Can Quantum Dots Compute?

4 August 2004--Researchers have long been trying to develop quantum computers based on the same semiconductor technologies that have so successfully powered conventional computers. Now, after years of exploration, two groups have begun to connect the dots--literally.

PHOTO: ALBERT CHANG, DUKE UNIVERSITY

CONNECTING THE DOTS

A scanning electron microscope photo shows a piece of gallium arsenide, viewed from above, with metal electrodes on top. Negative voltages applied to the electrodes repel the electrons underneath. The pattern of the electrodes cause two tiny puddles of electrons (quantum dots) to form, side by side, in the center of the image, where the electrodes meet

The dots in this case are quantum dots. They are nanoscale structures built within semiconducting materials that hold tiny puddles of electrons, which give each dot a collective quantum mechanical property called spin. The dots' spins, which can be either up or down, represent bits of quantum information, or qubits. Because quantum properties such as spin can exist in two states at once--being both up and down in the case of spin--computers using qubits can make many calculations simultaneously.

Separate groups of researchers at Duke University, in Durham, N.C., and at Harvard University, in Cambridge, Mass., have independently demonstrated how to connect quantum dots to form what may be the building blocks of a solid-state quantum computer.

The Duke and Harvard teams, which reported their work last April in the Physical Review Letters and Science , respectively, have shown how to make two quantum dots interact through the ghostly quantum connection known as entanglement. If two particles are entangled, when one is observed, fixing it into a particular state, the other is instantly fixed into a related state, regardless of how far apart the particles are. Einstein famously called it "spooky action at a distance." When the two quantum dots are entangled, the quantum states of their spins become inextricably linked to each other, an essential feature for quantum computations.

Peter Shor, a theorist who came up with a quantum computing algorithm for defeating encryption schemes, says the Duke and Harvard experiments are "very promising early steps." But he cautions that to build a quantum computer, it will be necessary to have a large number of these dots working together in a reliable way. "To give an analogy, this is like the first operation of a transistor," says Shor, a mathematics professor at the Massachusetts Institute of Technology, in Cambridge. "To get a quantum computer, we need to put many of these together and perform [calculations] reasonably fast and reasonably reliably."

In the past several years, other groups have built quantum computer prototypes using molecules in solutions or ions trapped by lasers and electric fields that were capable of performing simple, yet remarkable, quantum computations. But these prototypes, which required roomfuls of lasers, magnets, and other equipment, were limited in the number of qubits they could handle. They were also sensitive to interference from the environment, such as stray photons, that could disrupt the spins and introduce errors in the calculations.

Semiconductor technology could offer a better way. Because it can integrate a huge number of components in small areas, semiconductor-based quantum computers may be both more scalable and reliable. The Duke and Harvard researchers say these machines could start to fulfill the promise of quantum computers--machines that, among other things, would be able to factorize very large numbers. It's a feat that could make most cryptography systems useless, due to their dependence on the difficulty of such calculation.

The group at Duke, led by physics professor Albert Chang , began by growing a layer of aluminum gallium arsenide on top of a layer of gallium arsenide, a semiconducting material with highly mobile electrons that is used in many telecommunications systems. The resulting structure forced the material's free electrons to gather together at the interface of the two layers, forming a thin two-dimensional electron sheet.

The researchers then applied negative voltages to metal electrodes placed onto the top layer [see photo, "Connecting the Dots"]. The electrodes repelled the electrons underneath, creating a void in the electron sheet but leaving two tiny puddles of electrons, side by side, in the middle. These puddles--the quantum dots--are each about 200 nanometers in diameter and are just a few hundred nanometers apart.

Initially, both dots contained an even number of electrons. As if they were filling in the orbitals of an atom, the electrons in each dot automatically paired up to form spin-up-spin-down combinations. The researchers then injected a single extra electron into each dot.

Next, the researchers decreased the negative voltages applied to electrodes that were repelling electrons in the space separating the two dots. This caused the dots to be able to sense each other more strongly, to the point that their spins became entangled. In other words, the two spins carried a conjoined quantum state: changing one spin would instantaneously affect the other.

"What we have achieved here is the first demonstration of controlled entanglement of two spins, with each spin in [a different] quantum dot," Chang says. The researchers know the spins are entangled by observing what's known as the Kondo effect. Injecting an electron into a quantum dot produces a sudden increase in the dots' conductance. It is the result of the unpaired electron attempting to pair its spin to those of electrons outside the dot, in the electron sheet nearby.

So, when Chang and his colleagues entangled the spins of the two dots, the Kondo effect disappeared, because the spins had formed a pair between themselves. The Kondo effect won't tell you whether the dot's spin is up or down, but Chang says his group is working on a way to perform single spin readout --crucial for quantum computing.

The group at Harvard, led by physics professor Charles Marcus, performed a similar experiment. Essentially, the only, but significant, difference is that the two dots are separated by a greater distance--1 micrometer instead of the tenths of micrometers in Chang's trial. In the Harvard setup, there are two separate voids in the electron sheet, each containing an electron puddle.

The Harvard team also observed that, when putting an odd number of electrons on the dots, the dots' net spins became entangled. But now the entanglement didn't occur directly; it took place through the electron sheet between the two dots. They observed that a dot's spin tried to pair up with spins of the electron sheet nearby, and this influence propagated until it reached the spin of the other dot. (This kind of spin propagation is known as the Ruderman-Kittel-Kasuya-Yosida interaction.)

"The whole point of our experiment is that you have two dots that are not next to each other, and still they're able to communicate," Marcus says, adding that this method can provide a means to connect the qubits akin to the wiring system of a conventional chip. "You got a bit here and a bit there, and you have to connect them," he says. "But now it's all more difficult, because it's spin information that you have to convey down the wires" instead of voltage. His group is now trying to entangle three dots to extend the connection system.

But not all experts agree that this interaction is robust enough for quantum computation. David DiVincenzo, a researcher at the IBM Thomas J. Watson Research Center in Yorktown Heights, N.Y., says it's not clear that either of the groups really produced entanglement. "Proving that you have entanglement requires a rather specific regimen of experiment, which I don't believe that they undertook," he says.

The main problem with the experiments, says DiVincenzo, is that they involved too many electrons. The groups coupled the spins through interactions that required several electrons in the dots and in the electron sheet, and such an approach may be too error prone. Instead, DiVincenzo says, quantum computation should be done through the interaction of individual particles, possibly with a single electron in the dots, rather than having electron puddles. Eventually, he says, researchers will find the right way to entangle the spins--and, hopefully, connect the dots.