Reverse engineering of one-qubit filter functions with dynamical invariants

Understand

We derive an integral expression for the filter-transfer function of an arbitrary one-qubit gate through the use of dynamical invariant theory and Hamiltonian reverse engineering.

• We use this result to define a cost function which can be efficiently optimized to produce one-qubit control pulses that are robust against specified frequency bands of the noise power spectral density.
• We demonstrate the utility of our result by generating optimal control pulses that are designed to suppress broadband detuning and pulse amplitude noise.
• We report an order of magnitude improvement in gate fidelity in comparison with known composite pulse sequences.