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Control and learning are key to technological advancement, both in the classical and quantum domains, yet their interrelationship is insufficiently clear in the literature, especially between classical and quantum definitions of control and learning. We construct a framework that formally relates learning and control, both classical and quantum, to each other, with this formalism showing how learning can aid control. Furthermore, our framework helps to identify interesting unsolved problems in the nexus of classical and quantum control and learning and help in choosing tools to solve problems. As a use case, we cast the well-studied problem of adaptive quantum-enhanced interferometric-phase estimation as a supervised learning problem for devising feasible control policies. Our unification of these fields relies on diagrammatically representing the state of knowledge, which elegantly summarizes existing knowledge and exposes knowledge gaps., Comment: 28 pages, 11 figures, 1 table

Two-qubit gate performance is vital for scaling up ion-trap quantum computing. Optimized quantum control is needed to achieve reductions in gate-time and gate error-rate. We describe two-qubit gates with addressed Raman beams within a linear trapped-ion chain by a quantum master equation (QME). The QME incorporates the single-ion two-photon effective Rabi frequency, Autler-Townes and vibrational Bloch-Siegert energy shifts, off-resonant transitions, Raman and Rayleigh scattering, laser-power fluctuations, motional heating, cross-Kerr phonon coupling, laser spillover, asymmetric addressing beams and an imperfect initial motional ground state, with no fitting parameters. Whereas state-of-the-art methods are oblivious to these effects in the gate design procedure. We employ global optimization to design pulse sequences for achieving a robust rapid two-qubit gate for seven trapped $^{171}$Yb$^{+}$ ions by optimizing over numerically integrated QME solutions. Here, robust means resilient against slow drift of motional frequencies, and rapid means gate execution where the effective Rabi frequency is comparable to the detuning of the laser from the ion's bare electronic transition. Our robust quantum control delivers rapid high-quality two-qubit gates in long ion chains, enabling scalable quantum computing with trapped ions., Comment: Seven pages, two figures