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In adaptive experimental quantum control, parametrize a reproducible pulse by a finite real vector $c$, for example $f_c(t)={\sum }_{j=1}^p{c}_j{B}_j(t)$ in a calibrated waveform basis. Prepare the same initial state for each trial, apply that pulse without feedback during the run, and estimate the objective $J(c)$ from repeated measurements. No accurate dynamical model is required if the laboratory can evaluate the objective.

One concrete algorithm is experimental finite-difference gradient ascent. For every parameter, run trials at $c\pm \delta e_j$ and estimateUpdate $c$ to an admissible projection of $c+\eta g$, test the new pulse, and reduce the step size if performance deteriorates. Averaging many shots controls statistical noise; choose $\delta$ large enough for the difference to exceed the measurement uncertainty but small enough to approximate a derivative. Repeat until no statistically significant improvement remains. Multiple starting pulses help explore distinct basins, but this does not guarantee a global optimum. Resource penalties and hardware restrictions belong in the objective or the admissible parameter set.

The feedback is across experimental runs: a measured objective chooses the next pulse. Each individual trial is open-loop control. This distinction matters because the algorithm does not require an instantaneous nondestructive state measurement on the system being controlled.

Replace evaluation in a possibly inaccurate dynamical model by an experimental objective. Parametrize an admissible pulse as $f(t;a)$, with $a$ collecting time-slice amplitudes or basis-function coefficients. Prepare the same initial state, apply the pulse, measure performance, and update $a$ 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 ${\rho }_d$, with a nonempty closed convex set $\mathcal{A}$ 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 ${\rho }_a(T)$, 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 ${\Pi }_{\mathcal{A}}$ 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.