  Abstraction layers are of paramount importance in software architecture, as
they shield the higher-level formulation of payload computations from
lower-level details. Since quantum computing (QC) introduces many such details
that are often unaccustomed to computer scientists, an obvious desideratum is
to devise appropriate abstraction layers for QC. For discrete optimisation, one
such abstraction is to cast problems in quadratic unconstrained binary
optimisation (QUBO) form, which is amenable to a variety of quantum approaches.
However, different mathematically equivalent forms can lead to different
behaviour on quantum hardware, ranging from ease of mapping onto qubits to
performance scalability. In this work, we show how using higher-order problem
formulations (that provide better expressivity in modelling optimisation tasks
than plain QUBO formulations) and their automatic transformation into QUBO form
can be used to leverage such differences to prioritise between different
desired non-functional properties for quantum optimisation. Our quantitative
study shows that the approach allows us to satisfy different trade-offs, and
suggests various possibilities for the future construction of general-purpose
abstractions and automatic generation of useful quantum circuits from
high-level problem descriptions.
