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By virtue of being friends with the girlfriend of one of the organizers (HugMe) and knowing slightly more than the average idiot on the street about physics, I reluctantly gave a panel in 2000: Particle Physics 101. Maybe eventually I'll reconstruct what I said, but not just yet. You could probably get the same thing from a single chapter in any introductory Modern Physics book, but seeing how those cost around $80 and I'm free, maybe someone would find such a page useful.
I spent most of AtlantaCon 2001 with my hands in a pile of PlayDoh, but for a short time I was out in the panel room talking about
Hello, I'm Melon, and I'm going to tell you what little I know about quantum computers. I'll give you some references on the links page so you can find out more if you want. This speech will have two general parts: What quantum computers can do, and What they are made out of.
But first off... What the hell is a quantum computer?
There are many ways to construct a quantum computer. Most of them result in a machine that is much larger than a convention computer. What makes a computer quantum is that it can take advantage of the weird physics that occurs between individual particles. We call bits in a quantum computer qubits. This quantum physics is really weird. Some of the weirdness we have analogies for that make it easier to discuss and explain the phenomenon, and others are much more difficult to explain or even have a fraction of understanding for. Two of the major aspects that quantum computer use are superposition and entanglement.
First, though, a question that nags most people when they hear about this "new" kind of physics: why don't we see the weirdness in every day life? In a way, we do. That weirdness is responsible for a lot of the "normal" phenomenon we experience. For example, the basic structure of an atom is not stable unless we apply quantum physics! In another example, from our point of view, polarized sunglasses filter out some of the intensity of sunlight. From a quantum point of view, the polarized filter forces photons that were in a superposition state to choose a definite state, and there is a set probability that a photon will choose a definite state that allows it to pass through the filter; if it chooses any other state, it doesn't pass through, thereby lessening the number of photons that hit our eye. Another thing to think about is gravity. Just about everything we experience involves gravity, and gravity has no quantum aspect that we know about. Many physicists wish it did, it would make it much easier for them to create an all-encompasing Theory Of Everything (TOE). Anyway, gravity is the weakest of the four fundamental forces, but it has the longest reach. So, even though the other forces (strong, weak, electromagnetic) are much stronger, on the macroscopic (human-size) level, they pale in comparision to gravity. Thus, the weirdness never has a chance--it's overcome by the normality of gravity. (Maybe this explanation is a little too convenient for you, just use it to get over your initial misgivings once I start talking about entanglement and such.)
One of the aspects of quantum physics is superposition. Superposition can apply to any observable: energy, position, magnetic moment, whatever. Most bound systems (an electron bound to an atom) have a discrete (enumerated) set of values for their observables. That system is in a superposition (or an indefinite) state when an observable has more than one value at once. We cannot calculate or measure superposition states. Our equations involve probabilities only, and measurements force the quantum particle into a definite state. No one really knows why this is. There are lots of theories, such as parallel universes.
Stop thinking about how weird it is. Instead, just think of ways to make use of this. Superposition: putting a particle into two definite states at once. What if one of these states we label as 1, and the other as 0. Superposition: setting a bit to both zero and one at once. Imagine the data compression! That bit is literally both zero and one. If you have 8 bits, all in superposition states, the values 0 through 255 are represented there. Any operation performed acts on all values at once. It would be like having multiple coprocessors. Of course, reading out the answer poses some difficulties. How can you tell which answer matches with which starting value? There's a hideous amount of math that helps with this (Fourier transforms galore).
Clearly, the idea above would be exceedingly useful when we have to do identical calculations on a massive amount of numbers (finding primes, factoring large numbers). However, it would not be useful for calcuations that require a lot of decision making--if/then type statements. If you have to discriminate during processing between different values, you probably don't want to use a quantum computer, because you wouldn't be able to make use of superposition.
There's another reason why discriminating between values during processing would be difficult with a quantum computer. A little problem called decoherence. Particles that are all "in-step" with each other, such as the photons of a laser, are said to be coherent. Particles that have nothing in common are called incoherent. When a quantum particle was in a carefully built superposition state and then sudden collapses to a definite state, losing all the information in that superposition state, that's decoherence. It's a nasty problem. A stray photon can cause the superposition waveform to collapse (decohere) can cause the same damage a strong magentic field would to a hard drive.
