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 twoqubit 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 lowenergy state. An ion is in its lowenergy 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 demonstrationofprinciple experiments and
experimental demonstration of some special advantages of geometric quantum
computation [could happen] quite soon," he said.
Duan's research colleagues were JuanIgnacio 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
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July
25, 2001
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Sounds attract camera
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Quantum logic counts
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