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

Speeding up Fermionic Lattice Calculations with Photonic Accelerated Inverters