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Introduction to Quantum Information Science: Communication and Computation—ECE 4950

This course introduces the subject of quantum information science, tailored to senior undergraduate students. Quantum information science exploded in 1994 when Peter Shor published his algorithm that can break RSA\ encryption codes. Since then, physicists, mathematicians, and engineers have been determining the ultimate capabilities for quantum communication and computation. In this course, we study quantum communication, computation, and related topics. In particular, you will learn about quantum mechanics, entanglement, teleportation, quantum algorithms, quantum key distribution, and quantum error correction.

Course Syllabus

Office hours TBA

Homeworks

Homework 4, due Nov. 6, 2023

Homework 3, due Oct. 12, 2023

Homework 2, due Sept. 25, 2023

Homework 1, due Sept. 11, 2023

Lectures

Lecture 16

  • density matrices
  • partial trace
  • von Neumann equation
  • sample-based Hamiltonian simulation
  • density matrix exponentation

Lecture 15

  • review of Schroedinger equation
  • Hamiltonian simulation by Trotterization

Lecture 14

  • quantum natural gradient for optimizing variational quantum algorithms

Lecture 13

  • computing gradients on quantum computers
  • parameter shift rule

Lecture 12

  • basics of variational quantum algorithms

Lecture 11

  • circuit model of quantum computation
  • single-qubit unitaries as a product of three rotations
  • construction of controlled unitary gate
  • proof that single-qubit unitaries and CNOTs are universal for quantum computation

Lecture 10

  • circuit model of classical computation
  • reversible circuits and controlled SWAP
  • promotion of reversible circuits to quantum circuits
  • uncomputing and calling functions in superposition

Lecture 9

  • teleportation

Lecture 8

  • multiqubit controlled SWAP test and techniques for circuit depth reduction

Lecture 7

  • more Hadamard test
  • SWAP test as a primitive for quantum machine learning
  • destructive SWAP test

Lecture 6

  • super-dense coding protocol, and its secrecy properties
  • Hadamard test quantum circuit

Lecture 5

  • tensor-product calculations
  • Bell basis, Pauli matrices, functions of Hermitian matrices
  • postulates of quantum mechanics

Lectures 3 and 4

  • Review of linear algebra, especially concept of tensor product (Nielsen and Chuang, Section 2.1

Lecture 2

  • application of Hoeffding bound
  • review of probability theory: joint random variable, conditional probability, union bound

Lecture 1

  • review of probability theory: random variables, mean, variance, Bernoulli RVs
  • probabilistic algorithms, repetition and majority vote, Chernoff bound
  • repeat-until-success algorithms, geometric random variable
  • Hoeffding bound


Last modified: November 15, 2023.