∇Born machines

A parameterized circuit defines a probability distribution through computational-basis measurement.

Core idea

A parameterized circuit defines a probability distribution through computational-basis measurement. The central design question is what information the representation retains, which operations are physically implementable, and how prediction quality and total resource cost are measured. In QML, a mathematical formulation must be paired with an explicit data-access model and a reproducible evaluation protocol.

Worked example

How to study or implement it

Start with a minimal analytic case that can be checked by hand. Build a noiseless simulation, inspect intermediate states or predictions, and then repeat with finite sampling. Compare against a suitable classical reference using the same dataset, preprocessing, and evaluation split. Record circuit depth, qubit count, optimization steps, and measurement budget.

Interpretation and limitations

Modeling a distribution is different from proving a sampling advantage. When evaluating experimental claims, separate theoretical asymptotic statements from measured end-to-end performance. Include preprocessing, state preparation, parameter tuning and output extraction in the comparison.

Further exploration

See the chapter overview, interactive lab, guided learning path, and curated sources.