### Proving quantum computers feasible

##### November 27, 2012

A group of researchers at MIT, IBM, Masaryk University in the Czech Republic, the Slovak Academy of Sciences and Northeastern University proved that even in simple spin chains, the degree of entanglement scales with the length of the chain.

The research thus offers strong evidence that relatively simple quantum systems could offer considerable computational resources.

Quantum computers are devices — still largely theoretical — that could perform certain types of computations much faster than classical computers; one way they might do that is by exploiting “spin,” a property of tiny particles of matter. A “spin chain,” in turn, is a standard model that physicists use to describe systems of quantum particles, including some that could be the basis for quantum computers.

Many quantum algorithms require that particles’ spins be “entangled,” meaning that they’re all dependent on each other. The more entanglement a physical system offers, the greater its computational power. Until now, theoreticians have demonstrated the possibility of high entanglement only in a very complex spin chain, which would be difficult to realize experimentally. In simpler systems, the degree of entanglement appeared to be capped: Beyond a certain point, adding more particles to the chain didn’t seem to increase the entanglement.

In quantum physics, the term “spin” describes the way that tiny particles of matter align in a magnetic field: A particle with spin up aligns in one direction, a particle with spin down in the opposite direction. But subjecting a particle to multiple fields at once can cause it to align in other directions, somewhere between up and down. In a complex enough system, a particle might have dozens of possible spin states.

A spin chain is just what it sounds like: a bunch of particles in a row, analyzed according to their spin. A spin chain whose particles have only two spin states exhibits no entanglement. But in the new paper, MIT professor of mathematics Peter Shor, his former student Ramis Movassagh, who is now an instructor at Northeastern, and their colleagues showed that unbounded entanglement is possible in chains of particles with only three spin states — up, down and none. Systems of such particles should, in principle, be much easier to build than those whose particles have more spin states.

**Tangled up**

The phenomenon of entanglement is related to the central mystery of quantum physics: the ability of a single particle to be in multiple mutually exclusive states at once. Electrons, photons and other fundamental particles can, in some sense, be in more than one place at the same time. Similarly, they can have more than one spin at once. If you try to measure the location, spin or some other quantum property of a particle, however, you’ll get a definite answer: The particle will snap into just one of its possible states.

If two particles are entangled, then performing a measurement on one tells you something about the other. For instance, if you measure the spin of an electron orbiting a helium atom, and its spin is up, the spin of the other electron in the same orbit must be down, and vice versa. For a chain of particles to be useful for quantum computing, all of their spins need to be entangled. If, at some point, adding more particles to the chain ceases to increase entanglement, then it also ceases to increase computational capacity.

To show that entanglement increases without bound in chains of three-spin particles, the researchers proved that any such chain with a net energy of zero could be converted into any other through a small number of energy-preserving substitutions. The proof is kind of like one of those puzzles where you have to convert one word into another of the same length, changing only one letter at a time.

“Energy preserving” just means that changing the spins of two adjacent particles doesn’t change their total energy. For instance, if two adjacent particles have spin up and spin down, they have the same energy as two adjacent particles with no spin. Similarly, swapping the spins of two adjacent particles leaves their energy the same. Here, the “puzzle” is to convert one spin chain into another using only these and a couple of other substitutions.

**No bottlenecks**

If you envision every set of definite spins for a chain of three-spin particles as a point in space, and draw lines only between those that that are interchangeable using energy-preserving substitutions, then you end up with a dense network, with the points on the edges as well connected as the points in the center.

“If you want to go from any state to another state, it has high conductivity,” Movassagh says. “It’s like, if you have a town with a bunch of alleys, and you want to go from any neighborhood to any other, you can only go rapidly if there’s no one road that’s necessary to use and congested.” To prove that, in systems of three-spin particles, transitions between sets of spin were possible through these “back alleys,” Movassagh says, “we proved something that we think is new in probability theory.”

“It’s been known that if the particles can have constant but rather high dimension” — that is, number of possible spin states — “the entanglement can be pretty high,” says Sandy Irani, a professor of computer science at the University of California at Irvine who specializes in quantum computation. “But the requirement is that these little particles have something like dimension 14, 15, 16. In terms of what people are actually looking at experimentally, they’re looking at very low-dimensional things. Having particles of dimension of 15, 16, is much more difficult to bring about in the lab.”

Shor, Movassagh and their colleagues, Irani says, “have shown that if you just step up from two to three, the entanglement can actually grow with the number of particles.”

Irani cautions, however, that the new paper shows only that entanglement scales logarithmically with the length of the spin chain. “If you go up to these larger-dimension particles, in the teens, you get entanglement that can scale with the number of particles instead of the log of the number of particles,” she says, “and that may be required for quantum computing.”

## Comments (12)

November 28, 2012by Pommodore 94

But D-Wave produces already quantum computer or?

http://www.dwavesys.com/en/dw_homepage.html

http://en.wikipedia.org/wiki/D-Wave_Systems

November 28, 2012by eldras

2022 as I understand ibm is when efficiencies are expected to be good enough to be effectively error free.

This is pretty much as Einstein predicted…tat laws would be found in the quantum world proving it was a different but still causal system.

Entanglement scaling proportionately to distance (is this correct?) is a law and tons more should be found as A.I. take over research ((10 years?)

It is probable IMO that increasingly bizarre laws – but still laws- will be discovered.

https://sites.google.com/site/quantumarchaeology/

eldras

November 27, 2012by GAUSS

Even showing a logarithmic scaling with the number of elements in the system is pretty damned good. It seems there will definitely be some powerful graph-theoretic formulations of quantum processor architectures, which opens up a lot of interesting research for quantum physicists.

It will be a long while, but we will eventually get to something resembling a real quantum computer. (Here “quantum computer” is qualified as a computing device which completely leverages entanglement and superposition of elements – not partially, but completely.)

November 27, 2012by Gorden Russell

GAUSS, I’m glad you came to comment on this article today. When you say, “It will be a long while,” do you mean ten years or much more?

November 27, 2012by GAUSS

It’s always difficult ‘predicting’ these things, but a good twenty years seems a reasonable estimate. Until quantum mechanics figures out cleverer ways around the uncertainty principle, there are significant barriers to the control we can get over these atoms and particles.

November 27, 2012by Ralph Dratman

Just in time to power it with controlled fusion, then.

November 28, 2012by GAUSS

One can hope. :) There’s a trend here: at CERN, they need to sustain the interactions and particles for longer times; at ITER, they need to sustain the reaction for longer times; in spintronics, one needs to sustain the spin for longer times. A lot of this comes down to slowing particle decay and increasing measurement capability.

November 27, 2012by godot

Just because one can use a quantum computer as a Turing machine equivalent doesn’t mean it’s a good idea. And just because a quantum computer is not efficient at slinging bits around in exactly the way you are used to doesn’t mean it is useless. Given real-world constraints, quantum computers can solve problems that classical computers cannot. What is your problem with them being used to do so?

November 27, 2012by Marcos Marin

Illustration’s caption should have been:

“Metatron’s cube. Coincidence?”

November 27, 2012by Jay Bob

Yeah, right..

Quantum computers is a fantasy, one of many of modern physics. A government funding black-hole.

I’ll believe it when I see one.

November 27, 2012by Marcos Marin

Yes. For general universal computing, yes.

November 27, 2012by Gorden Russell

You’re still young, Marcos. You’ll live to see quantum computing.

###

Ms. Angelica, could you ask Ray when we can expect it to come to pass?