Just how annoying is it? Here's a table from the book Minds, Machines, and the Multiverse by Julian Brown:
|Switching Time||Decoherence Time||Figure of Merit||Scalability|
|Ion Traps||10-7||10-1||106||50 qubits ?|
|Cavity QED||10-14||10-5||109||2 - 5 qubits|
|NMR||10-3||104||107||10 - 50 qubits|
|Quantum Dots||10-9||10-6||103||1000 qubits|
I'll talk about the 4 types of quantum computers above in a few minutes. To explain the table entries: Switching time is the amount of time it takes for each process, almost like the inverse of processing speed. Decoherence time is the lifetime of the quantum bits (or qubits). Figure of merit is a ratio of the first two numbers, so even if a technology has a slow switching time, as long as it has a long decoherence time it can still be useful. Scalability is the theorized limit to the number of qubits that an individual quantum computer could have; technologies with few qubits would only be useful if they had a very large figure of merit or were chained together somehow. Technologies with really large numbers could compensate for a small figure of merit.
So, decoherence can be a big problem. Why does it happen? Aside from accidental measurement, entanglement can lead to decoherence. Entanglement is another of the weird quantum phenomena. When two particles are entangled, when one is affected, the other instantaneously feels those effects as well. So if a qubit becomes entangled with some of the particles in the surrounding equipment, which are not protected as the qubits themselves are, the qubit can be subject to decoherence.
Entanglement is a big problem for decoherence time, but useful in other ways. It can actually be used in qubit error correcting schemes in a somewhat baffling procedure called "entanglement transfer" where a processing qubit passes its entanglements on to an error correcting qubit. Unfortunately, this method requires having spare qubits that aren't involved in processing. Entanglement also has applications in quantum communication and is used in quantum cryptology schemes.
You might be wondering just how to entangle two particles. I know that question distracted me through a lot of my readings. I finally came to the realization that the reason I wasn't finding examples of how to entangle particles is because it is so easy. So easy that we have to worry about qubits accidentally becoming entangled. Two particles just look at each other funny and they're entangled. They're like teenagers.
Part II: What are Quantum Computers Made Out Of?
First off, the key to any quantum computer is to think up a method for having a conditional operation (if/then); specifically, something that acts like a controlled-NOT logic gate. Smart people who play with electronics have shown that any circuit can be represented as a series of controlled-NOT (sometimes known as XOR) gates. Another key to quantum computing is that all operations have to be reversible, because everything in quantum physics is invertible (aka reversible). Fortunately, the controlled-NOT is also reversible.
NMR stands for Nuclear Magnetic Resonance. This is the same technology used in MRI, or Magnetic Resonance Imaging, which has been used for years in the medical field. Physically, the experimental models have looked somewhat like a toaster. A test tube of liquid is placed between large magnets. The liquid is built to take advantage of the magnetic field many atomic nuclei possess. We could consider each atom in the liquid's molecule as a qubit, although there are usually a few atoms that are just there to keep everything stable. So, even though you have thousands of molecules in the test tube, the number of processing bits depends on the number of atoms making up the molecules. This makes for a lot of redunancy, reducing the impact of decoherence. The relatively fast switching time gives NMR a high figure of merit. Woo! However, we're limited in the size of molecules we can build and still easily distinguish between the behavior of individual atoms within the molecule.
How do we establish the conditional statement with NMR? The nucleus of many atoms has a magnetic moment just like the Earth has a magnetic pole. It's actually different, but otherwise just like that. The 1 and 0 would be different orientations of the magnetic pole. By setting up different kinds of external magnetic fields with our MRI-type machine, we can make the tiny magnetic poles of the atomic nuclei dance according to our will. And since the magnetic field of one atom will influence that of another, we can set up a conditional statement. Computers of 2 and 5 qubits have been made using this technology. The experiment using 2 qubits broke a combination lock of 4 possibilities in one computation.
Ion trapping is hard to do. Create an electric potential well with some electrodes. Put a bit of metal into near-vacuum. Heat it to around 800 degrees Celsius, causing it to vaporize. Fire a laser at the vapor, stripping some electrons--making ions. The ions, being charged particles, will be trapped by the electrodes. Hopefully you only have one ion in each trap; if not, nudge out the overcrowding ones. The ion does not want to be trapped. It has a lot of kinetic energy, and is vibrating like crazy. We want to carefully control the energy of the ion, switching between two low-level states. This is hard to do when the ion already has a lot of energy. So we need to calm the ion down. We do this with a laser.
