Quantum Computing: When Physics Meet Computation

There’s a lot of buzz surrounding Quantum Computation in recent years. The field received a lot of media attention, as well as rapid-spread rumours that claim issues like encryption that will soon be dead, Quantum Computers that will outperform the world’s Supercomputers, and many others.

To a certain extent, some of the claims are relatively true. For instance, encryption will indeed be negatively affected by Quantum Computers, but it doesn’t mean that there’s no workaround to it, neither can we assume that Quantum Computers will work according to the theory behind it.

Yes, you read that correctly, the Quantum Computer that everyone is hopeful about may not even come to life – according to experts like Mikhail Dyakonov. Let’s take a step back from all the hype and return to the basics and ask why Quantum Computers may or may not be plausible.

Google A.I. Quantum’s Sycamore processor. Erik Lucero/Google.

 

Why Quantum Computers?

First, we shall ask why we need to create Quantum Computers in the first place. Aren’t computers fast enough to do anything we’d ask it to? Aren’t engineers constantly innovating newer and faster GPUs (Graphics Processing Unit) already?

To answer that question, we shall take computation to the extremes. A lot of times, computers like the one we own at home can solve small-scale tasks like optimization. However, there are complex tasks that grow exponentially as the number of variables to consider increases. That’s a problem which even the fastest Supercomputers cannot address to this day.

Putting it more practically, Supercomputers struggle to simulate natural phenomena, – like simulating nature. IBM’s Senior Manager in Quantum Research Dr. Talia Gershon said, “simulating nature is something that’s really hard, because you take something like modelling atomic bonding, an electronic orbital overlap. Instead of now writing out a giant summation over many terms, you try and actually mimic the system you’re trying to simulate directly on a Quantum Computer.”

In fact, the task of simulating Iron Sulfide clusters (\text{Fe}_x\text{S}_y) of different sizes found in Nitrogenase enzymes is at the limits of Classical Computers – that is, computers which you and I own, as well as the Supercomputers of today. It’s important that we can simulate chemicals which are fatal to the development of medicine, just one out of many problems that Classical Computers have shown limitations at.

 

How does one Make Quantum Computers?

So, what are Quantum Computers, and how does one build them? Simply put, Quantum Computers are Applied Physics and Engineering. The idea of a Quantum Computer has been proposed even before we had the technology to develop them. Paul Benioff first proposed the idea of a quantum mechanical model of the Turing machine. Later on, Richard Feynman along with other scientists suggested that Quantum Computers may outperform a Classical Computer.

Feynman also famously said, “nature isn’t classical, dammit, and if you want to make a simulation of nature, you’d better make it quantum mechanical, and by golly it’s a wonderful problem, because it doesn’t look so easy.” The second half of the quote truly reflects the struggles of many tech giants who dedicate tons of hours to the development of Quantum Computers.

For one thing, Quantum Computers are superbly hard to implement. Even the world’s finest team of engineers admit that we are still in what experts call the NISQ (Noisy Intermediate-Scale Quantum) era of Quantum Computers. Specifically, the Quantum Computers we have today are noisy, which easily disrupts and interferes with the mechanics behind Quantum Computers.

And what mechanics you may ask? Well, Quantum Mechanics – the bread and butter of 20th-century Physics. Perhaps you’ve heard the likes of Max Planck, Albert Einstein, Erwin Schrödinger, Neils Bohr, Max Born, and many others who are the godfathers of Quantum Mechanics.

Quantum Computers build upon the findings of Quantum Mechanics and exploit Quantum Phenomenons like superposition and entanglement. Those phenomenons allow Quantum Computers to outrun Classical Computers since their building blocks behave quantum mechanically themselves.

IBM 50Q System: An IBM cryostat wired for a 50 qubit system. IBM.

 

What is Superposition?

While transistors are the back-bone of Classical Computers, subatomic particles are the legos of Quantum Computers. Some of the physical realizations of today’s Quantum Computers use physical systems like superconducting circuits, trapped ions, neutral atoms in an optical lattice, and many more. Regardless of what backend they use, all Quantum Computers rely on quantum mechanical phenomena, especially superposition. While we can talk on and on about superposition’s formal definition, I’ll attempt to explain it as I would to a high school student.

Say, for example, you have a wall which is placed in front of another wall. Then, carve out two holes in the front wall so that you can throw baseball balls through them. Now, if you randomly threw those balls towards the back wall, and gather statistics of where the ball landed, you would expect that the probability of the ball hitting any particular region of the back screen is just the sum of the probability of it going through the first hole p_a, plus the probability of it going through the second hole p_b.

 

p = p_a + p_b

 

This is a general probability rule which most people are familiar with. The 0.5 probability of the coin landing as heads plus the 0.5 probability of the coin landing as tails add up to a greater probability of 1.

 

Young’s double-slit experiment. ResearchGate.

 

If you replace those balls with photons instead, you will not observe the expected behaviour. Instead, you’ll see that they form a pattern of light and dark fringes, where the dark fringes are areas where the photons almost never land at.

