Quantum learning without quantum memory

A quantum learning machine for binary classification of qubit states that does not require quantum memory is introduced and shown to perform with the very same error rate as the optimal (programmable) discrimination machine for any size of the training set. At variance with the latter, this machine can be used an arbitrary number of times without retraining. Its required (classical) memory grows only logarithmically with the number of training qubits, while (asymptotically) its excess risk decreases as the inverse of this number, and twice as fast as the excess risk of an "estimate-and-discriminate" machine, which estimates the states of the training qubits and classifies the data qubit with a discrimination protocol tailored to the obtained estimates.