Laser cooling is pretty nifty. Atoms will absorb photons that are at the atom's "happy" or resonant freqency. When an atom and a photon are moving towards each other and the atom absorbs the photon, there's a recoil effect on the atom, slowing it down. When an atom and photon are moving in the same direction and the atom absorbs the photon, the atom speeds up. So, we want our ions to absorb photons from our laser only when the ion is moving towards the laser. This isn't as hard as it sounds. It takes advantage of the Doppler Effect: if you move towards or away from a wave-emitted source, or if it moves towards or away from you, the Doppler Effect is present. This is what makes cars and planes racing by have that Neeerrrroooong sound. When the wave-emitting source is moving towards you the observer, wavelenths appear shorter and frequency higher; vice versa when the wave source is moving away. If we tune the laser to a frequency slightly below that of the ion's resonant frequency, the Doppler effect will make the laser photons appear to be at the resonant frequency only when the ion is moving towards the laser. Otherwise, the photons will appear to be even further from the happy frequency.
Okay, so the ions are cooled. Now you switch them from one energy level (one) to another (zero), or to a superposition state with a laser. Decoherence times here are shorter than NMR technology's, but not unbearable (hard to imagine calling one tenth of a second good endurance time). The switching time is also pretty fast, making its Figure of Merit one order of magnitude smaller than NMR's. The number of possible qubits is comparable as well. However, set up is so much more painful, most experimentalists prefer to work with NMR.
Quantum Dots sound like very useful things. They are essentially very small superconductors. Conventional computers could be built with them as well, making wireless circuits that would use only a few electrons per dot and so would not get very hot. To make use of their quantum aspects, we would have to use lasers to stimulate the single electron in each dot. We would switch between energy levels much like with trapped ions.
Quantum dots have very bad decoherence times because of imperfections in the material. This is okay if there are multiple electrons, as there would be in a conventional circuit with quantum dots. But a quantum computer would only use one electron which we can't let wander off. Quantum dots have other uses, such as tagging microscopic material and then glowing under special lighting: www.qdot.org.
The fourth major avenue of research is in Quantum Electrodynamics Cavities (aka QED cavities). These use photons as the qubits, which is interesting because photons don't normally interact (so how do we make a conditional if/then statement). The ones and zeros of photons come from their polarizations. A photon of vertical polarization will act slightly differently than one at an angle (quick reminder--the superposition of vertical and horizontal polarizations does not equal 45 degrees, though it may be drawn that way. It is literally both polarizations at once). There is an ion inside the QED cavity that the photons interact with, a kind of middle man to create the if/then statement.
The "cavity" of QED cavity is a very small box to bounce the photons around inside. This cavity is specially designed in the same way organ pipes are specially designed to make standing waves (where even though the wave is still moving, it looks like it's stationary because of the way the reflected peaks and troughs line up with the incident peaks and troughs).
Decoherence times here are very short. Photons escape unexpectedly or become entangled with the cavity itself. However, their switching time is even faster, so this could still be a useful technology. Scientists see little hope for creating large amounts of qubits, though. Too difficult to keep track of dozens of individual photons.
One reason why QED could be very, very interesting is a recent experiment that managed to store light for a brief period of time.
This is pretty much the end of my "organized" speech. Now I'm going to babble a moment about the recent work in slowing, stopping, and speeding up light.
Firstly, it's easy to slow light down. The constant c is related to the speed of light in a vacuum. Speed of light not in a vacuum is nothing like a constant. Light is faster through air than it is through water than it is through a steel sheet. It's not even all that hard to stop light, or at least individual photons--atoms absorb and emit photons all the time. The reason the experiment stopping light was so interesting was because they managed to start it up again, with much of the information still intact.
The experiments speeding up light are usually just tricks with waves. All waveforms have two speeds: the phase speed and the group speed. The phase speed is determined by the time it takes for two successive crests of a single wave to pass a specified point. The group speed is related to a wave pulse made up of several individual waves, all with (probably) different phase speeds. Sometimes the pulse will go faster than most of the individual waves, sometimes slower, depending on how the individual peaks add up. In this experiment, they just made the peak go faster than c for a brief moment.