QIP2021 | Strongly Universal Hamiltonian Simulators (Leo Zhou)

Authors: Leo Zhou and Dorit Aharonov
Affiliations: Harvard University | The Hebrew University of Jerusalem

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 model Hamiltonians---such as Heisenberg or XY interaction on the 2D square lattice---are known to be universal. However, the known encodings can be very inefficient, requiring interaction strengths that scales exponentially with system size if the original Hamiltonian have complex, possibly all-to-all connectivity. In this work, we provide an efficient construction by which these universal families are in fact ``strongly'' universal; this means that the required interaction strengths as well as all other resources scale polynomially, regardless of the connectivity of the original Hamiltonian. This exponential improvement over previous constructions based on perturbative gadgets is achieved by combining the tools of quantum phase-estimation algorithm and circuit-to-Hamiltonian transformation in a non-perturbative way that only incurs polynomial overhead. Furthermore, we show that 1D Hamiltonians with nearest-neighbor interaction of 8-dimensional particles on a line are also strongly universal Hamiltonian simulators. Our results demonstrate that analog quantum simulation of general Hamiltonians can be made efficient for all target local Hamiltonians; this has potential application for future quantum technologies.