# gst: variational iterative rotation algorithm, combinatorial optimization with classical kicked tops.

<< ️(AA) investigate a classical formulation of the Quantum Approximate Optimization Algorithm (QAOA), realized as a Hamiltonian dynamical system of classical kicked tops, which (They) call the Variational Iterative Rotation Algorithm (VIRAL). The variational parameters are the transverse and longitudinal rotation angles at each of the p layers of the circuit. >>

<< ️(They) find that VIRAL outperforms QAOA on the canonical Sherrington-Kirkpatrick spin-glass benchmark at all circuit depths, with the energy density converging to the ground state value linearly in 1/p. For large circuit depths, the optimized dynamics follows a Floquet protocol in which a pitchfork bifurcation destabilizes the equatorial fixed point and drives the spins toward polar Ising configurations. >>

<< ️(Their) results demonstrate that the effectiveness of QAOA-like protocols derives primarily from their underlying iterative rotation structure, and that a classical implementation of it outperforms its quantum counterpart. (They) further elucidate its efficiency by reducing the many-body classical evolution to an effective Landau-Lifshitz dynamics for a single spin in a stochastic magnetic field. In this picture, the covariance matrix of the effective field reveals a nearly rank-one structure in which a single mode dominates the stochastic dynamics. In contrast, quantum fluctuations make the noise covariance of the effective quantum model of higher rank, hampering the control of the system. >>

Flaviano Morone, Andrew D. Kent, Dries Sels. Variational Iterative Rotation Algorithm: Combinatorial Optimization with Classical Kicked Tops. arXiv: 2604.01512v1 [cond-mat.dis-nn]. Apr 2, 2026.

https://arxiv.org/abs/2604.01512

Also: rotation, in FonT https://flashontrack.blogspot.com/search?q=rotation

Keywords: gst, kicked top, rotation, pitchfork bifurcation, quantum fluctuations.