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We introduce flexible high-fidelity passband (PB) composite pulse sequencesconstructed by concatenation of recently derived arbitrarily large andarbitrarily accurate broadband $\mathcal{B}$ and narrowband $\mathcal{N}$composite sequences. Our PB sequences allow to produce flexible and tunablenearly rectangular two-state inversion profiles as a function of the individualpulse area because the width and the rectangularity of these profiles can beadjusted at will. Moreover, these PB sequences suppress excitation around pulsearea $0$ and $2\pi$, and suppress deviations from complete population inversionaround pulse area $\pi$ to arbitrarily high orders. These features makes them avaluable tool for high-fidelity qubit operations in the presence of relativelystrong amplitude noise. We construct two types of PB pulses:$\mathcal{N}(\mathcal{B})$ in which a broadband pulse is nested into anarrowband pulse, and $\mathcal{B}(\mathcal{N})$ in which a narrowband pulse isnested into a broadband pulse; the latter sequences deliver narrower profiles.We derive exact analytic formulas for the composite phases of the PB pulses andexact analytic formulas for the inversion profiles. These formulas allow aneasy estimation of the experimental resources needed for any desired qubitinversion profile.

Arbitrarily accurate passband composite pulses for dynamical suppression of amplitude noise