# Tiny 'big bang' performs quantum computations

FAYETTEVILLE, Ark. — Using a computer model that "explodes" a single particle into an infinite regress of quantum waves, University of Arkansas physics professor William Harter has demonstrated a new approach to quantum computation.

"Our model reveals a fractal interference pattern emerging from quantum waves — after what we are calling a tiny big bang — that can perform useful calculations, such as calculating all the prime factors of any size integer," said Harter.

Harter has a history of staying one step ahead of the basic research community with his detailed computer simulations, dating back to his internship at Los Alamos National Laboratories. While there in 1986, he predicted the possibility of melding 60 carbon atoms into tiny geodesic spheres, which were not discovered experimentally until a decade later.

In his current simulations, Harter is modeling nothing less than the "big bang" that, according to theory, created our universe. In the beginning, big-bang theorists say, all the matter in the universe was squeezed into a uniform "singularity" that exploded. The resulting big bang spewed out the stars and planets according to an intricate fractal pattern that Harter is now reproducing.

"We call it a tiny big bang, because of the analogous fractal interference pattern, but my simulations are of the symmetries and dynamics of wave nodes and the principles behind recently discovered dephasing and rephasing phenomena known as revivals. Using one of the earliest quantum wave models, the Bohr rotor, we have seen a quasifractal structure related to chaotic circle maps that behave like quantum odometers, performing arithmetic operations on rational fractions. Devices built to realize these revivals may have applications in optical information technology and quantum computing," Harter said.

The principle can be applied to any quantum mechanism, Harter said. His research group investigates photons, but the principle can apply equally well to electrons. When orbiting an atom, an electron occupies an ascending hierarchy of quantum energy states, which can be thought of as higher and higher orbits. The lowest energy state — lowest orbit — can be thought of as analogous to the fundamental frequency of a plucked string.

The effect can be "frozen" for a plucked string with some kind of technical assistance like a strobe light, but an orbiting electron is occupying "all" of the various energy states simultaneously. If you pump the electron, say by hitting it with a laser, you can force it to simultaneously occupy more and more of these ascending energy states. However, instead of the electron orbits getting equally further and further away from the atom with each added energy state, they "crowd up" against the "escape velocity" or highest possible orbit, requiring more and more energy input to get less and less far away from the atom.

Harter's unique discovery is simply that if all the stored energy is released in a "pop," a microscopic big bang occurs. Plotting the electron's location after the big bang results in a blur of uncertainty due to the Heisenberg law, but a plot of where the electron is not located produces a fractal interference pattern that appears to perform useful calculations.

"Other researchers will say that I'm crazy — like they did when I predicted bucky balls. They'll say you can't get a fractal pattern this way, but that's because they are thinking of where the particle is. They've never looked where the particle isn't," said Harter.

Harter's plots are strikingly beautiful, as are many fractals, but they also encode patterns that appear to be the prime factors of the highest energy state. "When you take the particle up to the 15th energy state, for instance, the prime factor of three and five are readily apparent everywhere in the fractal — and there is no theoretical limit [to] how big an integer you can factor this way," said Harter.

Harter's approach to quantum computation has two principal advantages: first, the calculations result automatically and instantaneously regardless of integer size; second, the fractal pattern is repeated over and over for easy readout. "Most of the other approaches to quantum computers have to rely on very small and error-prone effects that are very difficult to observe — but these fractal patterns are obvious and redundant in and of themselves," said Harter.

His simulations of the quantum computations are independent of any particular physical mechanism for realizing them — for example, an orbiting electron was used for its ease of understanding. In fact, since Harter's research group concentrates on light, his next step will be to attempt to realize the effect in the lab with photons instead of electrons.

Harter also predicts that it may take a decade or more to achieve a sufficient understanding of the microscopic big-bang effect, before working quantum computers can be built based on it — similar to the decade it took to actually manufacture real bucky balls from his simulated results.