Quantum Machine Learning

Quantum machine learning encodes data into qubit states and hopes a quantum model separates patterns that classical models cannot; no end-to-end advantage on classical data has ever been demonstrated, and data loading is the structural reason. This chapter works the three encoding schemes with real arithmetic and runs an angle-encoding circuit you can verify by hand.

What does quantum machine learning actually propose?

Machine learning fits a flexible function to data so it predicts well on new inputs. The quantum variant, QML, replaces part of that pipeline with a quantum circuit: encode an input into the state of qubits (quantum bits whose configuration weights, called amplitudes, are complex numbers with squared magnitudes giving probabilities), apply a trainable sequence of gates (the elementary operations of a quantum program), measure, and feed the statistics to a classical optimizer.

Run the chapter 1 filter before any excitement: the claimed speedup is heuristic for essentially all QML on classical data (question 1 fails to give a proof), and data loading, question 2, is not an implementation detail here; it is the central obstacle, as the arithmetic below shows. The one structurally different case is quantum data, states produced by a quantum sensor or another quantum computer, where no loading step is needed; that case is scientifically promising and commercially distant. Everything in this chapter concerns the common claim: advantage on ordinary classical datasets. See the machine learning reality page for tracked claims.