  Machine learning is a crucial aspect of artificial intelligence. This paper
details an approach for quantum Hebbian learning through a batched version of
quantum state exponentiation. Here, batches of quantum data are interacted with
learning and processing quantum bits (qubits) by a series of elementary
controlled partial swap operations, resulting in a Hamiltonian simulation of
the statistical ensemble of the data. We decompose this elementary operation
into one and two qubit quantum gates from the Clifford+T set and use the
decomposition to perform an efficiency analysis. Our construction of quantum
Hebbian learning is motivated by extension from the established classical
approach, and it can be used to find details about the data such as eigenvalues
through phase estimation. This work contributes to the near-term development
and implementation of quantum machine learning techniques.
