Beginning of the Qubit I (The Double Slit Experiment)

Quantum mechanics took the world of physics by storm, phase by phase. But a paper by Richard Phillips Feynman changed the domain of computer science and the relationship between physics and computer science forever. Through that paper was born the qubit. Before we go in however, we must learn the tenets of quantum mechanics.

And to do that we need to go way back, perhaps to the days of Maxwell and Young. This is where it all starts – the Double Slit experiment.

Light perplexed scientists and all those with scientific inquisition. Isaac Newton believed it to be a stream of corpuscles and Maxwell showed its wave like properties. It was Einstein however who sealed the deal in 1905 with the photoelectric effect which showed that photons (or the particles of light) possessed both wave and particle like properties. However, this debate sparked an interest in electrons and in 1927 it was shown that electrons behave like both waves and particles. However, the theory that was used to explain it will haunt you, disturb you and mesmerize you for the rest of your life. It is also the place where the journey of the qubit begins.

Welcome to the quantum realm. The beauty of quantum mechanics is that it is counter-intuitive. And its journey begins with the double slit experiment. Take a source of light and it is shone through two identical and very thin slits and the resultant light falls on the subsequent screen.


Imagine a drunk holding a machine gun (go ahead, make your choice) and sprays bullets everywhere. When the drunk sprays those bullets some bullets don’t pass, some pass through the slits and make a pattern on the screen. If we close a slit, a large number of bullets won’t pass and the ones which pass will accumulate on the other end of the slit (on the screen) and the neighboring regions after the bullets ricochet off. Now let’s open both the slits. What is the probability that a bullet would land on a spot y on the screen? If the probability of it landing through slit 1 is P1 and through slit 2 is P2. Then the probability of the bullet landing on y is P12 = P1 + P2. Here, the bullets are akin to particles. What do you think electrons will behave like, particles? Wrong.

Imagine a pond and you and your friend randomly throw stones at it. The ripples will sometimes collide and die out or form larger waves. This is known as interference, the former destructive and the latter constructive. Now let’s take this setup somehow to our double slit experiment. Now, the water waves would pass only through the slits and waves are generated on the other side and these waves undergo interference. The intensity or the energy contained in the waves can be can be plotted by looking at the consequential waveforms on the subsequent screen. There will be alternating dark and light patterns. The dark patterns are caused when the wave from one slit arrives perfectly out of sync with the wave from the other slit and the bright patterns are caused by the waves from the corresponding slits being in sync with each other. Naturally (if you think a little), you will find that the center of the screen has the brightest spot because the waves reach there in perfect sync.

Here’s the catch – the amplitudes or heights of the waves are added and not their intensities. That really differs from our story of the frantic bullets where I12 = I1 + I2. Here I12 is not equal to I1 + I2 but it is rather h12 = h1 + h­­2. And I = h(y)2. So it is pretty obvious why the case is not in favor of intensity.

Before we enter the realm of light, let’s think what happens when we decrease the intensity in both cases. When we decrease the intensity of the bullets, i.e. the number of the bullets being fired is reduced, the amount of energy transferred to the screen is the same but the frequency of the bullets hitting the screen decreases accordingly. Whereas in the case of the water waves, reducing the intensity means lesser amplitude of the waves and less amount of energy is transferred. However, the frequency of the waves remains the same (comment in the section below why :)).

What happens to light is quite astounding as it confounded and baffled many. When Young conducted the double slit experiment in 1802, he observed the interference patterns on the screen and deduced that light has a waveform. Rightly so! He didn’t have any contraption to turn down the intensity of light (come on it was 1802 after all) so he couldn’t conclude what we had already posited before (which is because we know relatively more about light today).

Now imagine that the screen is made up of gazillions of tiny photodetectors (why not a huge photodetector?) that detect the energy they pick up from the incoming light. On high intensities, we would see an interference pattern much akin to that of the water waves. On turning it down low, we would see that the pattern more or less similar. However, when it reaches an extremely low value, say E0, we see what is called the quantization of light and this where the game begins.

In this case, the bright spots report E0 but at a high frequency. The darker spots still report E0! And the completely dark points report nothing at all. THIS IS THE BEHAVIOR OF BULLETS NOT WAVES!!!! And hence, light neither behaves like corpuscles of particles or the bullets nor waves. They are of an entirely new breed!

You are probably now thinking – what the heck!?! Wait, this gets crazier.

We turn down the intensity so low that the photodetector reports a surge only per second. In other words, we are making the source send only one photon per second. Each time a photon is detected; we note where it has landed and plot it on a graph. This will reflect the probability of a photon landing on a certain spot or y.

As per our intuition and logic, we would say that the photon will go through either slit 1 or 2 and like bullets, the probability that it lands up at y should be P12(y) = P1 + P2. And this is totally not what happens!!

What we actually see is the interference pattern from before! Albeit with different frequencies. For this, light coming from one slit must interfere with that from the other slit! But there’s only one photon!! The explanation hence is that the photon interferes with itself!  So the photon goes through both slits! It is mathematically analogous to the case of the water waves.

Now, you might ask what if we place photodetectors on the slits. Legitimate proposition. But here’s the fact, the interference pattern gets completely washed out. This is the first example we are seeing of how a quantum system alters a certain result.

So, what did we learn? We learnt that photons behave both like particles and waves. This is called wave particle duality and is usually thought of as a paradox. But it is merely a mystery because our intuitions are limited when it comes to quantum systems. You know what’s crazier- when you learn that electrons behave the same way. Even though it is natural to think of super tiny charged balls, electrons are really quantum entities. More about them later. But here’s how these photons relate to qubits.

We are all familiar with the notions and workings of a classical bit -0s and 1s. However, we take a lot of things to be granted, most importantly that they exist in standalone independent states. A bit can be represented as states of an electron, ground state for 0 and an excited state for 1. But qubits or quantum bits remain in a superposition of states (spook alert!).
Well, I am gonna sign off for today. Leave a comment below if you loved it, hated it or have question in general! Baibhav out!



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