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Saint Petersburg State University

Quantum Computing. Less Formulas - More Understanding

Saint Petersburg State University via Coursera

Overview

This is yet one more introductory course on quantum computing. Here I concentrate more on how the mathematical model of quantum computing grows out from physics and experiment, while omitting most of the formulas (when possible) and rigorous proofs.

On the first week I try to explain in simple language (I hope) where the computational power of a quantum computer comes from, and why it is so hard to implement it. To understand the materials of this week you don't need math above the school level.

Second and third weeks are about the mathematical model of quantum computing, and how it is justified experimentally. Some more math is required here. I introduce the notion of a linear vector space, discuss some simple differential equations and use complex numbers.

The forth week is dedicated to the mathematical language of quantum mechanics. You might need this if you want to dig deeper into subject, however I touch only the tip of the iceberg here.

On the week 5 I finally introduce some simple quantum algorithms for cryptography and teleportation.

Syllabus

  • Two Basic Questions
    • Why quantum computers are believed to be so powerful, and yet why they aren't implemented on the industrial scale? We will briefly discuss these questions and maybe some more.
  • The Origins of the Mathematical Model. Part 1
    • In this module we will discuss the origins of the mathematical model of quantum computing. Where all these weird notions like wavefunctions and state superposition come from? All our knowledge on the subject we will derive from a simple yet maybe most confusing physical experiment - the double slit experiment.
  • The Origins of the Mathematical Model. Part 2
    • We continue to discuss the origins of the mathematical model of quantum computing, and finally we start learning something useful! We meet and understand qubits at last, and learn how they entangle to produce quantum speedup for many problems. And why do we need complex numbers to describe them? Let's find out!
  • The Language of Quantum Mechanics
    • Quantum mechanics has a very specific language for describing things. It is indeed havily based on linear algebra, but for me personally this didn't help much to understand what quantum mechanics has to say. In this module we will take a look at this language, so you would be able to read scientific papers on the subject and understand the notation of quantum computing. You may even find some mistakes in my advanced course!
  • Quantum Cryptography and Teleportation
    • At last we are ready to approach the algorithms! And the algorithms we discuss in this module are not some toy algorithms, they are really useful. Some of them are even implemented on the industrial scale. Let's dive in the exciting world of quantum cryptography and quantum teleportation!

Taught by

Сысоев Сергей Сергеевич

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