Biologically inspired computing devices and architectures are expected to overcome the limitations of conventional technologies in terms of solving computationally demanding problems, adapting to complex environments, reducing energy consumption, and so on. We previously demonstrated that a primitive single-celled amoeba (a plasmodial slime mold), which exhibits complex spatiotemporal oscillatory dynamics and sophisticated computing capabilities, can be used to search for a solution to a very hard combinatorial optimization problem. We successfully extracted the essential spatiotemporal dynamics by which the amoeba solves the problem. This amoeba-inspired computing paradigm can be implemented by various physical systems that exhibit suitable spatiotemporal dynamics resembling the amoeba's problem-solving process. In this Article, we demonstrate that photoexcitation transfer phenomena in certain quantum nanostructures mediated by optical near-field interactions generate the amoebalike spatiotemporal dynamics and can be used to solve the satisfiability problem (SAT), which is the problem of judging whether a given logical proposition (a Boolean formula) is self-consistent. SAT is related to diverse application problems in artificial intelligence, information security, and bioinformatics and is a crucially important nondeterministic polynomial time (NP)-complete problem, which is believed to become intractable for conventional digital computers when the problem size increases. We show that our amoeba-inspired computing paradigm dramatically outperforms a conventional stochastic search method. These results indicate the potential for developing highly versatile nanoarchitectonic computers that realize powerful solution searching with low energy consumption.