Quantum machine learning is the study of how quantum computers might run, accelerate, or reshape machine-learning tasks. A quantum computer manipulates qubits, which can hold combinations of 0 and 1 at once (superposition) and interfere with one another, so that a register of n qubits explores a space of 2^n configurations in parallel. The hope is that this lets certain linear-algebra operations at the heart of learning - matrix inversion, eigenvalue estimation, distance computations - run far faster than on classical hardware.
The field rests on a handful of building blocks. The 2009 HHL algorithm for linear systems is the most cited, because so much of machine learning reduces to solving or inverting large matrices. Variational quantum circuits, sometimes called quantum neural networks, take a different tack: a quantum circuit with tunable parameters is trained by a classical optimizer, much as a neural network is, so that near-term noisy machines can still be useful. Quantum versions of support vector machines, principal component analysis, and clustering have all been proposed on paper.
The honest summary is that demonstrated, practical advantage on a real problem does not yet exist. The theoretical speedups carry heavy preconditions - the data must be loadable into quantum states efficiently, the matrices must be sparse and well-behaved - and “dequantization” results have repeatedly shown that some proposed quantum routines can be matched by clever classical algorithms. Today’s hardware is also noisy and small. Google’s 2019 quantum-supremacy experiment showed a quantum machine beating classical computers on a contrived sampling task, not on anything resembling machine learning.
Why business readers should care: quantum machine learning is a long-horizon research bet, not a near-term tool. Claims that quantum computers will soon transform AI should be read skeptically; the present reality is theoretical promise plus hard engineering, with the payoff date genuinely uncertain.