Replace evaluation in a possibly inaccurate dynamical model by an experimental objective. Parametrize an admissible pulse as , with collecting time-slice amplitudes or basis-function coefficients. Prepare the same initial state, apply the pulse, measure performance, and update before the next run. This is adaptive experimental quantum control: the loop closes through experimental results, even though each individual pulse is applied open loop.
For example, minimizefor a pure target , with a nonempty closed convex set enforcing amplitude and bandwidth bounds. The overlap is an experimentally estimable probability. An observable objective can use its measured expectation instead; a gate objective generally needs more input states and measurement settings. The true dynamics constrain the physically produced , but no accurate formula for those dynamics is required to evaluate this objective.
A direct search compares measured scores for candidate pulses, accepts improvements and refines the search region. Alternatively estimate a gradient experimentally by finite differences,where is the Euclidean projection onto a convex set. Population-based searches can also explore several candidates in parallel. These methods use experimental data rather than simulated propagation or a model-derived adjoint gradient.
Each score needs enough repeated preparations to manage measurement noise; uncertainty in score differences should determine replication and stopping decisions. Excessively small finite-difference steps amplify that noise. A model-based pulse can provide a useful starting point, but adaptation corrects its systematic mismatch using the device itself. This mitigates model uncertainty, not arbitrary fluctuations: reproducible preparation, calibrated measurements and sufficiently slow drift remain necessary. Nor does a local numerical search guarantee a global optimum.
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