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We present a protocol for encoding $N$ real numbers stored in $N$ memoryregisters into the amplitudes of the quantum superposition that describes thestate of $\log_2N$ qubits. This task is one of the main steps in quantummachine learning algorithms applied to classical data. The protocol combinespartial CNOT gate rotations with probabilistic projection onto the desiredstate. The number of additional ancilla qubits used during the implementationof the protocol, as well as the number of quantum gates, scale linearly withthe number of qubits in the processing register and hence logarithmically with$N$. The average time needed to successfully perform the encoding scaleslogarithmically with the number of qubits, in addition to being inverselyproportional to the acceptable error in the encoded amplitudes. It also dependson the structure of the data set in such a way that the protocol is mostefficient for non-sparse data.

Quantum state preparation protocol for encoding classical data into the amplitudes of a quantum information processing register's wave function