Quantum Computing — the big picture
The past, present and future of the world’s most mind-bending technology.
Computing beyond Moore’s law
Since the 1960‘s the speed of computation has kept increasing exponentially, but with the size of datasets constantly growing and Moore’s law coming to an end, we might soon smash into our physical wall of limitations, wherein, the current traditional computers will no longer be sufficient, or simply put, they will just stop making sense.
That is not to say that all is lost. However, I think we can all agree that it’s time to look for an alternative for the future of computing and electronics, and drastically rethink computers from the ground-up; right from the smallest possible unit of digital information — a bit.
A leap from bits to Qubits: This small letter-change could lead to entirely new horizons for the computational world
Let’s first look at a classical bit
A classical bit is the basic unit of information in regular computers. It can be in two states — either 0 or 1 but never both.
Now if we take two bits, we will end up with four possible states (00, 01, 10, or 11), but only one of them at any given moment. This limits the computer to processing one input at a time. And due to this limitation, quantum computers are taking the role of a game-changer in the race of computation.
In the quantum realm, things behave quite differently from the predictable ways we’re used to. Instead of usual bits, quantum computers use quantum bits, or ‘Qubits’ for short.
Qu what?
You can consider a qubit as the equivalent of the classical bit. Similarly, it’s the fundamental building block of Quantum Computers which we also measure using our binary system of 0s and 1s. The crazy thing is that they can hold both 0 and 1 states simultaneously.
Jaw-dropping, isn’t it?
But how is this even possible?! Hold on a little bit buds,
We have three-qubit properties to thank for this — superposition, entanglement and interference
But before we delve into these properties, let me first introduce you to the so-called Bloch’s sphere.
Bloch’s Sphere : a mathematical representation of the Qubit
The unlimited amount of states that a qubit can take at any given moment is traditionally illustrated in a sphere where North = 0 and South = 1. This sphere is called the Bloch sphere. Its purpose is to give a geometric explanation to single-qubit operations.
A convenient choice of basis to denote states 0 and 1 is the eigenstates |0> and |1> respectively — The set {|0>, |1>} forms a two dimensional basis in Hilbert space called the computational basis
Mathematically, the state of a Qubit is represented by a vector from the Hilbert space — the state vector.
In quantum mechanics, a vector has a special notation, the Dirac notation. A vector — also called a ket — is denoted by ψ
What you need to keep in mind is that at any time, a QuBit can be written as a superposition of two states as the following :
|ψ> = α |0> + β |1>
Where
α is a real number expressing the probability of the 0 state
β is a complex number expressing the probability of the 1 state
|0> refers to the ground state of the qubit
|1> refers to the excited state of the qubit
The relationship that links between α and β according to the Max Born rule and related to the Schrödinger wave function is:
|α| ² +|β| ² = 1
To make things clear, here is the difference between Classical bits and Qubits :
Now if you want annoying people to stay away from your birthday party or scare off unwanted relatives from visiting, just start talking about quantum computing. Most of them will never show up again, I bet.
Enter the realm of quantum computing
“ If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet” — Niels Bohr
What sets quantum computing apart from the computational herd is, in fact, the three fundamental properties of quantum physics: superposition, interference, and entanglement.
It’s all about Quantum Superposition!
Superposition: (also known as coherence) expresses the ability of the quantum system to exist in all of its theoretically possible states at once. In other words — as long as no measurement is performed, there is a certain probability to have one state AND a certain probability to have another state concurrently. But once we observe, only one result is obtained. Here is an example:
Say we roll a dice with sides numbered from one to six. As long as it doesn’t stop rolling, it takes all the six values — 1,2,3,4,5, and 6. But once landed, it becomes a normal dice with only one value — 1 or 2 or 3 or 4 or 5 or 6.
One other famous example is Erwin Schrödinger’s cat.
According to what we have seen so far; when a qubit is in a state of superposition, it forms a linear combination of an infinite number of states between 1 and 0. However, you will never know which state it will take until you actually look at it, which brings up our next phenomenon, quantum measurement.
Quantum measurement: (also known as decoherence) refers to the act of observing or measuring a quantum particle. This latter collapses or ruins the superposition state and the particle takes on a classical binary state of either 1 or 0 — nothing in-between.
Entanglement — The most romantic notion in physics.
“Spukhafte Fernwirkung” or ”Spooky action at a distance”
That’s how Albert Einstein described quantum entanglement. Weird huh?
Intrigued by the mind-bending phenomenon, he derided the notion, citing it as proof that quantum theory was flawed and incomplete. Is entanglement that baffling?!
While we don’t really want to go down the rabbit hole of entanglement, here is a simple explanation:
Unlike in classical physics, pairs of particles are said to be coupled or entangled with each other, when they form a system such that the state of one particle is dependent on the state of the other particle. Simply put, whatsoever process the particle experiences, it correlates to the other particle as well.
Not to mention that even if separated, across insanely large distances of space and time — say light-years. These entangled particles, however, can remain perfectly connected.
What if a measurement is applied?
Since there is a correlation between the entangled qubits, measuring a state of one qubit provides the information of the other qubit such that if one of them collapses — due to measurement, the other one collapses too.
Now let’s go back to Einstein’s spukhafte Fernwirkung thing.
He believed there must have been something wrong with quantum mechanics. But thanks to scientists, this phenomenon has been proved with countless quantum physics experiments.
Sorry, Einstein, you missed it.
Remember, in the quantum theory, once two particles undergo a shared state, they are no longer separate entities but exist as one. Thus if entanglement reminds you of something, it won’t be other than the experience of falling in love. Does entanglement make sense now?
Quantum entanglement is awesome. Think about it. Entangled particles are bound to each other in a way they aren’t to any other particle in the universe. And when something happens to one, it immediately affects the other.
How beautiful!
Interference: is another incredible property of quantum mechanics, one that makes you think what in the world is going on behind the scenes of our reality. The great physicist Richard Feynman once said about interference:
“The essentials of quantum mechanics could be grasped from an exploration of interference and the double-slit experiment.”
Microsoft researchers defined interference as the intrinsic behavior of a qubit, due to superposition, to influence the probability of it collapsing one way or another.
It’s considered as one of the most challenging principles of quantum theory which states that the building particles cannot only be in more than one place at any given time (due to superposition), however, that an individual particle, such as a photon (light particles) can cross its trajectory and interfere with the direction of its path.
Knocking on ML’s door
A team based in China claimed that a quantum computer had performed a calculation in 200 seconds that would take an ordinary computer 2.5B years — 100 trillion times faster. That’s mind-blowing, right?
Luckily, doing the necessary math on any ordinary computer would literally take years of trial and error. But a quantum computer with exponential speed-up and the ability to perform an indefinite number of superposed tasks in parallel could do it in a breeze.
A reason that pushed the researchers to investigate the power of quantum computers in learning and recognizing enormous amounts of data. And to study the intersection between the Quantum realm and a common branch of AI — Machine Learning.
Wondering what we will get if we combine both?
It’s a topic we will cover later, so stick around.
