# Quantum Computing Candidates: Ion Traps

Some time back, I wrote about what you need to make a quantum computer. Given that it’s election season, I thought I’d revisit the topic by looking in detail at the candidate technologies for quantum computing.

The first up is Ion Trap Quantum Computing, probably the most well-established of any of the candidates. The field really starts with Dave Wineland’s group at NIST, though there is outstanding stuff being done by Chris Monroe at Maryland, and a host of others.

So, how do they stack up? Here are the facts about ion traps as a quantum computing system:

What’s the system? Ion traps are, as the name suggests, devices for trapping atoms that have lost one or more electrons. They use the fact that these ions interact very strongly with electric fields to confine them to small volumes using high-voltage electrodes.

Once they’re stuck in the trap, the ions can be cooled to very low temperatures using laser cooling. Laser cooling was actually first demonstrated with ions, by the Wineland group– cooling of neutral atoms came later.

What’s the qubit? The two states needed for computation (“0” and “1”) are two energy levels of the ion. Generally, these are two hyperfine levels of the ground state. These states are generally separated by a small amount of energy, and thus have extremely long lifetimes, long enough that you don’t need to worry about one spontaneously decaying to the other. The exact choice of states is different for different experiments.

How do you manipulate the qubits? In order to do quantum computation, you need to be able to manipulate the states of individual ions. This is done by hitting them with lasers tuned to drive transitions between states. Generally, this is done via “Raman transitions,” which use two lasers with very slightly different frequencies to make a coherent two-photon transition between states. The basic idea is that one photon excites the ion to a high energy state (much higher than either the “0” or “1” states), while the second causes stimulated emission back down into the other of the two computation states. This isn’t quite right– the atoms is never actually in the upper state– but it gets the idea.

You can use this Raman technique to do any excitation you want. You can take an ion in “0” and move it to “1,” you can take an ion in “1” and move it to “0,” or you can take an ion in either “0” or “1” and move it into an arbitrary superposition of “0” and “1” at the same time. It’s all a matter of timing– by leaving the lasers on for different amounts of time, you make different states.

How do you entangle the qubits? The ion trap system offers a novel method for entangling separated bits. In addition to the quantized internal states of the ions, the traps allow collective modes. If you have two or more ions in a trap, they can be sloshing back and forth in the trap in a couple of different ways. This motion is also quantized.

So, if you want to entangle two bits– say, the first one, and the fourth– you can do it using the collective motion as a “data bus.” You do an operation that puts the collective motion into a state that depends on the state of the first bit– not moving if the state is “0,” moving if the state is “1.” Then you do an operation on the fourth bit that depends on the state of the motion– flip the bit if the ions are moving, or leave it alone if they’re not. Then you stop the collective motion.

You now have a system in which the state of the fourth ion depends on the state of the first ion. If the fourth ion started as a “0,” it’s a “1” if the first bit was a “1” and a “0” if the first bit was a “0.” And if the first bit was in a superposition of “0” and “1,” the fourth bit is now in a superposition of “0” and “1,” entangled with the state of the first bit.

This lets you do all the operations you need to do to make a quantum computer.

How do you read the result out? You can detect the state of an individual bit by illuminating it with a laser tuned to a “cycling transition,” which drives the ion back and forth between two energy states, absorbing and emitting lots of photons. If you tune your laser correctly, ions in “0” will absorb photons from the laser, and then re-emit them, while ions in “1” will do nothing. If you look at the trapped ions with a sensitive CCD camera, you’ll see bright spots at the positions of ions in “0” and nothing at the position of ions in “1.” That lets you read out the values of all the ions in the trap.

Does it scale? Yes and no. It’s possible to put multiple atoms in a single trap, but not enough of them to do useful computations (“useful” here meaning things like “factoring products of 100-digit prime numbers”). It’s also possible to build arrays of lots of little traps, and shuttle ions back and forth between computation and storage regions– Chris Monroe’s group has done some really excellent work in this area.

It’s hard work, but it looks like it’s at least in principle possible to build a large quantum computer using ion traps.

What about decoherence? One of the problems plaguing quantum computation is “decoherence,” a term referring to random interactions with the environment that destroy fragile quantum superposition states, and wreck the operation of the computer. In the ion trap system, the main source of decoherence is heating of the ions in the trap– if you cool all the ions in a trap down to the not-moving state, and hold them for a while, after some time, they start moving. Since this motion is your “data bus,” this is a killer.

Finding the source of this heating has been a long and tedious process. As I understand it, the current thinking is that it’s due to random areas of extra charge on the electrodes making up the trap, which push the ions in different directions.

A lot of hard work has gone into nailing this problem down, and it looks like they finally have a handle on it. The last decoherence rates I remember seeing were still a little too high to do practical quantum computing, but they’ve made great strides, and the future looks promising.

Summary: As I said at the beginning of this, ion traps are the most established of the candidate technologies, and probably the farthest along by most measures. The Wineland group in particular has been working on this stuff for better than twenty years, and they’ve got a lot of the bugs worked out, or at least identified.

They’re not ready to make an ion-based quantum computer yet, and the complexity needed for a large system might mean that it never will be the basis for a practical computer. Ion traps are the best test and demonstration system we have at the moment, and they’re likely to remain so for the forseeable future.

If they were running for President, they would be: Joe Biden. They’ve been around forever, and are a central part of the quantum computing establishment. They may not be the most exciting candidate out there, but nobody doubts that they could get the job done.

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