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

TL;DR

This paper introduces a quantum state preparation protocol that efficiently encodes classical data into quantum amplitudes, optimizing resource use and success probability for quantum machine learning applications.

Contribution

The protocol combines partial CNOT rotations with probabilistic projection, scaling linearly with qubits and logarithmically with data size, improving efficiency for non-sparse data.

Findings

Resource scaling is linear with qubits and logarithmic with data size.

Encoding success time scales logarithmically with the number of qubits.

Protocol is most efficient for non-sparse data sets.

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 $\log_2N$ 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 ancilla qubits used during the implementation of the protocol, as well as the number of quantum gates, scale linearly with the number of qubits in the processing register and hence logarithmically with $N$. The average time needed to successfully perform the encoding scales logarithmically with the number of qubits, in addition to being inversely proportional to the acceptable error in the encoded amplitudes. It also depends on the structure of the data set in such a way that the protocol is most efficient for non-sparse data.