Quantum gases in optical lattices offer a powerful tool to study condensed matter phenomena in a controllable environment where the geometry and depth of the potential are tuned by optical means. The wide tunability range and control level accuracy of the potential landscape render optical lattices a good candidate for quantum simulation, i.e. for the study of classical magnetism, although the readout process and the single site control remain challenging. Recently, we proposed polariton graphs as a new platform for analogue simulation. Polariton graphs benefit by the continuous optical readout of the phase, energy, momentum and spin of the individual polariton vertices, the strong inter-particle interactions −mediated through the exciton component−, room temperature operation −with appropriate choice of materials−, and even the potential for electrical injection utilizing well-developed semiconductor technologies.
In this project, we investigate the potential of polariton graphs as a platform for analogue simulation and in particular in solving non-deterministic polynomial problems. Unlike a proposal for a quantum computer that is intended as a universal platform, analogue simulators are proposed to solve specialized classes of problems suited for the architecture and capabilities of the underlying physical system. For example, the intensely investigated superconducting quantum bits platform intends to simulate the Ising model with transverse fields through the quadratic unconstrained binary optimization model (QUBO). Trapped ions were used to simulate Ising, XY, and XYZ interactions between effective spins. Another scalable platform that benefits from high temperature operation is the coupled degenerate OPOs Ising Machine, which solves the MAX-CUT. Our polariton platform simulates the XY model, which can be formulated as a quadratic non-convex constrained optimization model (QNCO). The hardest instances of all mentioned problems are in the NP-hard classical complexity class of problems. QUBO or MAX-CUT can be mapped into QNCO and vice versa but with a huge overhead on the number of nodes. Therefore, assuming that all platforms eventually show better than classical computer behavior it is likely that each platform will be used to address its own type of problems.
Dr Alexis Askitopoulos, Dr Namig Hasanov, Dr Fauzia Jabeen, Dr Matteo Silva