Simulating a quantum magnet in the hybrid approach
Having demonstrated accurate analog evolution, we then combined it with our more traditional specialty, high-precision digital gates, to study new physical phenomena. Leveraging our hybrid approach, we simulated a magnet, the behavior of which is very closely mimicked by the natural dynamics on our hardware. Each qubit can be thought of as a magnetic spin — think a little bar magnet — that interacts with its neighbors. We wanted to study what happens to the magnet when the interactions are turned on at varying rates, both because it is an interesting physics question that has attracted substantial attention in the field, and because it can improve our understanding of important techniques in quantum computing, such as quantum annealing.
To simulate this, we first used digital gates to initialize the qubits in an alternating pattern of 1s and 0s, representing spins pointing up and down, respectively. Then we ramped up the analog interactions between the spins at varying rates before switching back to digital mode for measurements. Intuitively, if the interactions are turned on very quickly, the magnetic spins are expected to not have time to react and remain stuck in their initial positions. If turned on slowly, on the other hand, they pull and twist on each other, as bar magnets do, and start pointing in the same direction. Indeed, we found that when the analog couplings were turned on very slowly, we were able to reach quantum states in which the spins align in the horizontal plane in a strongly correlated way, equivalent to a very low temperature. Importantly, here we are not referring to the temperature of the quantum chip itself (which is also very cold), but rather to that of the simulated magnet.
Interestingly, we reached sufficiently low temperatures to observe a famous phenomenon known as the Kosterlitz-Thouless transition, which is a sudden change in the degree of alignment of the magnetic spins in a material. Conceptually, this is similar to the way water molecules suddenly align when they freeze.
Highly correlated, low-temperature quantum states, such as those we observed, are the source of many fundamental puzzles in physics and were previously much less accessible with our purely digital scheme. Moreover, the hybrid approach allowed us to probe the transition in a versatile way, including the observation of several characteristic behaviors of the Kosterlitz-Thouless transition, which would not be possible in a purely analog simulation.
