Geometric filter function approach to dynamically corrected gates that suppress time-dependent noise

We present a geometric filter function method for designing smooth control pulses that dynamically correct time-dependent noise errors. Under this framework, robust qubit evolution is mapped to geometric curves that satisfy certain constraints that guarantee the suppression of the leading-order error. We use the damping Newton method to numerically solve the constraints, obtaining a series of polynomial-like solutions that produce pulses for a range of single-qubit gates. Several of these pulses are not only non-negative but also have the advantage of relatively low bandwidth and amplitude. These features make the pulses experimentally feasible for platforms like semiconductor quantum dot spin qubits or superconducting qubits by respecting hardware and pulse generation constraints. We also provide simulation results of our pulses against different types of time-dependent noise. We find high fidelities across a range of noise parameters, demonstrating the effectiveness of this approach.