## 7102 put it in a “one state” or

7102

Quantum Computing

To find the prime factors of a 2048 number, it would take a

classical computer millions of years, a quantum computer could do it in just

minutes. And that is because a quantum computer is built on qubits, these

devices which take advantage of quantum superposition to reduce the number of

steps required to complete the computation.

A classical computer performs operations using classical

bits, which can be either zero or one. In contrast, a quantum computer uses

quantum bits (qubits), and they can be both zero and one at the same time. It

is this that gives a quantum computer its superior computing power.

What is a qubit ?

There are a number of physical objects that can be used as a

qubit. A single photon, a nucleus or an

electron. Some researchers used the outermost electron in phosphorous as a

qubit. But how does that work ?

All electrons have magnetic fields, so they basically like

tiny bar magnets, and this property is called spin. If you place them in a

magnetic field, they will align with that field, and this would be the lowest

energy state “zero state” which is called for the electron “spin

down”. You can put it in a “one state” or “spin up”,

but that takes some energy to reach that highest energy state. If you were so

delicate to really put it exactly against the magnetic field, it would stay

there.

So far, this is basically just

like a classical bit. It has got two states, spin up and spin down, which are

like the classical one and zero. But what is interesting about the quantum

objects is that they can be in both states at once. When you measure the spin,

it will be either up or down. But before you measure it, the electron can exist

in a quantum superposition.

;

where the

coefficients a & b indicate the

relative probability of finding the electron in one state or the other.

Entanglement

It is hard to imagine how this

enables this incredible computing power of quantum computers without

considering two interacting qubits. Now there are four possible states of these

two electrons.

In the case of a

& a , this quantum superposition of up down and

down up is what we call an entangled state. The two electrons

no longer have a direction of their own, so you cannot say that one electron is

down and the other one is up. The two electrons are in a state where they have

the opposite direction, but they do not have a direction of their own.

So it is only when

you measure one of them and you find it is “down”, the other ends up

being “up”. But until you measure them, they are in a state where their

only property is being opposite to each other.

Now if you have two bits in a classical computer, you can

write

00

01 10

11

There is four numbers, but they are still just two bits of

information. All I need to determine which one of the four numbers you have in

your computer code is the value of the first bit and the value of the second

bit.

In a qubit, instead, quantum

mechanics allows us to make a super position of each one of the four possible

states. So I can write a quantum mechanical state, that is some coefficients

times each one of the four states, i.e.

So to determine the state of this two spin system, I need to

give you four numbers, four coefficients. Whereas in the classical example of

the two bits, I only need to give you two bits. This how to understand why two

qubits actually contain four bits of information. I need to give you four

numbers to tell you the state of this system.

Now if we make three spins, we would have eight different

states and it could give you eight different numbers to define the state of

those three spins, whereas in classical it is just three bits. If you keep

going, what you will find is that the amount of equivalent classical

information contained by N qubits is classical bits. And, of course, the power of

exponentials tells you that once you have, for example, 300 of those qubits in

what we call fully entangled state, you will be able to create states where

there is a superposition of all 300 qubit states, then you will have like classical bits, which is as many particles as

there are in the universe.

Although the qubits can exist in any combination of states,

when they are measured they must fall into one of the basis states. And all the

other information about the state before the measurement is lost. So you do not

want generally to have as the final result of your quantum computation

something that is a very complicated super positional state, because you cannot

measure a superposition. You can only measure one of the basis states. So what

you want is to design the logical operations that you need to get to the final

computational result in such a way that the final result s something you are

able to measure, just a unique state.

This is the reason why quantum computers are not a

replacement of classical computers. They are not universally faster. They are

only faster for special types of calculations where you can use the fact that

you have all these quantum superpositions available to you at the same time, to

do some kind of computational parallelism. If you just want to watch a video in

high definition or browse the internet or write some documenting work, they are

not going to give you any particular improvement if you need to use a classical

algorithm to get the result.

You should not think of a quantum computer as something

where every operation is faster. In fact, every operation is probably going to

be slower than in the computer you have at your desk. But it is a computer

where the number of operations required to arrive at the result is

exponentially small. So the improvement is not in the speed of the individual

operation, it is in the total number of operations you need to arrive at the

result. But that is only the case in particular types of calculations,

particular algorithms. It is not universally, which is why it is not a

replacement of a classical computer.

How to make a quantum bit ?

How do you actually make a qubit in practice? and how do you

read and write information on it ?

Some researchers use the outermost electron in a phosphorous

atom as a qubit. A single phosphorous atom is embedded in a silicon crystal

right next to a tiny transistor. To differentiate the energy state of the

electron when it is in spin up and spin down, you need to apply a strong

magnetic field using a super conducting

magnet, which is a large solenoid.

The electron will line up with its spin pointing down in its

lowest energy state. And it would take some energy to put it into the spin up

state, but actually not that much energy. And if it were at room temperature

the electron would have so much thermal energy that it would be bouncing around

from spin up to spin down and back. And so, you need to cool down the whole

apparatus to only a few hundredths of a degree above absolute zero. That way

you know that the electron will definitely be spin down and there is not enough

thermal energy in the surroundings to flip it the other way.

Now, if you want to write information onto the qubit, you

can put the electron into the spin up state by hitting it with a pulse of

microwaves. But that pulse needs to be a very specific frequency and that

frequency depends on the magnetic field that the electron is sitting in. And

you can stop at any point. So if you just make a new tape and stop your pulse

at some specific point, what you have created is a special quantum

superposition of the spin up and spin down states with a specific phase between

the two super positions.

To read out the information, you use the transistor that the

phosphorous atom is embedded next to. In this transistor there is, in fact, a

little bundle of electrons. This bundle of electrons is filled up to a certain

energy and all these electrons line up in energy levels just like the electrons

on the shells of an atom. So now if the electron is pointing up, it can jump

into the transistor, because it has more energy than all the others. It leaves

behind the bare nuclear charge of the phosphorous with a positive charge. So it

is as if you have a positive voltage applied to the gate which comes from the

atom. It is like the transistor has been switched more on, and so you see a

pulse of current that indicates that the electron was in the spin up state.

Summary

A quantum computer consists of quantum bits (qubits), which

are quantum devices that can exist in different superpositions and can be used

to store information. Each qubit can be given a known initial state, then a

quantum logic gate acts on it to give the result that can be read out by making

a quantum measurement.