Fundamentals of Quantum Computing

LTFY.04.012 Fundamentals of Quantum Computing: Theory and Practice
Responsible: Dr. Veiko Palge
Next session: Fall 2022

This course is aimed at undergraduate students without any prior exposure to quantum mechanics or even basic mathematics (no complex numbers, just simple ones).

The target audience is students of physics, mathematics, chemistry & material science, engineering, and even computer science.

The course was held for the first time in Fall 2020. The course as well as quantum computing teaching infrastructure at the Institute of Physics is supported by HITSA. Thank you, HITSA!

Why this course?

The first “quantum revolution”, which started about a hundred years ago, changed physics drastically: God plays dice and there are spooky actions at a distance. It brought us lasers, tiny semiconductor devices, and MRI.

The “second quantum revolution” is taking place now, powered by the ability to create, manipulate, and read out quantum states. Devices based on that ability are starting to be used commercially, and over the next decade or so, quantum technologies are expected to change how we communicate and compute (and many other lower profile activities).

The development and deployment of quantum technologies requires a work force educated in quantum mechanics. It is necessary to educate more students, earlier in their studies, in a way that is geared towards quantum technologies. This is particularly true for quantum computing, where developing hardware or software requires mastery of quantum mechanics.

What this course is about

The course aims to teach beginning undergrad students in physics, mathematics, engineering, and computer science the quantum mechanics (including the math) and the practical skills that are necessary to embark on the journey into quantum computing. The design principle is to accompany all quantum theory with experiments on cloud quantum computing devices (or simulators, where appropriate).

Here’s a draft of the syllabus. (Expect changes.)

  1. Superposition (in real numbers only), the qubit; Hadamard gate, Pauli X & Z
  2. Bloch sphere, complex numbers, superposition done properly, Pauli rotations
  3. Dirac notation, Finite level systems, Hilbert space concept
  4. Combined systems, orthonormal bases, tensor products; CNOT and other 2-qubit gates, creating entangled states
  5. Measurement of an observable, operator concept, commuting operators, projectors and the spectral theorem
  6. Schrödinger equation, unitarity of state evolution
  7. Solution to the Schrödinger equation, exponential function for complex numbers and operators
  8. Hamiltonian simulation on a quantum computer, Trotter-Suzuki formula, Hello Mr. Feynman!

The course is organized in 3 types of learning experiences:

  • Independent reading
  • Challenge Sessions to make sure reading material is completely understood
  • Lab Sessions, where students implement experiments using Qiskit or similar.