Symmetry-induced quantum-inspired parallelism of classical dynamic systems

Abstract: Performing multiple computations within the same system, without spatial or temporal separation of tasks, requires encoding multiple data items into a well-defined physical state. The most widely explored mechanism for such encoding is the superposition of physical states representing computational states. However, superposition requires the system to be linear, which significantly limits the set of achievable operations. We show that system symmetries provide an alternative mechanism for encoding multiple computational states. Notably, this mechanism also applies to nonlinear systems and therefore does not impose inherent limits on computed functions. Using the evaluation of Boolean functions as an example, we show that a relaxed spin network driven by the V-2 model supports this mechanism. We relate the resulting simultaneous computations enabled by symmetry-induced parallelism to properties of the evaluated functions. We demonstrate symmetry-induced parallelism for a logical AND/OR gate and an N-bit adder.