I am a newbie to quantum computing and a data scientist/computer programmer by profession .When I heard about quantum computer first ,I was really excited about its potential .But When I started exploring about quantum computing through videos and blogs ,I got really confused .I primarily got two types of video and blogs around it ,one explains benefits of quantum computer at very high level like quantum computer are way to faster than traditional computers means 50 qubits can simultaneously store information equivalent to 2^50 bits,How? Through superposition and entanglement .Entanglement specially is very tricky- It can be used for sending information ,without actually sending it, intriguing ha 😊.
Other videos explains these concepts at physicist level -like quantum tunnelling ,quantum chromo dynamics etc woof!. Difficult to understand these too
So I decided to write something which will help non-physicist understand quantum computing . So if you are also in the same boat ,I hope you will find this blog useful .
This post is about origination of quantum computing ,but if you want to jump directly to some intricate concepts of Quantum Computing .Then Please follow below blog posts . Although I will recommend to follow these post in order for better understanding
To unravel quantum computing ,first let’s see what people are talking about quantum computing
- Quantum computer can exponentially speedup the computational power of traditional computers ,because 2 qubits can simultaneously store information equivalent to 2^2 bits, so this processing power exponentially increases with number of qubits
- Quantum computer achieves this phenomena because of superposition and entanglement
- Quantum computer will be necessity in next 10 years ,because to gain more computational power every new device is coming with more number of transistors per chip ,in one apple phone around 1 billion transistors are available .Because of that distance between n-type and p-type doping of transistors is shrinking ,after a certain extent ,we won’t be able to control the flow of electrons because of quantum tunneling effect ,which is very much required for bit representation .Because transistors represents bit 1 when current is flowing or electrons are flowing ,and bit 0 represents when electrons are not flowing. So when we can’t control the flow of current ,we can’t increase the number of transistors also on a chip and processing power of existing computers can also not increase after we will reach to that limit . So it means ,quantum computers are inevitable after that point .Veritasium video on this is must watch .Don’t worry about it ,if you don’t understand it ,we will cover this in detail later
- Many applications of quantum computers are sought out like quantum internet ,quantum search. Other application could be Artificial Intelligence ,Particle Physics, Molecular Modelling, Financial Modelling, Weather Forecasting etc.
That’s ok ,if you don’t understand ,how quantum computing will be helpful in all these areas .We will build that understanding ,once we will be able to visualize ,how quantum computing works.
Let’s understand first
- what are quantum computers ,
- how the concept of quantum computers was originated
- how does they provide exponential speed up .
- Most important question ,does they provide exponential speed up for every problem .
But before going there, first I want to explain what is wave and what is particle ,because entire quantum theory is dependent on wave-particle duality ,so in our mind ,we should create a clear picture that what is wave and what is particle and what are there properties
So how we distinguish between wave and particle ,without even understanding of physics –
Let’s take some examples -water stream is a wave ,light is a wave ,but a ball moving up and down is it a wave or particle
I think everyone will agree with me here that it’s a particle ,not a wave ,but why is it so – answer is simple – when ball is moving we can exactly see the ball at a time at one place ,but waves are continuous steam of particle ,so if I am tracking the projectile motion of a ball between points x and y ,then I can clearly say that at time t ,ball is a some point between x and y ,but not present at all the points simultaneously . but if I will follow the water stream, then there is no empty space in this stream ,same is true for light as well.
So basically wave is a disturbance spread through out the space ,but particles has well defined position.
A very good distinction between wave and particle could be found here
In terms of mathematical properties wave is defined by
Wavelength – the wavelength is the spatial period of a periodic wave—the distance over which the wave’s shape repeats.(Wikipedia definition).
Amplitude – Amplitude represents the power of the wave ,in case of electromagnetic waves amplitude represents the highest energy ,in case of sound waves -you can say that more amplitude means louder sound
Frequency – Frequency is the number of waves produced per second
So basically wave is a pattern of propagation which can be measured by above terms
While particles/matters are defined by
Because particle is one unit ,so we can measure the mass,volume,density,position of a particle.
I think now we are clear what is a wave and what is particle
Now let’s see what’s the difference between wave and particle in terms of their properties
Two particles can not exists at the same position? -try to mix salt and pepper -salt and pepper particles will still take the separate place in space , But Waves can exists together at the same position in space ,example take two different colored lights, these two light waves will superpose and create an another wave .Now this super positioned wave could either show constructive interference or destructive interference ,that will depend on the coherence of waves, which is dependent on direction, wavelength and phase of two waves ,below are some examples of constructive and destructive interference.
Constructive Interference Destructive Interference
Another example -just hit a glass with ball ,what will happen ,if the glass is not unbreakable ,then it will break into multiple pieces .
Now hit a glass with a light ,will it break the glass -no , either it will pass through it or bounced back by the glass.
