Local Gradient Optimization of Modular Entangling Sequences

Implementation of logical entangling gates is an important step towards realizing a quantum computer. We use the L-BFGS-B method to find single-qubit rotations which can be interweaved between applications of a noisy entangling gate to dramatically suppress any unknown logical error present in the entangling gate while preserving the entangling power. This approach is completely modular, and is not specific to any particular Hamiltonian. Remarkably, this modular sequence works for 1/f time-dependent gate noise as well as for quasi-static noise. We show how sequence fidelity depends on the fidelity of the local rotations and the noise strength. The modularity of this approach allows for application to any two-qubit system, regardless of the details of the experimental implementation.