Quantum Expectation Extremum Estimation Under Measurement Uncertainty

The patent introduces a surrogate model as an intermediary between the noisy quantum measurements and the optimization algorithm. This surrogate model learns from the noisy measurements and provides clean gradient information to the optimizer, effectively mediating the interaction between quantum noise and classical optimization. The surrogate model acts as a buffer that filters out noise while preserving useful optimization signals.

The patent replaces direct mechanical gradient computation (which is sensitive to noise) with a machine learning-based surrogate model that learns the gradient structure. Instead of directly computing gradients from noisy measurements, the system uses neural networks to approximate the energy landscape and its derivatives, substituting a noisy mechanical process with a learned statistical model.

The patent performs preliminary action by training the surrogate model on initial noisy measurements before the main optimization loop. This pre-training phase allows the surrogate model to learn the underlying energy landscape structure from relatively few noisy samples. Once trained, the surrogate model can provide accurate gradient information without requiring additional noisy quantum measurements, thus reducing the total number of iterations needed.

The patent creates a copy of the energy landscape through the surrogate model. Instead of repeatedly querying the noisy quantum system to obtain gradient information, the system creates a learned copy (the surrogate model) that can be queried indefinitely without additional quantum measurements. This copy captures the essential features of the energy landscape and provides accurate gradients at minimal cost.

The patent segments the optimization process into two distinct parts: a quantum subroutine that only needs to provide noisy energy measurements, and a classical surrogate model that handles the complex optimization logic. This segmentation allows the quantum system to operate at lower depths with higher fidelity, while the surrogate model performs the heavy computational lifting classically, avoiding the decoherence problem.

The surrogate model serves as an intermediary that bridges the gap between limited-capability noisy quantum hardware and the requirements of complex optimization algorithms. It translates noisy quantum measurements into reliable optimization signals, enabling the use of sophisticated optimization techniques without requiring correspondingly sophisticated quantum hardware.