Chapter 04 / Concept 14 of 48

Variational quantum classifier

Convert expectation values into binary scores and optimize a classification loss.

Input / assumptions→ Quantum or learning model→ Measurement / inference→ Validation

Core idea

Convert expectation values into binary scores and optimize a classification loss. 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.

$$p_\theta(y=1|x)=\frac{1-f_\theta(x)}2$$

Worked example

Use binary cross entropy on $p_\theta$ and train the circuit against labeled samples.

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

Avoid interpreting one observable as a calibrated probability without checking calibration. 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.

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