Quantum Computation and Information-CS 405
Instructor: Jaideep Mulherkar
Win 2023
DA-IICT, Gandhinagar
Course description: Quantum computation is a new paradigm for computing based on the principles of quantum mechanics. The basic unit of a quantum computer is a quantum bit or a qubit. Quantum mechanics has some peculiar properties that have no analogues in the classical world. The principles of quantum mechanics allows the qubit to be in a superposition of a '0' and '1' state. Another principle of quantum mechanics allows a quantum state of two qubits to be in an 'entangled' state. In an entangled stated of two qubits one cannot refer to the state of qubit 1 without referring to the state of qubit 2 and vice versa. Properties like superposition and entanglement allow quantum computers to operate in a fundamentally different way than that of classical computers. An example of the power of quantum computation is a quantum algorithm for factoring factors a large composite number as a product of its prime factors. The quantum factoring algorithm which is based on the quantum Fourier transform is asymptotically exponentially faster than any known classical algorithm. This result by Peter Shor of MIT in 1994 gave a major boost to the field of quantum computation which is now an active area of research. The course builds up from axioms of quantum mechanics to quantum gates and circuits and eventually to the most important quantum algorithms like Shor's factoring, Grovers search and HHL algorithm. The latter part of the course deals the topic of information transmission over quantum channels where the topics of quantum error correction and quantum cryptography are studied. Of recent interest is the foray of various commercial players like IBM, Microsoft, D-Wave etc. to build a quantum computer. We will look at these recent developments and their toolkits for quantum algorithms using software. The course is of theoretical nature but there will be some practical work in the form of programming assignments or projects.
Prerequisites: Linear algebra and groups (SC-220). No prior knowledge of quantum mechanics will be assumed.
Textbooks:
Quantum computation and information, M. Nielsen and I. Chuang, Cambridge university press, 2010.
Quantum Computing Lecture Notes, Ronald de Wolf: Available online
An introduction to quantum computing, P. Kaye, R. Laflamme, M. Mosca, Oxford university press, 2007.
Quantum computing since Democritus, S. Aaronson, Cambridge university press, 2013.
Quantum Software:
The programming for projects can be done using IBM qiskit or Amazon bracket platform
Course Notes:
Grading:
20% each for 2 midterms
35% final
25% for project