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

Abstract

We present a protocol for encoding N real numbers stored in N memory registers into the amplitudes of the quantum superposition that describes the state of log 2 N qubits. This task is one of the main steps in quantum machine learning algorithms applied to classical data. The protocol combines partial CNOT gate rotations with probabilistic projection onto the desired state.The number of additional qubits, as well as the number of quantum gates, scale linearly with the number of qubits in the processing register. In addition to the linear scaling with the number of qubits, the average time needed to perform the encoding scales as the inverse of a sparsity measure of the data, and it scales as ǫ −1/2 , where ǫ is the acceptable error in the encoded amplitudes.