What Is A Quantum Computer? The 30,000 Foot Overview
Title slide from the quantum computing presentationCHAD ORZEL
I was part of a panel at the 2018 meeting of the National Association of Science Writers on communicating quantum physics, and they asked me to do a brief overview of the field suitable for non-physicists. In 10-12 minutes.
I ended up going for what I think of as the view from 30,000 feet, covering the basic physics principles that make quantum computers interesting. Having spent a bunch of effort making this, I’m both thinking of ways to re-purpose it for other venues, and typing up the following blog version of what I said at the panel:
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My goal here is not to describe any specific quantum computer, because all the various platforms that are under development are really complicated, and would take too much time. Rather, my goal is to describe the fundamental physics that makes quantum computing powerful and an interesting topic to study. In very general terms, that boils down to a one-sentence description:
A quantum computer exploits properties of quantum physics to perform certain types of calculations more efficiently than any classical computer
Of course, like any field more complicated than digging holes and immediately filling them back in, this one-sentence description needs a bit of unpacking, starting with the “properties of quantum physics” in play here.
As always when talking quantum, the first property that comes into play is the idea of wave nature. Quantum physics tells us that everything in the universe, including material objects that we normally think of as particles, has wave nature. The wave character of an electron picks out particular energy states for an electron inside an atom– you don’t go too terribly wrong if you imagine this as analogous to the standing-wave modes you see for sound waves in an organ pipe or on a guitar string.
These special states are the conceptual justification of the Bohr model of electrons in atoms, in which an electron can only be found in certain states of well-defined energy. Electrons move between these states by absorbing or emitting photons of light, with the light frequency corresponding to the energy difference between the initial and final states. (The actual states aren’t literally planetary-style orbits as in the actual Bohr model, but the conceptual picture isn’t wrong.)
What does this have to do with computing? Well, a quantum system with discrete states lets you pick out two of those states and call one of them “|0>” and the other “|1>” and treat them as the two states of a binary bit. You can drive this bit back and forth between states by applying light of the appropriate frequency, so these can form the base elements needed to do computation.
Waves and a jumping fish, highlighting some of the superposed wave patterns.CHAD ORZEL
Of course, if this were the only thing quantum physics had to offer, nobody would be interested in quantum computing. The wave nature of everything, though, leads to another interesting property that’s characteristic of waves. If you look at a picture of waves like the vacation photo shown above, you can identify multiple discrete wave patterns: there are several sets of concentric rings where something broke the surface of the water at a particular point, and also a larger pattern of straight-line waves running diagonally across the photo.
If you pick a random bit of water, such as the orange box highlighted, you can’t associate that element of water with a single wave. It’s affected by all of these patterns at the same time. That’s a very general property of waves, and carries over to quantum objects: they can be in multiple wave-like states at the same time.
This superposition property leads to some problems, as in the infamous Schrodinger Cat thought experiment with a boxed feline that’s both alive and dead. It’s the second property exploited for quantum computing, though: a qubit is not restricted to being either 0 or 1, but can be a superposition of both |0> and |1> at the same time. At the end of the computation, you’ll measure it to be one or the other, but during the computation process the exact state is indeterminate, and contains bits of both.
The ambiguous Necker cube and the two states it can resolve into.CHAD ORZEL
This two-things-at-once situation seems really strange, but if you’ve ever tried to learn three-dimensional drawing, you’ve seen a nice visualization of this: the Necker cube. You can see one of these wire-frame cubes as either facing up and to the right, or down and to the left, and with a bit of effort you can make your brain flip back and forth between the two. The unshaded cube is a mix of the two states, both up-and-right and down-and-left, in a manner analogous to the |0>-and-|1> superposition of a qubit.
This ambiguous cube also provides a nice way to illustrate the third property of quantum objects exploited for quantum computing, which is the idea of entanglement. If you put two Necker cubes side-by-side, you get a pair of objects whose individual states are indeterminate– both up-and-right and down-and-left at the same time– but where each is guaranteed to be the same as the other. You can’t really get your brain to see the cube pair in a split state where they face in different directions.
A pair of Necker cubes as a metaphor for entanglement.CHAD ORZEL
This is very much like the state of a pair of quantum particles that have interacted with each other to produce a correlation between their states. This entanglement means that the two particles each remain in a superposition until they’re measured, but once you know the state of one of them, you know the state of the other with absolute certainty. Unlike the cubes, where the illusion depends on the lines overlapping a little, these entanglement correlations, once established, remain even if the particles are widely separated, so a given qubit in a computer can have its state entangled with the state of any other qubit or collection of qubits involved in the calculation.
