One of the more exciting prospects for near-term experimental quantum computation is to realize a large-scale quantum simulator. Now getting a rigorous definition of quantum simulator is tricky, but intuitively the concept is clear: we wish to have quantum systems in the lab with tunable interactions which can be used to simulate other quantum systems that we might not be able to control, or even create, in their “native” setting. A good analogy is a scale model which might be used to simulate the fluid flow around an airplane wing. Of course, these days you would use a digital simulation of that wing with finite element analysis, but in the analogy, that would correspond to using a fault-tolerant quantum computer, a much bigger challenge to realize.
We’ve highlighted the ongoing progress in quantum simulators using optical lattices before, but now ion traps are catching up in interesting ways. They have literally leaped into the next dimension and trapped an astounding 300 ions in a 2D trap with a tunable Ising-like coupling. Previous efforts had a 1D trapping geometry and ~10 qubits; see e.g. this paper (arXiv).
J. W. Britton et al. report in Nature (arXiv version) that they can form a triangular lattice of beryllium ions in a Penning trap where the strength of the interaction between ions and can be tuned to for any , where is the distance between spins and by simply changing the detuning on their lasers. (They only give results up to in the paper, however.) They can change the sign of the coupling, too, so that the interactions are either ferromagnetic or antiferromagnetic (the more interesting case). They also have global control of the spins via a controllable homogeneous single-qubit coupling. Unfortunately, one of the things that they don’t have is individual addressing with the control.
In spite of the lack of individual control, they can still turn up the interaction strength beyond the point where a simple mean-field model agrees with their data. In a) and b) you see a pulse sequence on the Bloch sphere, and in c) and d) you see the probability of measuring spin-up along the z-axis. Figure c) is the weak-coupling limit where mean-field holds, and d) is where the mean-field no longer applies.
Whether or not there is an efficient way to replicate all of the observations from this experiment on a classical computer is not entirely clear. Of course, we can’t prove that they can’t be simulated classically—after all, we can’t even separate P from PSPACE! But it is not hard to imagine that we are fast approaching the stage where our quantum simulators are probing regimes that can’t be explained by current theory due to the computational intractability of performing the calculation using any existing methods. What an exciting time to be doing quantum physics!