Now hit two waves together ,they will superimpose with each other and create a new wave ,wave function of this new wave will depend on whether interference of original wave was constructive or destructive. In Nut Shell Waves don’t collide but particle does.
So basically by keeping these things in mind ,physicist did many experiments .Most famous among them was below three .
Photo Electric Effect – Most famous experiment in physics is Photo Electric Effect .In this experiment ,it was shown that when light was thrown on a particle ,light collide with particle and it release some of the particle electrons ,in simple words we can say that at subatomic level ,light broke the particle because some of the electron from the particle leave the particle .That’s weird ,because waves don’t collide and light is wave
Double Slit Experiment – Anyway ,photo electric effect proved that light can exhibit particle like properties .Another important experiment which was conducted before photo electric was Double slit .In this experiment there was one wall and in front of this wall at some distance ,one other wall was there ,but in this other wall only two holes were there ,now they throw colored balls from these holes to another wall .Below picture shows this setup
Now what you will think will happen.
These colored balls will create marks on the wall at different points ,most of the marks will be created on the portion of the wall ,which is just behind the open slits .
Why,because the balls which will collide with the covered portion of the wall won’t be able to pass through ,so the balls which were able to pass through the slits ,reaches to the portion of the wall which are in line with the slit and create a mark over there.
So if light is a particle ,light should also behave the in the same manner ,light should pass through these 2 slits and should fall on different points at the wall,which are inline with open slits ,because the light which will fall on the the covered portion of the wall can’t pass through ,so no light should reach to the other wall which is behind this covered portion of the wall .
But light doesn’t do that ,instead light passes from these 2 slits interfere with each other and creates a diffraction pattern on other wall ,or we could say create a new light wave ,which is dark at places where destructive interference happened and bright at places of constructive interference.This diffraction pattern looks like as below
But superposition and interference is property of a wave not of a particle ,it means light is not a particle .Later on,many more experiments were conducted similar to this ,some said that light is a wave ,others said light is a particle .
So after multitude of these experiments, unanimously physicist reach to this conclusion that light is both wave and particle
Now I am sure ,you were also thinking that, so what even if light show dual behavior ,how would it help in making quantum computers and achieving exponential speed up .Our computers are not made of light particles ,instead they are made of transistors and transistors are made up of n-type and p-type silicon .
That’s where De-Broglie revolutionary theory comes into picture
De Broglie wave length – De Broglie stated that not only light ,particles also at sub atomic level (like electrons) exhibits wave like properties . Wavelength of this matter wave is defined by
λ= h/p where h is the planck constant
and p is the momentum and p=mv where m is mass and v is velocity
This theory of De Broglie was later proved by Davisson and Germer (https://en.wikipedia.org/wiki/Davisson%E2%80%93Germer_experiment).
They shoot electrons in double slit experiments ,so if electrons are particles they should create two spots on other side of the wall, just like the tennis balls did ,but that’s not what they did ,they created a diffraction pattern on other side ,just like light
Khan academy has a very good video on this .
de-broglie theory proved that at sub atomic level matter particles can behave like wave .This was the turning point in Quantum theory,why?
Let’s take an example – Suppose if I want to draw a diffraction pattern on other wall using particles ,I need to create multiple holes on the wall from which I am throwing particles and then need to send particles from all those holes to create the diffraction pattern.
But here with matter waves we are sending only 1 electron at a time and its creating a diffraction pattern on the other wall ,that’s amazing ,because when light create this diffraction pattern -it does with multitude of photons ,but here only 1 electron is doing the same thing .
So somehow if we will control the wave function of electrons ,then we can send entire spectrum of information using only 1 electron ,that’s what quantum computing is all about.
But now the next question arises ,what is the wave function of a particle
As mentioned earlier that wave function can be defined by the frequency ,amplitude and wavelength of a wave .
De-broglie stated wavelength of matter wave is defined by
λ= h/p where h is the plank constant
and p is the momentum
But to define a wave function we need frequency and amplitude too.
Erwin Schrödinger comes up with the equation of matter wave function ,which describes the shape of matter wave
where V=V(r,t)=r and t are the position vector and time respectively,
m is mass and
Ђ=h/2π ,h is planck’s constant
But before even defining the wave function of a particle ,first we need to understand what does it even mean ?
As we know that a wave is a pattern of propagation which should be defined at every position. But in case of electron ,its just one electron ,it can’t be present simultaneously at all the location ,then does it mean that wave function of electron is not defined ,when electron is not present at the location .
Max Born comes up with the interpretation for this wave function. He said in case of matter waves ,wave function represents actually the probability of finding the electron at certain position. So basically wave function tells us that, at which position you will find this electron most likely and least likely .
How we will measure this wave function ,will discuss in next tutorial.