Methods, systems and apparatus for simulating a physical system described by an electronic structure Hamiltonian expressed in an orthonormal basis. In one aspect, a method includes decomposing the electronic structure Hamiltonian into a sum of sub-Hamiltonians, wherein each sub-Hamiltonian in the sum of sub-Hamiltonians is expressed in one of multiple bases; simulating evolution of the physical system using the decomposed electronic structure Hamiltonian; and using the simulated evolution of the physical system using the decomposed electronic structure Hamiltonian to determine properties of the physical system.