This quantum computing is complex stuff.

Indeed, University of Waterloo physicist David Gosset says he’s not sure he could explain the driving force behind the preposterously fast devices to an audience of relative experts. “It would be an hourlong discussion and we wouldn’t get anywhere,” he says.

Bear in mind that the speaker — an associate professor with the school’s Department of Combinatorics and Optimization and its Institute for Quantum Computing of all things — is a top-drawer theoretician and teacher in the field.

And he’s speaking specifically about the very algorithms that would propel exponential increases in the speed of the future computers, his area of expertise.

Quantum computers crashed into the headlines late last month when Google claimed, through a widely publicized paper in the journal Nature, that it had built and successfully run such a blindingly fast machine.

That device — the chip-like brains of which could fit in the palm of your hand — made computations in about 3.5 minutes that would take a conventional computer the size of two basketball courts 10,000 years to achieve, Google scientists said in the paper.

But that “quantum supremacy” — a proof that such machines could solve something even the largest traditional devices could not in a reasonable amount of time — was achieved on a computer that’s too primitive to utilize the algorithms that will give its true quantum heirs their power in coming years, Gosset says.

“You think of an algorithm as a recipe,” he says. “Well, there are steps you can do in a quantum algorithm that you just cannot do in a classical algorithm, they just don’t exist.

“So it just unlocks a new set of algorithms and certain problems that were thought to be (too) hard.”

Gosset explains, sort of, that instead of using the digital zeros and ones of conventional computers, the algorithms that will run quantum devices would rely on the complex properties of quantum mechanics itself.

And they would basically work because … well … because quantum mechanics itself works.

“I don’t know how to describe it, you can’t point to one thing,” Gosset says with a frustrated chuckle.

“There is a fundamentally different way that quantum mechanics stores and processes information.”

Quantum mechanics is a branch of science describing the infinitesimal, phantasmagorical world that — in its atomic-level realm — could have Sir Issac Newton’s head-plonking English apple falling in Japan.

“It’s a weird thing,” says York University’s Randy Lewis, before launching into his five-minute explanation of the elementary mechanics behind quantum computing.

“As everyone says, classical computers are made of classical bits, and quantum computers are made of quantum bits,” or qubits, says Lewis, a professor in the Toronto school’s Department of Physics and Astronomy. (They’re pronounced CUE-bits).

Classical computer bits, using digital zeros and ones, can be pictured as tiny switches that are either on or off, he says.

“And we can picture a quantum bit (qubit) as a tiny Spin-1/2 (Spin one-half) particle,” Lewis says, pretty sure he’ll have to take an explanatory detour on that.

Spin-1/2 particles, he says, include such subatomic phenomena as electrons, neutrons and protons and many types of full atoms.

“So they’re out there in nature, they’re common and we’re used to them,” Lewis says.

(Companies and organizations racing to build quantum computers are either using such natural particles or trying to mimic them to create their qubits.)

And to picture the particles’ funky spin — a quantum phenomenon — you might visualize a baseball twirling, but otherwise stationary in midair, Lewis says. The rotation axis of that spinning baseball could point up, down, sideways or any way it wanted, he says.

“And if I measured the (vertical component) of its spin it could be large, it could be small, it could be zero,” Lewis says.

With any specific Spin-1/2 particle, on the other hand, the vertical component of the spin is always exactly the same size, Lewis says.

“It’s never larger, it’s never smaller, it’s never zero, there’s a very specific number it can be,” he says. “The only question is whether it’s pointing up or pointing down.”

But this constant “spin up” or “spin down” positioning is — head-scratchingly — only true when the particles are being measured.

The useful part of the clockwise or counter-clockwise duality of the particles for computing purposes, Lewis says, is that they can exist when not being measured — and through quantum mechanics wizardry — in any combination of both options.

This is known as a superposition state, he says.

“So if I take my electron, or my qubit in my quantum computer, and I measure the vertical component of its spin I will always get that it is pointing up or pointing down, there’s no other option,” Lewis says.

“But during the calculation, before I measure it, there are all kinds of options. It’s in this superposition state, it can have pieces of up and down at the same time.”

Quantum mechanics theory, Lewis says, allows scientists to calculate the probabilities that these fluctuating superposition states will produce an up or down spin in an individual particle or qubit when it’s measured.

“And if my calculation said 75 per cent of the time it should be spin up, then if I do a million runs on my computer I should find 75 per cent of them give me spin up and the other 25 per cent will give me spin down,” he says.

“We really can do that calculation.”

