Towards algorithm-free physical equilibrium model of computing
This could address the long-standing problem of efficiently solving NP-complete problems for computing and AI, though it appears foundational and speculative.
The paper tackles the challenge of solving NP-complete problems by proposing a new computing model that replaces sequential algorithms with physical processes, where equilibrium states correspond to solutions, and suggests quantum circuits for implementation.
Our computers today, from sophisticated servers to small smartphones, operate based on the same computing model, which requires running a sequence of discrete instructions, specified as an algorithm. This sequential computing paradigm has not yet led to a fast algorithm for an NP-complete problem despite numerous attempts over the past half a century. Unfortunately, even after the introduction of quantum mechanics to the world of computing, we still followed a similar sequential paradigm, which has not yet helped us obtain such an algorithm either. Here a completely different model of computing is proposed to replace the sequential paradigm of algorithms with inherent parallelism of physical processes. Using the proposed model, instead of writing algorithms to solve NP-complete problems, we construct physical systems whose equilibrium states correspond to the desired solutions and let them evolve to search for the solutions. The main requirements of the model are identified and quantum circuits are proposed for its potential implementation.