IntroductionThe research of part of the theoretical physics group require the use of supercomputers to solve equations. Currently classical computers are used. There is a lot of work on developing "quantum computers", which use quantum mechanics to speed up many calculations. The student will investigate the possibilities of using quantum computers rather than classical computers and report back to the group on what they found out. The goal of these exercises is for the student to gain enough familiarity with quantum mechanics to use the simulators of a quantum computer. We will investigate the quantum computer from IBM. The student will also learn the basics of the underlying mathematics of quantum mechanics, such as complex numbers.
There are many exciting possible applications of quantum computing, if they can be built. See this article in Time magazine. Possible applications are:
The video below gives an overview of the basic ideas of quantum computing. To learn about quantum physics we will use a number of simulations and background material.
Basic ideas of quantum physicsThere are a number of key ideas in quantum physics
Important back ground topics to quantum mechanics are waves and complex numbers. Experimental foundations of quantum mechanicsThe theory behind quantum mechanics can be developed from a mathematical viewpoint. However, it is useful to see some of the concepts in quantum mechanics in their original experiments (although you will use computer simulations to investigate the experiments). Discrete light spectral linesThis exercise investigates the discrete lines in the spectrum of the lamps. This video shows a real experimental set up, note however that Thomson's idea of an atom as a plum pudding is no longer correct.You can download the java based simulation from here. See the video instructions on using the application. The details of the exercises are here. The majority of the simulation codes are written in java, so may require some configuration of your computer.
As background information to the application you can read some of the videos from
the Khan academy on quantum physics.
Some specific short lectures (each of length roughly 10 minutes) are:
Quantum interferenceThis exercise is based on the wave function application from PHet. This requires java to run.
The Photoelectric effect
Mathematical background to quantum mechanics
The language of quantum mechanics involves complex numbers and matrices from mathematics. A good review of the formulation is in the book below. This section provides supplementary background information to the formalism of quantum physics. There are a variety of different ways of formulating quantum mechanics. The best formalism is Heisenberg matrix mechanics.
Quantum Mechanics: The Theoretical Minimum by Leonard Susskind and Art Friedman. Chapter 1
As background information there is
Quantum ComputingOne important application of quantum mechanics is to the building of quantum computersBasic ideas of classical computers
Basic ideas of quantum computersIn a quantum computer, the 0s and 1s are replaced by Qubits and the logic gates are replaced by quantum gates.
Background to quantum computing
See the lectures by Michael Nielsen on quantum computing: Lecture 1: The qubit
Lecture 2, Tips for working with qubits
Lecture 2, The quantum not gate
IBM quantum experience
Conceptual Quantum Mechanics
Quantum simulator via python