So, the wave nature of quantum matter picks out two qubit states that we can call |0> and |1>, and allows those bits to be in superposition states, giving us a much richer range of possibilities than you can get with classical bits. And entanglement allows those qubits to continue to be in superposition states during the calculation, but have the final state depend on the state of all the rest of the qubits in the calculation.
These properties of wave nature, superposition, and entanglement combine to give a set of qubits options that wouldn’t exist for an equal number of classical bits. For most ordinary sorts of operations, that doesn’t really matter, and a qubits are just a more fragile and expensive way of doing computing. For certain types of problems, though, these extra options offer the ability to do calculations more efficiently.
What kind of problems? Well, we can get a sense of the possibilities by remembering that the root of all this is wave nature. A wave is, more or less by definition, something that extends throughout a system, and that means that quantum computers have an advantage over classical ones when it comes to looking for collective properties of the entire system.
The classic example of this is the problem of factoring a number into the two prime numbers that you would need to multiply together to make it. With a classical computer, this requires dividing the number of interest by each of the numbers smaller than it until you happen to hit one of the prime factors. That’s not too bad if you’re dealing with smallish numbers, but if you’re dealing with numbers having hundreds of digits, it’s an enormously time-consuming process.
The prime factors of a number are a sort of collective property of the system of that number and all the numbers smaller than it. There’s a mathematical pattern to the system (having to do with a periodic pattern in the remainder when you do certain division operations; see this explanation from Scott Aaronson for more detail) that you can explore by putting together the right number of qubits and letting the waves explore the whole range of possibilities. There’s a quantum algorithm, a specially designed set of operations that you do on this system, that’s engineered to cause those waves to evolve from a state that’s spread over the whole system to one that entangles all those qubit superpositions in a way that gives a high probability that measuring the state will give one of the two prime factors as the output.
Factoring is the biggest of the big-money applications, because some modern(ish) cryptographic systems rely on factoring being a hard problem to secure their encoding against brute-force hacking. A quantum computer could speed that process up enormously, and as a result spies and bankers care very deeply about whether it’s possible to make a quantum computer that can factor big numbers, and are willing to throw flipping great wodges of cash at the problem. There are other algorithms useful for computation, though, which also involve these sorts of collective properties of the system as a whole– the next most important is a kind of array search, to find a particular element within an unsorted collection of data.
There’s another category of problems, though, for which qubits are more useful than classical bits, and that has to do with the simulation of quantum systems. The classic example of this is an array of spins that can be either spin-up or spin-down, whose energy depends on the interactions between neighboring spins. Classically, you would expect this to require something like one bit per spin: call it 0 if the spin is down, 1 if the spin is up, and you’re done.
Cartoon of the resources required to simulate quantum spinsCHAD ORZEL
If the spins are quantum particles, though, the resources required for this sort of computation simply explode. For one thing, each spin can now be in a superposition of |up> and |down> at the same time, so you need extra bits to cover both parts of that. And there’s also the possibility of entanglement between spins, so you need additional bits to keep track of the correlations between the state of any given spin and the states of all the rest of the spins in the system. The resources needed to keep track of these quantum states and correlations grow exponentially, and for a relatively modest number of spins– somewhere between 50 and 100– become too great to handle with any practical classical computer.
If you replace classical bits with qubits, though, you go back to only needing one per spin in the system, because all the quantum stuff comes along for free. You don’t need extra bits to track the superposition, because the qubits themselves can be in superposition states. And you don’t need extra bits to track the entanglement, because the qubits themselves can be entangled with other qubits. A not-too-big quantum computer– again, 50-100 qubits– can efficiently solve problems that are simply impossible for a classical computer.
These sorts of problems pop up in useful contexts, such as the study of magnetic materials, whose magnetic nature comes from adding together the quantum spins of lots of particles, or some types of superconductors. As a general matter, any time you’re trying to find the state of a large quantum system, the computational overhead needed to do it will be much less if you can map it onto a system of qubits than if you’re stuck using a classical computer.
So, there’s your view-from-30,000-feet look at what quantum computing is, and what it’s good for. A quantum computer is a device that exploits wave nature, superposition, and entanglement to do calculations involving collective mathematical properties or the simulation of quantum systems more efficiently than you can do with any classical computer. That’s why these are interesting systems to study, and why heavy hitters like Google, Microsoft, and IBM are starting to invest heavily in the field.
(Credit where due: I got the Necker cube analogy from an article by Chris Monroe and Dave Wineland in Scientific American quite a few years ago now; they may have gotten it from somewhere else, but I don’t know the source. The “collective properties of the system” description of what problems are suited to quantum algorithms from a talk by Shelby Kimmel. The good aspects of those are a credit to them; any errors in the presentation are undoubtedly my fault.)
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