Social media was abuzz a while ago with Canadian Prime Minister Justin Trudeau’s explanation of quantum computing. Check it out.

The Guardian wrote an article about his response lauding him for his efforts, and the piece has gained a lot of media attention. People are really, really interested in the quantum, and they are fascinated as to whether he’s correct or not!

I agree with The Guardian’s analysis in that Trudeau’s response really shows that he cares about learning some of the physics involved in important government-funded projects, such as quantum computing. However I have to disagree with The Guardian calling his explanation “quite a good one”. The science isn’t quite right.

Trudeau talks about a wire. It can either be on (have current flowing through it) or off (no current flowing). The idea Trudeau presents is that a given wire can be on, off, or in a superposition of on and off. Trudeau says that putting states in a superposition allows us to encode more information in the same amount of space. The idea is there, but it’s a little misleading. This makes it sound like quantum computing will give us bigger hard drives that can store more data. Or make our computers smaller. Or make them all-around faster. Quantum computing won’t do any of those things!

To explain why not, let’s go over a little bit of… physics!

What is Classical Physics?

Physics is all about asking questions and getting answers. Let’s look at classical physics for a moment. Say I chuck my laptop out of a window. I can ask questions about it, such as:

• Where is it? (outside)
• How fast is it moving? (too fast)
• Why did I do that? (because of the prime minister of canada)

In classical mechanics, I can ask these questions at any point in time. I can get the information whenever I want, and glancing at the flying laptop brings me answers to as many questions as I want. I can also phrase the physics that I do in terms of the answers to these questions. When you talk about Newton’s laws, you talk about the position and velocity as definite numbers – that is, you assume the answers to those questions exist, with definite values, at every point in time.

You can do the same thing with a wire in classical physics. It can be either on or off, and I can glance at the wire to check whether it’s on or off. I can get the information about the state of the wire however I want and whenever I want. If I don’t actually look at the wire, it makes no difference to me: I can posit that the information existed all of the time I wasn’t looking, I just didn’t know it.

What is Quantum Physics?

Now let’s look at the quantum wire. I can ask the same question: is the wire on? In quantum physics, you still get answers to your questions. You ask, “is the wire on”, and you get a definite “yes” or a definite “no”. However, quantum physics weakens one assumption above: You can’t assert that the information existed all along! You get definite answers to your questions, but answers to your questions don’t have to exist with certainty in-between measurements.

This is one of the phenomena that troubles highschoolers in chemistry courses. You may have learned about light being emitted from hydrogen atoms. An electron around the nucleus also has an “on” (excited) and an “off” (ground) state. The atom absorbs energy and lets the electron go from ground to excited, and it emits energy in the form of a photon as the electron goes from excited to ground.

In classical physics, the only explanation is a “jump”. One moment the electron was in the ground state, and the next it’s in the excited state.

In quantum physics, a definite “on” or “off” doesn’t exist. If you observe the electron at any point in time, you get a definite answer – “on” or “off”. If you keep observing it constantly in a vain attempt to find the moment when it “jumps”, you even find that it stays put in the ground state! However, if you let it be, the probability to find it in an excited state slowly ramps up. Therefore, one consequence of quantum mechanics: changes between two discrete states can happen continuously.

How does this relate to computers?

Remember the classical wire. At any moment in time, it is either on or off, with absolute certainty.

Remember the quantum wire. It can be in a superposition of on and off. The question, “is the wire on or off”, does not have a definite answer at any given moment in time.

This means that quantum physics gives more freedom than the suppositions of classical physics. You no longer have the restriction of having to assume answers to all questions (position, velocity) exist with certainty, before you actually make the measurements.

Back to Trudeau

Quantum computers exploit this extra freedom. Instead of operating on things that are on or off with absolute certainty, you operate on superpositions. Where Trudeau gets it right: there are many more possible quantum superpositions than there are classical states. This slight bit of extra freedom – not having to suppose a definite answer exists to all questions you ask – allows you to use a myriad of tricks, but it is not a magic cure-all! It doesn’t exponentially speed up all computer programs, and it doesn’t directly give you more storage space on your computer. Quantum computing allows you to exploit this change of treatment of what it means to know something.

Quantum computing will give very very exciting results. It will revolutionize cryptography and computing as a whole. But the boon of quantum mechanics is also its bane. If you ask a question of a quantum – whether a wire is on or off – before the whole computation is done, you break the superposition. You have to shut your eyes while the computation is being done. “Shut your eyes” isn’t literal, here. It simply means that you’re not allowed to have any physical interaction with the quantum state while it’s being performed. Not due to light, heat, touch, or anything else! This makes it exceedingly difficult.

For the interested reader, please look at Scott Aaronson’s Quantum Computing since Democritus.