Quantum Computers, Explained with Quantum Physics

If you believe the hype, this nascent technology embodies the promise of the future, and has the potential to revolutionize our lives with its turbo-charged computation. But quantum computers aren’t the next generation of supercomputers, they’re something else entirely. And before we can even begin to talk about their potential applications, we need to understand the fundamental physics that drives the theory of quantum computing. We’ll need to dive into another dimension, smaller and more alien than anything we intuitively understand: the subatomic world of quantum mechanics.

Feynman’s Idea In the 1980s, one of the most important physicists of the 20th century encountered a major roadblock. Richard Feynman was hungry for a window into the quantum universe. But quantum systems, by nature, are fragile, and the information they hold hides from us. Because Feynman couldn’t directly observe quantum events, he wanted to design a simulation. It quickly became clear that his computer wasn’t up to the task. As he added particles to the quantum systems, he was modeling, the cost of computation began to rise exponentially. Feynman concluded that classical computers just can't scale up fast enough to keep pace with the growing complexity of quantum calculations.

Then he had a breakthrough. What if he could design a tool made up of quantum elements itself? This instrument would operate according to the laws of quantum physics, making it the perfect way to probe the mysteries of the quantum realm. The idea of the quantum computer was born. And by dreaming it up, Feynman had started to build a bridge between quantum physics and computer science. To understand how quantum computing works, it’s essential to start by understanding what makes it quantum in the first place. This means that we need to talk about what’s at the heart of quantum physics: a concept called amplitudes.

what the classical rules of probability tell us about getting tails if we toss a coin 20 times. We add up the probabilities for all the possible outcomes resulting in tails. That’s just common sense. But common sense doesn’t govern the quantum universe. Before you measure a subatomic particle, you can think about it as a wave of probability that exists in a kind of black box, a quantum system with many different chances of being in many different places. Quantum mechanics, at its core, is a change to the rules of probability. This is also where the power of quantum computing comes from these different rules of probability than the ones that we are used to. Amplitudes are closely related to probabilities.

But they're not probabilities. A key difference is probability is always a number from zero to one. But amplitudes are complex numbers. And what this means is that they obey different rules. So, if I want to know the total amplitude for something to happen, I have to add up the amplitudes for all the different ways that it could have happened. But when I add up amplitudes, I see something new, which is that a particle might reach a certain place one way with a positive amplitude and another way with a negative amplitude. And if that happens, then those two amplitudes can cancel each other out so that the total amplitude would be zero, and that would mean that that thing would never happen at all. the amplitudes are connected to the probability that you actually see something when you look there.

This is sort of the central thing that quantum mechanics says about the world: that the way that you describe a physical system is by a list of amplitudes. And the way that a physical system changes over time is by a linear transformation of these amplitudes, by some change to these amplitudes. But how can quantum computers use amplitudes to store and manipulate information quantumly? This is a qubit. It’s the basic computational unit in quantum computing. Qubits are like bits in a classical computer, but with a crucial difference. A bit is binary, it stores information in strings of binary digits that can only be 0 or 1. But qubits are made of subatomic particles, so they operate according to subatomic logic. Qubits can be 0, 1, or what we call a linear combination of 0 and 1.

This fluid combination of amplitudes is at the core of quantum computing. Before you measure a qubit, it exists in a state called superposition. You can think about it as a quantum version of a probability distribution, where each qubit has some amplitude for being 0, and some amplitude for being 1. Superposition is the reason that quantum computers can store and manipulate vast amounts of data compared to classical computers. When two or more qubits are in this closed state of superposition, they relate to one another through the phenomenon of entanglement. This means that their final outcomes, when we measure them, are mathematically related. Quantum entanglement is the word we use for the characteristic correlations among parts of a quantum system, which are different from the correlations that we normally encounter in the classical world, in ordinary experience.

You could think of it as like a book. When you look at the pages one at a time, you don't see any information—you just see random gibberish because the information isn't encoded in the individual pages, but in the correlations among them. And to read the book, you have to collectively observe many pages at once. But if you want to describe very highly entangled states using ordinary bits, it's extremely expensive. Imagine that you had a primitive 10-qubit computer. It could store 2^10 values in parallel. To describe this entangled configuration with a classical computer, you’d need 16 kilobytes, or 16 thousand bits. Expand to a system with 500 entangled qubits, and you now require more classical bits than there are atoms in the known universe.

This is exactly what Feynman meant when he said that classical computers weren’t scalable for simulating quantum mechanics. For a quantum computer to be of any use, you need to measure information from the qubits to get an output. The problem is, when a quantum system is measured, it collapses into a classical state. If you look at a qubit, let's say to ask it whether it's zero or one, then you collapse its state, right? You force it to decide whether to be a zero or one. Anything carries away information about whether that qubit is zero or one—so for example, if that information gets recorded in some radiation that's escaping from the quantum computer, then the effect on the qubit will be exactly as if someone had measured it to see whether it was 0 or 1.

When you look at the system, then the amplitudes become probabilities. To extract an answer from the quantum system that isn’t just a random outcome of probability, like the flip of a coin, we have to use interference. Interference can be seen in classical physics when waves in a pool hit each other, and one wave is above the surface, and the other wave is below the surface, and they cancel each other. Interference is just what amplitudes do when you add them up. If something can happen one way with an amplitude of a half and another way with an amplitude of minus a half, then the total amplitude for it to happen would be zero. This is what you do in the famous double slit experiment. You close one of the paths, and then you see that now the thing that previously never happened, can happen.

This is a quantum algorithm. Scientists can harness interference by creating a deterministic sequence of qubit gates. These qubit gates cause the amplitudes to add up constructively. This means that they’re mathematically guaranteed to boost the probability of seeing one of the right answers. This is a quantum algorithm. Scientists can harness interference by creating a deterministic sequence of qubit gates. These qubit gates cause the amplitudes to add up constructively. This means that they’re mathematically guaranteed to boost the probability of seeing one of the right answers. You might ask, how could you possibly concentrate all this on the right answer when you yourself don't know in advance which answer is the right one?

This is exactly why designing quantum algorithms is so difficult and why we have a whole field that's been studying it for decades. Since 1994, there have been a few major breakthroughs in quantum algorithms, with theoretical applications in fields such as cybersecurity and search optimization. But according to most experts in the field, quantum computers are most likely to be useful for what they were born to do—when a curious physicist wondered about the deep structure of our world. I find quantum computing exciting as a way to explore physics. Now, whether that's going to make anybody any money—whether there'll be practical applications in the near-term—that's still very much an open question. But at least for physicists, it's an exciting time. The truth is, that the most important application, I believe, of quantum computers is something that we don't know yet.