  Toxicity is a roadblock that prevents an inordinate number of drugs from
being used in potentially life-saving applications. Deep learning provides a
promising solution to finding ideal drug candidates; however, the vastness of
chemical space coupled with the underlying $\mathcal{O}(n^3)$ matrix
multiplication means these efforts quickly become computationally demanding. To
remedy this, we present a hybrid quantum-classical neural network for
predicting drug toxicity, utilizing a quantum circuit design that mimics
classical neural behavior by explicitly calculating matrix products with
complexity $\mathcal{O}(n^2)$. Leveraging the Hadamard test for efficient inner
product estimation rather than the conventionally used swap test, we reduce the
number qubits by half and remove the need for quantum phase estimation.
Directly computing matrix products quantum mechanically allows for learnable
weights to be transferred from a quantum to a classical device for further
training. We apply our framework to the Tox21 dataset and show that it achieves
commensurate predictive accuracy to the model's fully classical
$\mathcal{O}(n^3)$ analog. Additionally, we demonstrate the model continues to
learn, without disruption, once transferred to a fully classical architecture.
We believe combining the quantum advantage of reduced complexity and the
classical advantage of noise-free calculation will pave the way to more
scalable machine learning models.
