Addressing the worlds climate emergency is an uphill battle and requires a multifaceted approach including optimal deployment of green-energy alternatives. This often involve time-consuming optimisation of black-box models in a continuous parameter space. Despite recent advances in quantum computing, real-world applications have thus far been mostly confined to problems such as graph partitioning, traffic routing and task scheduling, where parameter space is discrete and graph connectivity is sparse. Here we propose the quantum nonlinear programming (QNLP) framework for casting an NLP problem - in continuous space - as quadratic unconstrained binary optimisation (QUBO), which can be subsequently solved using special-purpose solvers such as quantum annealers (QA) and coherent Ising machines (CIMs). QNLP consists of four steps: quadratic approximation of cost function, discretisation of parameter space, binarisation of discrete space, and solving the resulting QUBO. Linear and nonlinear constraints are incorporated into the resulting QUBO using slack variables and quadratic penalty terms. We apply our QNLP framework to optimisation of the daily feed rate of various biomass types at Nature Energy, the largest biogas producer in Europe. Optimising biomass selection improves the profitability of biomethane production, thus contributing to sustainable carbon-neutral energy production. For solving the QUBO, we use D-Waves quantum annealers. We observe good performance on the DW-2000Q QPU, and higher sensitivity of performance to number of samples and annealing time for the Advantage QPU. We hope that our proposed QNLP framework provides a meaningful step towards overcoming the computational challenges posed by high-dimensional continuous-optimisation problems, especially those encountered in our battle against man-made climate change.
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