Serialized quantum classifiers decouple the number of parameters from the number of qubits

Quantum machine learning models are usually compared with classical networks that have far more parameters and no restriction on how features are represented. We introduce a serialized classifier that reads four features at a time on a fixed seven-qubit register. Each input position has its own trainable block, and a three-qubit memory, coherent or measured, links the positions, so the parameter count grows with the input, not with the register. These parameters remain trainable: from a near-identity start, local-cost gradients do not decay as the register grows from five to eleven qubits. On MNIST, accuracy generally rises with the parameter count. On twelve further datasets the circuit is within 2.5 points of a same-size MLP on eight, ahead on two and behind on two with many classes, and beats amplitude encoding on eleven. Sharing one block across positions, removing entanglement or training only the readout lowers accuracy. No quantum advantage is claimed.