  Lattice field theory (LFT) is the standard non-perturbative method to perform
numerical calculations of quantum field theory. However, the typical bottleneck
of fermionic lattice calculations is the inversion of the Dirac matrix. This
inversion is solved by iterative methods, like the conjugate gradient
algorithm, where matrix-vector multiplications (MVMs) are the main operation.
Photonic integrated circuits excel in performing quick and energy-efficient
MVMs, but at the same time, they are known to have low accuracy. This can be
overcome by using mixed precision methods. In this paper, we explore the idea
of using photonic technology to fulfil the demand for computational power of
fermionic lattice calculations. These methods have the potential to reduce
computation costs by one order of magnitude. Because of the hybrid nature of
these methods, we call these 'photonic accelerated inverters (PAIs)'.
