Compensating sequences for robust quantum control of trapped-ion qubits

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Merrill, James True
Brown, Kenneth R.
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Universal quantum computation requires precision control of the dynamics of qubits. Frequently accurate quantum control is impeded by systematic drifts and other errors. Compensating composite pulse sequences are a resource efficient technique for quantum error reduction. This work describes compensating sequences for ion-trap quantum computers. We introduce a Lie-algebraic framework which unifies all known fully-compensating sequences and admits a novel geometric interpretation where sequences are treated as vector paths on a dynamical Lie algebra. Using these techniques, we construct new narrowband sequences with improved error correction and reduced time costs. We use these sequences to achieve laser addressing of single trapped 40Ca+ ions, even if neighboring ions experience significant field intensity. We also use broadband sequences to achieve robust control of 171Yb+ ions even with inhomogeneous microwave fields. Further, we generalize compensating sequences to correct certain multi-qubit interactions. We show that multi-qubit gates may be corrected to arbitrary accuracy if there exists either two non-commuting controls with correlated errors or one error-free control. A practical ion-trap quantum computer must be extendible to many trapped ions. One solution is to employ microfabricated surface-electrode traps, which are well-suited for scalable designs and integrated systems. We describe two novel surface-electrode traps, one with on-chip microwave waveguides for hyperfine 171Yb+ qubit manipulations, and a second trap with an integrated high numerical aperture spherical micromirror for enhanced fluorescence collection.
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