Kavli Affiliate: Alireza Marandi
| First 5 Authors: Gordon Li, Alireza Marandi, , ,
| Summary:
Networks of coupled nonlinear optical resonators have emerged as an important
class of systems in ultrafast optical science, enabling richer and more complex
nonlinear dynamics compared to their single-resonator or travelling-wave
counterparts. In recent years, these coupled nonlinear optical resonators have
been applied as application-specific hardware accelerators for computing
applications including combinatorial optimization and artificial intelligence.
In this work, we rigorously prove a fundamental result showing that coupled
nonlinear optical resonators are Turing-complete computers, which endows them
with much greater computational power than previously thought. Furthermore, we
show that the minimum threshold of hardware complexity needed for
Turing-completeness is surprisingly low, which has profound physical
consequences. In particular, we show that several problems of interest in the
study of coupled nonlinear optical resonators are formally undecidable. These
theoretical findings can serve as the foundation for better understanding the
promise of next-generation, ultrafast all-optical computers.
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