0Introduction
III Quantum Computation
0 Introduction
Quantum computation is currently a highly significant and important subject,
and is very active in international research.
First of all, it is a fundamental connection between physics and computing.
We can think of physics as computing, where in physics, we label states with
parameters (i.e. numbers), and physical evolution changes these parameters.
So we can think of these parameters as encoding information, and physical
evolution changes the information. Thus, this evolution can be thought of as a
computational process.
More strikingly, we can also view computing as physics! We all have com-
puters, and usually represent information as bits, 0 or 1. We often think of
computation as manipulation of these bits, i.e. as discrete maths. However, there
is no actual discrete bits — when we build a computer, we need physical devices
to represent these bits. When we run a computation on a computer, it has to
obey the laws of physics. So we arrive at the idea that the limits of computation
are not a part of mathematics, but depend on the laws of physics. Thus, we can
associate a “computing power” with any theory of physics!
On the other hand, there is also a technology/engineering asp ect of quantum
computation. Historically, we have b een trying to reduce the size of computers.
Eventually, we will want to try to achieve miniaturization of computer compo-
nents to essentially the subatomic scale. The usual boolean operations we base
our computations on do not work so well on this small scale, since quantum
effects start to kick in. We could try to mitigate these quantum issues and
somehow force the bits to act classically, but we can also embrace the quantum
effects, and build a quantum computer! There is a lot of recent progress in
quantum technology. We are now expecting a 50-qubit quantum computer in full
coherent control soon. However, we are not going to talk about implementation
in this course.
Finally, apart from the practical problem of building quantum computers, we
also have theoretical quantum computer science, where we try to understand how
quantum algorithms behave. This is about how we can actually exploit quantum
physical facts for computational possibilities beyond classical computers. This
will be the focus of the course.