Emergence of Deterministic Chaos and Quantum Variational Solvers

This paper demonstrates that the Lorenz system and the structure of hybrid classical–quantum solvers, such as the Variational Quantum Linear Solver (VQLS), emerge directlyand naturally from the universal Ψ field Lagrangian. The self-referential variationalterm of L(6)Ψ generates deterministic chaos, attractors, and coherent quantum optimizationdynamics as two projections of the same underlying informational field. Weexplicitly derive the Lorenz equations as a three-dimensional projection of the universalvariational operator and show that the VQLS minimization algorithm corresponds tothe intrinsic variational principle of L(6)Ψ .