Quantum logic counts on geometry

By Eric Smalley, Technology Research News

Imagine you are holding a beach ball in one hand and a doll in the other. Place the doll on its back on top of the ball and slide it feet first half way down the side of the ball, then slide it sideways halfway around the ball, and then slide it head first back to the top. Notice that even though you kept the doll straight, the doll's head and feet are reversed from their original orientation.

You have just demonstrated a basic principle of spheres. If you consider the doll's head 1 and the doll's feet 0, you have also computed. You have performed a NOT gate, which is a logic operation that flips a bit from a 0 to a 1 or a 1 to a 0.

This idea of computing by geometry is at the heart of a proposed scheme for quantum computing that could yield prototype systems that are sturdier and easier to control than experimental computers based on previous schemes, which involve manipulating the energy levels of particles.

Quantum computers could solve certain types of very large problems almost instantaneously because quantum bits, or qubits, can represent every possible solution to a problem and quantum computers can check every possibility in relatively few steps. Ordinary computers have to check each possibility one at a time.

Researchers at the University of Innsbruck have devised a scheme for quantum computing that builds all the necessary binary logic operations from one- and two-qubit geometric operations.

The scheme is designed for trapped ions, but it can be generalized to other quantum computer hardware, said Luming Duan, a researcher at the University of Innsbruck and an associate professor of physics at the University of Science and Technology in China.

An ion is an atom that has an electric charge because it has gained or lost one or more electrons. An ion trap is a device that uses magnetic fields to hold an ion in one position so that researchers can focus laser beams and/or radio waves on it.

In geometric quantum computing, the ion doesn't move through physical space but through a virtual space determined by the range of possible changes to the subtle interactions between the ion's nucleus and its electrons.

Electrons occupy regions, or orbitals, around the nucleus. These orbitals exist only at certain distances from the nucleus, but the magnetic interactions between the nucleus and electrons cause slight variations, termed hyperfine levels, in these orbitals. The parameters of an ion's hyperfine levels form a mathematical space that, like a real space, can be described using geometry.

Quantum bits perform geometric computations by walking through parameter space, said Duan. These transformations, which compose all the quantum computation tasks, "result from nontrivial geometric structures, such as curves, of this... space."

Using the scheme, the 1 and 0 of a bit could be encoded as two hyperfine levels of an ion's low-energy state. An ion is in its low-energy state when its electrons are in the lowest orbitals. Computing would be performed by firing a series of laser pulses at the trapped ion. The wavelength and polarization of the lasers would be tuned to subtly alter the relationship between the ion's nucleus and its electrons, resulting in one of the two hyperfine levels.

The transformations in most other quantum computing schemes are dynamic, meaning they shift particles from one energy state to another. In some cases this makes the information the particles hold more susceptible to interactions with the environment, said Duan. When particles interact with the environment they are knocked out of their quantum state, which destroys the bits encoded in the particles' quantum attributes.

Many researchers say it will be at least 20 years before quantum computers that outperform classical computers can be developed. The geometric quantum computing scheme is not likely to accelerate this timeframe, said Duan.

However, "some interesting demonstration-of-principle experiments and experimental demonstration of some special advantages of geometric quantum computation [could happen] quite soon," he said.

Duan's research colleagues were Juan-Ignacio Cirac and Peter Zoller of the University of Innsbruck. They published the research in the June 1, 2001 issue of the journal Science. The research was funded by the Austrian Science Foundation, the European Union, the European Science Foundation and the Chinese Science Foundation.

Timeline:   20 years
Funding:   Government
TRN Categories:   Quantum Computing
Story Type:   News
Related Elements:  Technical paper, " Geometric Manipulation of Trapped Ions for Quantum Computation," Science, June 1, 2001


July 25, 2001

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Quantum logic counts on geometry

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