It's Quick to be Square: Fast Quadratisation for Quantum Toolchains

Many of the envisioned use-cases for quantum computers involve
optimisation processes. While there are many algorithmic primitives to
perform the required calculations, all eventually lead to quantum gates
operating on quantum bits, with an order as determined by the structure
of the objective function and the properties of target hardware.
When the structure of the problem representation is not aligned with structure
and boundary conditions of the executing hardware, various overheads degrading the 
computation may arise, possibly negating any possible quantum advantage.

Therefore, automatic transformations of problem representations play
an important role in quantum computing when descriptions (semi-)targeted at humans must be cast into forms that can be
``executed'' on quantum computers. Mathematically equivalent formulations are known
to result in substantially different non-functional properties depending on hardware,
algorithm and detail properties of the problem. Given the current state
of noisy intermediate-scale quantum (NISQ) hardware, these effects are considerably
more pronounced than in classical computing. Likewise, efficiency of the
transformation itself is relevant because possible quantum advantage may easily be
eradicated by the overhead of transforming between representations. In this paper,
we consider a specific class of higher-level representations, that is, PUBOs, and devise novel automatic transformation mechanisms 
into widely used QUBOs that 
substantially improve efficiency and versatility over the state of the art.
In addition, we conduct a comprehensive investigation of industry-relevant problem formulations and their conversion into a quantum-specific representation, identifying significant obstacles in scaling behaviour and demonstrating how these can be circumvented.