But if many qubits are involved then such chalkboard and classical computer calculations would be far too time-consuming to allow for devices that string massive numbers of qubits together. This is where quantum computers will help.

“We can just say we know that quantum mechanics works, we’re going to build a huge computer with many qubits and we’re going to run (a) code on the computer many, many times,” he says.

“You add up all the times the answer was ‘spin up’ qubit-by-qubit and add up all the times it was ‘spin down’ qubit by qubit, and that is the answer quantum mechanics would have given us if we’d done that hard calculation.”

By discovering how each of the component qubits works, programmers can go on and use those known states to write code.

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And as with the ones and zeros in conventional computers, where the state of the next bit is often dependent on the programmed state of the one beside it, so the quantum computer can change the up or down status of the next one as it exists in its fluctuating, superposition state.

“You can say ‘rotate qubit number one only if qubit number two is spin up,’ ” says Lewis, adding this interaction is known as entanglement. “So the whole big quantum computer becomes a big entangled quantum state where all the qubits are interdependent on the other qubits.”

Manipulating one qubit so it can influence the next one down the line can be achieved by training such things as microwaves or magnetic fields on them.

But adding just one more qubit to a machine doubles the complexity of that computer. Thus the permutations and combinations these qubit by qubit interactions can generate are almost unfathomable.

Indeed, the calculation that Google touted as being beyond the reasonable reach of any conventional machine involved solving a part of this complexity on the so-called Sycamore device that had only 53 qubits to its name.

(Though it only boasted this small qubit array, the number of possible outcomes of up and down spins the device could have produced in the experiment was about nine million billion.)

Still the Google achievement — compared by some to the Wright brothers’ first flight — might look somewhat meagre when its key import is explained.

“If you can do something on your quantum device that cannot be computed … on a classical computer in a comparable amount of time then sort of by definition you have a little bit of additional power, or maybe a lot,” Gosset says. “You have the hope of having additional power with that device, (and) that is what Google has aimed for and that is what they have claimed.”

But the calculation that Sycamore churned through in 200 seconds was basically “useless” outside of the doing it, Gosset says.

“And I don’t say ‘useless’ to be derogatory,” he says. “It’s that they were not aiming for something useful, it’s that they were aiming only to do some computation that we don’t know how to do in a comparable amount of time using (normal) computers.”

But the geological time frame that Google scientists estimated it would take a powerful digital computer to achieve the punky Sycamore’s solution was quickly challenged by electronics behemoth IBM — a major builder of conventional computers, and a competitor in the quantum race.

Using the world’s biggest supercomputer and some canny strategies — like storing memory on hard disks — IBM scientists said they could do the Google calculation in two and a half days; that’s not 3.5 minutes but it’s a far cry from 10,000 years.

“But either way,” says Gosset, “it’s somehow we’re either on the border, or just beyond what can be done using classical supercomputers. And so that’s where the excitement is coming from.”

And that excitement is warranted, says the University of Toronto’s Hoi-Kwong Lo, a Canada Research Chair in Quantum Information at the school.

“People used to say quantum computers are impossible, it’s infeasible,” Lo says. “But this demonstration I think actually proves in some ways that things are much more optimistic — that quantum computers could be useful.”

Gosset agrees.

“This will be an important part of what will be a really fascinating story,” says Gosset. “And nobody is saying this is not progress — it is definitely progress.”

But Gosset stresses that none of the algorithms needed to run a truly useful device will be possible without the technological and theoretical advances needed to correct the errors and interfering factors that impact current qubit operations and that represent the biggest impediment in the quantum computing field.

Lo says there has been an infusion of talent into the field over the past several years and that this could help overcome such problems and expand the potential areas for which the computers might prove valuable. He says solutions will involve hardware and software fixes.

Lo believes the complications will delay meaningful, full-scale quantum computers, possibly for decades.

“But I think in the long run it is inevitable,” he adds.

Surprisingly, the things that the computers are likely to be used for when they do appear are now imagined to be quite limited.

“Two things might come to mind,” says Lewis, adding that one of them is quantum science itself.

“It seems natural that if we wanted to study particles that are quantum in physics or in chemistry or in medicine or technology, there are a lot of important calculations that need to be done,” he says.

The other likely use for the computers — and one that had many fretting over the Google paper — is in the field of information encryption.

Many expressed fears, wholly unfounded, that the announced quantum supremacy would make any encryption-protected information vulnerable across the globe.

“But I think it’s entirely possible quantum computers could have much more applications than people have thought so far,” Lo says.

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