Discrete Attractor Isomorphism: Unifying Classical Annealing (DSA+CSI), Neural Dynamics, and Quantum Ground States

For half a century, computational science has been overshadowed by the myth of the “Scaling Law,” attempting to brute-force the truth in continuous spaces using massive computational power. However, biological brains achieve efficient intelligence with only 20 watts of power, and quantum computing faces an insurmountable exponential wall for classical simulation. This paper proposes a unified theoretical conjecture: classical discrete topological search (DSA+CSI), neural dynamics in biological brains, and quantum computing systems are fundamentally isomorphic at the physical and mathematical levels. We formalize this isomorphism using graph theory and Markov chains, demonstrating that while continuous gradients fail in discrete spaces, pure stochastic exploration (DSA) leads to chaotic oscillations. True convergence requires Corrigible Structural Intelligence (CSI)—topological hard constraints that act as a universal inhibitory pruning mechanism. We provide empirical evidence through a quantum qubit routing engine evaluated on a 16-qubit Quantum Fourier Transform (QFT) benchmark. The hardware environment is emulated using the IBM Heavy-Hex coupling map with a simulated calibration noise model. Experimental results show that the DSA+CSI framework achieved a circuit fidelity of 75.12%, compared to 1.27% for traditional greedy algorithms, with an ultra-low compilation time of 5.63 ms. This result demonstrates the necessity of shifting from “continuous approximation” to “discrete topological optimization” and implies that under extreme energy constraints, intelligence and computation inevitably converge on the same underlying physical structure.