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.