Abstract
A universal family of Hamiltonians can be used to simulate any local Hamiltonian by encoding its full spectrum as the low-energy subspace of a Hamiltonian from the family. Many spin-lattice Hamiltonians -- such as the Heisenberg or XY model on the 2D square lattice -- are known to be universal. However, the known encodings require interaction energy scaling exponentially with system size for target Hamiltonians in some situations (e.g. when the target has long-range interactions).
In this talk, we give an efficient construction by which these 2D spin-lattice models are in fact "strongly universal." This means the required interaction energy and all other resources scale polynomially in the system size and precision parameters, regardless of the target Hamiltonian's connectivity. Furthermore, we show that even 1D Hamiltonians with nearest-neighbor interaction of 8-dimensional particles on a line are strongly universal. In fact, these models can efficiently simulate any systems that circuits can. Our results establish that analog quantum simulations of general systems can be made efficient, greatly increasing their potential as applications for near-future quantum technologies.
Based on joint work with Dorit Aharonov.