Methods, systems and apparatus for determining properties of a physical system described by an electronic structure Hamiltonian. In one aspect, a Hamiltonian describing the physical system is transformed into a qubit Hamiltonian describing a corresponding system of qubits. The qubit Hamiltonian comprises multiple two-qubit interaction terms, each comprising a respective translation invariant coefficient. The system of qubits is evolved under a unitary operator generated by the multiple two-qubit interaction terms. The evolution includes applying layers of quantum logic gates to the system of qubits, wherein each application of a layer evolves the system of qubits under a unitary operator generated by a respective subset of the multiple two-qubit interaction terms and wherein the value of the coefficients of the subset of the multiple two-qubit interaction terms that generate the unitary operator is constant. The evolved system of qubits is measured and properties of the physical system is determined.