*Laboratory Equipment* points the way for the next big breakthrough in thinking machines:

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 Univ. in the Czech Republic, the Slovak Academy of Sciences and Northeastern Univ. 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 other words, it’s possible to get sophisticated results from a simple starting point… something beyond the yes/no of conventional circuit switches.

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.

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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.