Posts Tagged ‘complex numbers α and β’

Are Quantum Computers Even Feasible

November 29, 2018

IBM has toned down its enthusiasm for quantum computing. Even last spring it already was backing off a bit at Think 2018. Now the company is believes that quantum computing will augment classical computing to potentially open doors that it once thought would remain locked indefinitely.

First IBM Q computation center

With its Bristlecone announcement Google trumped IBM with 72 qubits. Debating a few dozen qubits more or less may prove irrelevant. A number of quantum physics researchers have recently been publishing papers that suggest useful quantum computing may be decades away.

Mikhail Dyakonov writes in his piece titled: The Case Against Quantum Computing, which appeared last month in Spectrum IEEE.org. Dyakonov does research in theoretical physics at Charles Coulomb Laboratory at the University of Montpellier, in France.

As Dyakonov explains: In quantum computing, the classical two-state circuit element (the transistor) is replaced by a quantum element called a quantum bit, or qubit. Like the conventional bit, it also has two basic states. But you already know this because DancingDinosaur covered it here and several times since.

But this is what you might not know: With the quantum bit, those two states aren’t the only ones possible. That’s because the spin state of an electron is described as a quantum-mechanical wave function. And that function involves two complex numbers, α and β (called quantum amplitudes), which, being complex numbers, have real parts and imaginary parts. Those complex numbers, α and β, each have a certain magnitude, and, according to the rules of quantum mechanics, their squared magnitudes must add up to 1.

Dyakonov continues: In contrast to a classical bit a qubit can be in any of a continuum of possible states, as defined by the values of the quantum amplitudes α and β. This property is often described by the statement that a qubit can exist simultaneously in both of its ↑ and ↓ states. Yes, quantum mechanics often defies intuition.

So while IBM, Google, and other classical computer providers quibble about 50 qubits or 72 or even 500 qubits, to Dyakonov this is ridiculous. The real number of qubits will be astronomical as he explains: Experts estimate that the number of qubits needed for a useful quantum computer, one that could compete with your laptop in solving certain kinds of interesting problems, is between 1,000 and 100,000. So the number of continuous parameters describing the state of such a useful quantum computer at any given moment must be at least 21,000, which is to say about 10300. That’s a very big number indeed; much greater than the number of subatomic particles in the observable universe.

Just in case you missed the math, he repeats: A useful quantum computer [will] need to process a set of continuous parameters that is larger than the number of subatomic particles in the observable universe.

Before you run out to invest in a quantum computer with the most qubits you can buy you would be better served joining IBM’s Q Experience and experimenting with it on IBM’s nickel. Let them wrestle with the issues Dyakonov brings up.

Then, Dyakonov concludes: I believe that such experimental research is beneficial and may lead to a better understanding of complicated quantum systems.  I’m skeptical that these efforts will ever result in a practical quantum computer. Such a computer would have to be able to manipulate—on a microscopic level and with enormous precision—a physical system characterized by an unimaginably huge set of parameters, each of which can take on a continuous range of values. Could we ever learn to control the more than 10300 continuously variable parameters defining the quantum state of such a system? My answer is simple. No, never.

I hope my high school science teacher who enthusiastically introduced me to quantum physics has long since retired or, more likely, passed on. Meanwhile, DancingDinosaur expects to revisit quantum regularly in the coming months or even years.

DancingDinosaur is Alan Radding, a veteran information technology analyst, writer, and ghost-writer. Follow DancingDinosaur on Twitter, @mainframeblog, and see more of his work at technologywriter.com.


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