∇Qubits and Bloch sphere

Pure qubit states are points on a sphere, while mixed states lie inside it. Global phase is unobservable.

Core idea

Pure qubit states are points on a sphere, while mixed states lie inside it. Global phase is unobservable. 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

A Bloch sphere represents one qubit, not arbitrary many-qubit entanglement. 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.