  Natural language processing (NLP) is the field that attempts to make human
language accessible to computers, and it relies on applying a mathematical
model to express the meaning of symbolic language. One such model, DisCoCat,
defines how to express both the meaning of individual words as well as their
compositional nature. This model can be naturally implemented on quantum
computers, leading to the field quantum NLP (QNLP). Recent experimental work
used quantum machine learning techniques to map from text to class label using
the expectation value of the quantum encoded sentence. Theoretical work has
been done on computing the similarity of sentences but relies on an unrealized
quantum memory store. The main goal of this thesis is to leverage the DisCoCat
model to design a quantum-based kernel function that can be used by a support
vector machine (SVM) for NLP tasks. Two similarity measures were studied: (i)
the transition amplitude approach and (ii) the SWAP test. A simple NLP meaning
classification task from previous work was used to train the word embeddings
and evaluate the performance of both models. The Python module lambeq and its
related software stack was used for implementation. The explicit model from
previous work was used to train word embeddings and achieved a testing accuracy
of $93.09 \pm 0.01$%. It was shown that both the SVM variants achieved a higher
testing accuracy of $95.72 \pm 0.01$% for approach (i) and $97.14 \pm 0.01$%
for (ii). The SWAP test was then simulated under a noise model defined by the
real quantum device, ibmq_guadalupe. The explicit model achieved an accuracy of
$91.94 \pm 0.01$% while the SWAP test SVM achieved 96.7% on the testing
dataset, suggesting that the kernelized classifiers are resilient to noise.
These are encouraging results and motivate further investigations of our
proposed kernelized QNLP paradigm.
