INF587 Quantum Information and Applications
Introduction
This course is an introduction to the concept of a quantum computer. It
uses quantummechanical principles and generalizes
classical computers. It has been demonstrated that such a computer can
solve in polynomial time problems that are considered
to be hard for a classical computer such as factoring large integers or
solving the discrete logarithm problem (this is Shor's algorithm).
The security of virtually all publickey cryptography used in practice
right now relies on the hardness of these problems
and a quantum computer would break those cryptosystems. It has also been
found that such a computer is able to search in an unstructured
set much more efficiently than a classical computer (this is Grover's
algorithm).
We will cover in this course the bases of quantum computation and
present the main quantum algorithms that offer a speedup over classical
algorithms.
We will also cover other applications of quantum mechanics, such as
simulating physical systems or quantum cryptography. The latter exploits
the laws of quantum physics to establish the security of certain
cryptographic primitives, such as key distribution protocols.
Lectures
 January 8, Introduction
 qubits and quantum registers
 measurement and unitary evolution
 elementary gates
 quantum teleportation, superdense coding
 The first algorithms : DeutschJosza and BernsteinVazirani
Lecture 1.
 January 15, Fundamentals of quantum information
 density matrix
 quantum evolutions
Lecture 2.
 January 22, The circuit model
 classical and quantum circuits
 universality of quantum computation with a restricted set of
elementary gates
Lecture 3.
 January 29, Advanced algorithms based on the quantum Fourier
transform
 the quantum Fourier transform
 the abelian hidden subgroup problem
 application : phase estimation
 application : Shor's algorithm for factoring and solving the discrete
logarithm problem
Lecture 4.
 February 5, Advanced algorithms
 Grover's algorithm,
 the amplitude amplification algorithm,
 other algorithms that are relevant to
cryptography such as collision algorithms
Lecture 5.
 February 12, Quantum walks
 classical random walks and applications
 quantum random walks
 applications
Lecture 6.
 February 26, Hamiltonian simulation; an advanced algorithm for solving large linear systems the
HarrowHassidimLloyd algorithm
 Hamiltonians
 applications to quantum chemistry
 the LieSuzukiTrotter method
 the block encoding method
 the HarrowHassidimLloyd algorithm
Lecture 7.
 March 4, Quantum error correcting codes
 March 11 Quantum cryptography, quantum key distribution
Project/Final exam
 Breaking symmetric cryptosystems with Simon's algorithm,
Crypto 2016 paper by
Marc Kaplan, Gaetan Leurent, Anthony Leverrier and María NayaPlasencia
 The hidden nonabelian subgroup problem and the Kuperberg
algorithm,
see Chapters 1113 in the
lecture notes on quantum computing by
Andrew Childs
 A nice application of the HHL algorithm
Quantum recommendation systems
by Iordanis Kerenidis and Anupam Prakash
 Another nice application of the HHL algorithm
Quantum support
vector machine for big data classification
by Patrick Rebentrost, Masoud Mohseni and Seth Lloyd
 The Phd thesis of Stuart Andrew Hadfield contains several
chapters that are a good introduction to several approximation
algorithms, some of them are potentially implementable on noisy quantum
devices

Approximating ground and excited state energies on a quantum
computer
Chapter 3

Divide and Conquer Approach to Hamiltonian Simulation
Chapter 4

Quantum Approximate Optimization
Chapter 6
 Quantum query lower bounds
Chapter 11 of
the lecture notes of Ronald de Wolf
 Quantum communication complexity
Chapter 14 of
the lecture notes of Ronald de Wolf
Bibliography
 Michael A. Nielsen, Isaac L. Chuang, "Quantum Computation and Quantum
Information: 10th Anniversary Edition". Cambridge, 2010.