However, if you decide to cover one of those holes, you’ll find that there are photons that would land in the dark region where no photons landed when both holes were opened! That means the probability of the photon landing at a particular region when only one hole is opened is greater than when two holes are opened.

 

p_a > p

 

How can it be that a probability decreases as you provide more “pathways” to reach the destination? Wouldn’t it make much more sense that with more routes you have at your disposal, the less chance it is for you to get stuck in traffic within a busy road?

The answer behind this is tested after the famous double-slit experiment by Thomas Young in 1801. The conclusion is that photons, like many other subatomic particles, behave like waves. This would later translate to the famous wave-particle duality, such that every particle or quantum entity may be described as either a particle or a wave. Most notably, a subatomic particle can behave like a wave, including when determining their position.

 

This is in line with the popular Schrödinger’s Cat thought-experiment. Say you’re given a box with a cat, a flask of poison, and a radioactive source are placed in a sealed box. If an internal monitor detects radioactivity, the flask is shattered, releasing the poison, which kills the cat. However, according to the Copenhagen interpretation of Quantum Mechanics, the cat is alive and dead simultaneously until you open the box.

For the case of a classical bit in a transistor, it can either be on (one) or off (zero). However, if we use a Quantum Bit (qubit), say from an electron, it can be in the superposition of one and zero at the same time. That means, one qubit can be in two states at a time, whereas a classical bit can only take up one state at a time. Mathematically, you can thus simulate 2^n states with n qubits, instead of only n states with n classical bits.

 

Shor’s Algorithm

Shor’s Algorithm Implementation Circuit. Qiskit.

The theoretical knowledge of subatomic particles’ superposition would rapidly inspire generations of scientists and researchers to develop algorithms that exploit this very fact. Probably the most well known Quantum algorithm is Shor’s Algorithm – the algorithm that is dubbed to be the death-reaper of modern encryption.

Most of today’s encryption systems rely on the fact that computers take a long time to factor large prime numbers, such that, in a Computer Science term, it is a problem in the NP class. To be more precise, the most efficient known classical factoring algorithm, the general number field sieve, has the time complexity of O(e^{1.9(\log N)^{1/3}(\log \log N)^{2/3}}). In layman’s term, it takes a long long long time.

On the other hand, Shor’s Algorithm can solve prime factorization in O((\log N)^3) order of Quantum Gates. Given that massive speedup, many people started to believe that encryption will soon be doomed. However, Shor’s Algorithm takes several qubits to work. Moreover, those qubits should not succumb to quantum noise and other forms of quantum decoherence – a major problem that researchers and engineers are still striving to solve.

Even if one day people will have access to such a powerful technology, there are workarounds to this. Most public-key cryptography schemes like the one used by RSA depend on the extreme difficulty of factorization. However, other encryption algorithms do not build upon factorization’s complexity.

For example, elliptic curve cryptography is based on the algebraic structure of elliptic curves over finite fields. This shows that while yes, the widespread RSA scheme can be killed by Shor’s algorithm, we may someday replace it with a different scheme that’s immune to Shor’s and might need a different quantum algorithm to break.

 

A high-level abstract overview of the computational steps involved in the end-to-end pipeline for inference and training of a hybrid quantum-classical discriminative model for quantum data in TensorFlow Quantum. Google AI Blog.

Therefore, as long as brilliant minds have not attained noise-free Quantum Computers in the meantime, we can still safely believe in the encryption methods of today. Besides, the development of Quantum Computers can bring more positive impacts to the table. Perhaps if we’ve created a quantum algorithm to break encryption, there someday maybe another which would turn the algorithm on its head by creating quantum encryption.

 

Closing Remarks

A few other examples of the ways we can leverage Quantum Computers include quantum matter simulation, quantum imaging, quantum machine learning, quantum communication networks, and many others. The field is an ever-evolving world and the possibilities are endless.

For the time being, if you’re a programmer yourself, there are ways to access real Quantum Computers like the one built by IBM. Alternatively, there is always a classical simulation of Quantum Computers found in Google’s Cirq, Julia’s Yao.jl package, Xanadu’s Strawberry Fields, and more.

There are also tons of Massive Open Online Courses (MOOCs) that teach the basics of Quantum Computers and Quantum Algorithms. A personal favorite is BerkeleyX: CS-191x Quantum Mechanics and Quantum Computation, taught by Berkeley’s very own Umesh Vazirani.

 

Quantum Philosophy. The Mysearch Website.

Quantum Mechanics is indeed weird. Quantum Mechanics have influenced not only the creation of Quantum Computers but also countless Philosophical ideas of the past. Debates, arguments, and questions are being raised regarding this matter to this very day. Who knows? Perhaps one day we shall comprehend the Master’s secret language of Nature and use it to our advantage.

Wilson Wongso

Wilson Wongso

Indonesian Computer Science Student, Private Tutor, and Content Writer. At times I read, game, or watch. My boss calls me Jack of All Trades; I could not agree more.

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