With a new contribution to probability theory, researchers show that relatively simple physical systems could yield powerful quantum computers.
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.
This month, however, in the journal Physical Review Letters, 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.
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.
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.