General, efficient, and robust Hamiltonian engineering

Abstract: Implementing the time evolution under a desired target Hamiltonian is critical for various applications in quantum science. Due to the exponential increase of parameters in the system size and due to experimental imperfections this task can be challenging in quantum many-body settings. We introduce an efficient and robust scheme to engineer arbitrary local many-body Hamiltonians. This is achieved by applying simple single-qubit gates simultaneously to an always-on system Hamiltonian, which we assume to be native to a given platform. These sequences are constructed by efficiently solving a linear program (LP) which minimizes the total evolution time. In this way, we can engineer target Hamiltonians that are only limited by the locality of the Pauli terms in the system Hamiltonian. Based on average Hamiltonian theory and by using robust composite pulses, we make our schemes robust against errors including finite pulse time errors and various calibration errors. To demonstrate the performance of our scheme, we provide numerical simulations. In particular, we solve the Hamiltonian engineering problem for arbitrary two-body Hamiltonians on a 2D square lattice with $225$ qubits in only $60$ seconds. Moreover, we simulate the time evolution of Heisenberg Hamiltonians for smaller system sizes with a fidelity larger than $99.9\%$, which is orders of magnitude better than non-robust implementations.