  In recent years, advances in quantum computing have led to accelerating
research on quantum applications across fields. Here, we introduce a quantum
machine learning model as a potential solution to the classical question in
database research: the estimation of metrics for SQL queries. This work employs
a quantum natural language processing (QNLP)-inspired approach for constructing
a quantum machine learning model that can classify SQL queries with respect to
their cardinalities, costs, and execution times. The model consists of an
encoding mechanism and a training phase, including classical and quantum
subroutines. The encoding mechanism encodes SQL queries as parametrized quantum
circuits. In the training phase, we utilize classical optimization algorithms,
such as SPSA and Adam, to optimize the circuit parameters to make predictions
about the query metrics. We conclude that our model reaches an accuracy
equivalent to that of the QNLP model in the binary classification tasks.
Moreover, we extend the previous work by adding 4-class classification tasks
and compare the cardinality estimation results to the state-of-the-art
databases. We perform a theoretical analysis of the quantum machine learning
model by calculating its expressibility and entangling capabilities. The
analysis shows that the model has advantageous properties that make it
expressible but also not too complex to be executed on the existing quantum
hardware.
