Universal Hamiltonian simulators in one and two dimensions

Understand

A major quantum computing application is analog Hamiltonian simulations, in which the low-lying spectrum of a simulator Hamiltonian $H'$ encodes the physics of a target Hamiltonian $H$.

• Some families of 2D spin-lattice Hamiltonians---such as the Heisenberg or XY model on the square lattice---are known to be ``universal'' simulators, in the sense that they can simulate any target Hamiltonian.
• Unfortunately, while the known simulations of 1D or 2D target Hamiltonians are efficient, they require resources growing exponentially with system sizes for target Hamiltonians with general connectivity.
• This leaves many important cases such as 3D or all-to-all-connected target Hamiltonians out of reach in practice.