Building 'The Matrix'

By Davide Castelvecchi

Simulating the complexity of quantum physics would quickly overwhelm even the most advanced of today’s computers.

If The Matrix really existed, it would probably have to be a quantum simulator. The fictional computer in that story can create virtual worlds indistinguishable from the real one and project them into people’s minds. But the real world includes quantum phenomena, something ordinary computers can’t fully simulate.

Now physicists have created a rudimentary prototype of a machine that simulates quantum phenomena using quantum physics, rather than using data kept in a classical computer. While the new device can't make people fly like the Matrix does, it demonstrates a technique that could enable physicists to create, in the virtual world, materials that don't yet exist in nature and perhaps figure out how to build, in the real world, superconductors that work at room temperature, for example.

Tobias Schätz of the Max Planck Institute for Quantum Optics in Garching, Germany and his collaborators built a model of the smallest solid object imaginable — one made of two atoms — by suspending two ions in a vacuum. The researchers used laser light to vary the electrical repulsion of the ions in order to simulate the magnetic interaction of atoms. Essentially, the machine could use one force of nature to simulate the other.

In a paper published online by Nature Physics on July 27, the researchers describe how their system reproduced the magnetic alignment of atoms that takes place when certain materials are exposed to magnetic fields.

“This is pretty important that they’ve been able to demonstrate the principle,” says John Chiaverini of the Los Alamos National Laboratory in New Mexico.

“I feel the experiment is an important initial step in the emerging field of quantum simulation,” says David Wineland of the National Institute of Standards and Technology in Boulder, Colo., whose group in 2002 pioneered a more limited quantum simulation technique by trapping single ions. The new experiment “demonstrates important tools that can potentially be implemented on much larger systems whose simulations are intractable by classical means,” he says.

It was the late physicist Richard Feynman who pointed out in 1982 that ordinary computers can’t possibly simulate true quantum behavior of a large number of particles. That’s because of the phenomenon of superposition, which allows a particle to be in two states at the same time. For example, the spin of an atom — the quantum version of a bar magnet — can point simultaneously up and down.

Feynman reasoned that to simulate, say, the spin states of an object made of two atoms, a computer has to keep track of four possible combinations of spins: up-up, up-down, down-up, and down-down. For three atoms, eight possibilities exist, and the number keeps growing exponentially. For n atoms, the number is 2ⁿ, which gets very large very quickly. “This 2ⁿ — that’s what kills classical computers,” says Schätz.

Chiaverini says even state-of-the-art supercomputers quickly get overwhelmed with all the calculations required to predict how all those spin states will evolve in time. “You run out of steam at about 40 spins,” he says.

And simulating the spin of just one additional atom would be more than one step more difficult. Although computer power has been doubling every two years or so, simulating that extra atom would require a machine with twice the power. So even waiting 100 years won’t help much. If you need to simulate 300 particles, you need to keep track of 2³⁰⁰ different combinations of spins,

Schätz says. “That’s more than the number of protons in the visible universe.”

A system of quantum objects, on the other hand, is itself able to exist in a number of different states that grows exponentially. Several different teams of physicists are developing techniques for quantum simulation. The two leading approaches are to use ions in an electrostatic trap, as Schätz and colleagues have done, or to use atoms in an optical trap, which holds things into place using the pressure of light.

Last year, David Weiss of Pennsylvania State University in University Park and his colleagues demonstrated an optical trap able to hold hundreds of atoms in a cubical array, image and manipulate the atoms individually, and make them interact with one another. The researchers even took videos of glowing atoms staying in place or, occasionally, jumping from site to site along the array. “It took a couple of days until I could get my graduate student and my postdoc to stop taking pictures and actually start the experiment,” Weiss said at a meeting of the American Physical Society last March in New Orleans.

Each approach may eventually prove useful for particular simulations, researchers say.

The trapped-ion approach Schätz’s team followed was first proposed by his Garching colleagues Diego Porras and Ignacio Cirac in 2004. In the experiment, the team suspended two magnesium ions in a vacuum, keeping them in place with electrostatic fields. The positive ions were just a few microns apart — close enough to feel mutual electrostatic repulsion, but far enough that they would not feel each other’s (real) spins.

The researchers then used a laser to simulate the application of an external magnetic field, which could give the ions any initial state. “It’s much better than a real magnetic field, because, for example, you can individually address your atoms. It would be hard to have a real magnetic field ‘on’ on one atom, and ‘off’ on the other.” Schätz says.

Using the laser, the researchers were also able to tune the electrostatic interaction of the two particles. In future, more complex experiments, researchers could for example create a model of a superconductor and then selectively change the physical parameters to understand how the material is able to conduct electricity with minimal loss of energy.

Such control would be impossible in a real solid material, such as a superconducting crystal. “If you tell a solid-state physicist, ‘reduce your spin-spin interaction by a factor of two because I want to see the physics,’ he can’t do it,” Schätz says.

Together with his colleague Warren Lybarger Jr. and others, Chiaverini is working on a similar setup, also based on Cirac and Porras’ idea. At the same time, the team is also developing an alternative approach that would use radio frequency, or RF, fields, instead of lasers, to manipulate the states of the ions.

Two ions, of course, don’t make a real solid object, but researchers say that in the future they may be able to scale up the Garching device to larger arrays of ions. Currently, researchers who want to experiment with new materials, such as superconductors, have to first create actual crystals in the lab and then test their properties. Quantum simulations could make that task a lot easier. “Some day, hopefully, we can apply this to making designer materials from the ground up,” Chiaverini says.

Eventually, Feynman envisioned, a general purpose, programmable quantum computer could itself carry out quantum simulations. But such machines are still decades away, most researchers say, while machines designed only for quantum simulations may become available sooner.

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