Every time particle physicists look for the Higgs boson or any other members of a large collection of theoretical particles, they have to do a bit of statistics. Well, quite a lot of statistics, actually. The Standard Model of physics helps tell them what they'll probably see when two particles smash together at nearly light speed. To find something new, they have to look for places where the signals they see don't match up to the pattern predicted by the Standard Model.

Those predictions, however, require impressive amounts of computing power and are only approximations at best. There are some conditions where there are simply no effective methods of calculating the result with a classical computer. But a quantum computer doesn't have to play by the same rules, and researchers have now produced an algorithm that can solve the equations that dictate what goes on within particle colliders like the LHC.

The problem (or at least one of them) with simulating particle collisions is that it requires a combination of quantum mechanics, which describes the behavior of the particles involved, and relativity, since the particles are moving at nearly the speed of light. Although these two descriptions of reality are incompatible in some ways, Quantum Field Theory (which Richard Feynman helped develop) can provide a description of the interactions of fundamental particles like quarks and electrons.

However, Feynman's equations don't apply to all situations, and there are many cases—like when a system is far from equilibrium—where they simply can't be solved, at least not with a classical computer. As the paper describing the new algorithm puts it, "Quantum field theory, which applies quantum mechanics to functions of space and time, presents additional technical challenges, because the number of degrees of freedom per unit volume is formally infinite."

So the authors of the new paper (one each from Caltech, Pittsburgh, and the NIST), have turned to quantum computing, explicitly simulating a system where two particles collide and scatter off each other. This may sound simple, but they note a couple of things that make matters a bit more complex. Some of the particles' energy may be converted into mass, meaning more particles come out of the collision than go in. In addition, the incoming momentum doesn't determine exactly how fast the particles that exit will be moving, but only influence the probability distributions typical of quantum objects.

The algorithm itself involves preparing a bunch of particles as quantum wave packets, then getting these packets to interact. The details of how to do this physically aren't specified, and the nature of the interactions are such that the authors describe things by saying, "within the interaction picture, our algorithm is more naturally described in the formalism of Hamiltonians and within the Schrödinger picture." The key thing is that, even though there is an indeterminate number of potential states, the algorithm allows the simulation to work with only a finite number of qubits.

Unfortunately, finite does not necessarily mean "small." The authors estimate that the minimum number of qubits needed is at least 1,000, and may be closer to 10,000. Considering that having more than a couple qubits working together is currently a major accomplishment, actually implementing this algorithm is left for the indefinite future.

That said, if we can ever implement this, it will be a validation of the promise of quantum computing. The algorithm can clearly solve some problems that classical computers can't touch. But the authors also compared its performance on related problems that classic computers can solve, and showed that the quantum version provides an exponential speed-up.

This gets back to the P vs. NP issue (where P are problems that classical computers can solve relatively easily). As an accompanying perspective points out, this is further evidence that the equivalent of P in the quantum world (called BQP, and representing problems that quantum computing handles relatively painlessly) probably includes all P problems, but is probably larger. That means there will be things that quantum computers really do handle well.

In any case, the perspective also points out that the development of effective quantum algorithms has sometimes led to insights that improved the algorithms we use on classical computers. So we may not need to build a 1,000-qubit quantum computer for the folks running the LHC experiments to see some benefits from this work.

Science, 2012. DOI: 10.1126/science.1217069, 10.1126/science.1223010 (About DOIs).