?" and then move on to study the basics of linear algebra and computer science needed to understand the theory of quantum computation. Then, we will talk about quantum circuit model in which most of the quantum algorithms are designed. The final part of the course will look at quantum algorithms and the advantage they offer over classical counterparts. The only pre-requisite for the course is the basic understanding of linear algebra. There are lot of other interesting topics in quantum computing which will not be covered in this course. In particular, we will miss topics like physical realization of quantum computers, quantum information theory and quantum error correcting codes. Students are encouraged to take them as part of the project in the course.

Notes

### Course notes:

Topic |
Link |

Introduction to quantum computing | Introduction |

Linear operators and spectral decomposition | Operators |

Operator functions and tensor products | Tensor Product |

Postulates of quantum mechanics | Postulates |

Computation, quantum and classical | Computation |

Deutsch-Jozsa, Fourier transform and phase estimation | Basic algorithms |

Simon's algorithm, factorization | Factor |

Guest Talk: Anand Kumar Jha, IIT Kanpur | Experiments with entangled photons |

Grover search, Query complexity | Search |

References

### Quantum computing

- Quantum Computation and Quantum Information, M A Nielsen and I L Chuang.
- An Introduction to Quantum Computing, P Kaye, R Laflamme and M Mosca.

### Linear Algebra

- Linear Algebra and its Applications, G. Strang.
- Matrix Analysis, Bhatia.

### Quantum courses