Symmetry-Instantiated Computation: Physical Computing as Next-Generation Information Processing

This paper presents physical computing as a paradigm shift from digital abstraction to the direct instantiation of computation through native physical processes. The framework is grounded in the principle that symmetry, particularly circular symmetry formalized by groups such as $SO(2)$ and $U(1)$, provides a universal architecture for information processing. By leveraging Noether’s theorem, which links continuous symmetries to conservation laws, this approach enables computational designs that are intrinsically efficient and robust. We critique the inherent limitations of von Neumann architectures and propose their resolution through symmetry-instantiated computation. The core of the framework is the informational loop model, where physical reality emerges from three fundamental operations—pattern writing, evolution, and projection—on a circular, information-theoretic substrate. These operations are formalized using the control theory of open quantum systems, providing a rigorous basis for state preparation, unitary processing, and measurement. Key concepts include topological protection, derived from global system properties for innate fault tolerance, and the universality of exponential mathematical patterns as a native computational language. This framework is supported by experimental validations across photonics, materials science, and quantum systems, and it outlines a path toward hybrid quantum-classical architectures integrating specialized physical co-processors.