Study of Non-Abelian Quantum Turbulence using Qubit Unitary Lattice Simulations

In 3D classical incompressible turbulence, one obtains the k$^{\mathrm{-5/3\thinspace }}$Kolmogorov energy cascade. In quantum turbulence one has vortex reconnection without viscosity. The topological properties of the order parameter manifold restrict the collision dynamics of vortex-vortex interaction. For scalar quantum turbulence [1], with only Abelian vortices, a triple total energy cascade region is seen on a 5760$^{\mathrm{3}}$ grid, while the incompressible part of the energy shows a single cascade of k$^{\mathrm{-3}}$. Non-Abelian turbulence [2] requires 5 coupled NLS equations (c.f., spin-2 BEC). We perform unitary qubit analysis for vortex reconnection of non-Abelian equivalence classes. Following these studies we are in a position to perform high resolution non-Abelian quantum turbulence simulations. Previous CFD studies [2] required the addition of numerically stabilizing dissipation and compensating energy influx. Our qubit unitary lattice algorithm requires no such numerical artifacts and is immediately transferable to a quantum computer. [1] J. Yepez, G. Vahala, L. Vahala and M. Soe, Phys Rev. Lett \textbf{103}, 084501 (2009) [2] M. Kobayashi et. al. Phys. Rev. Lett. \textbf{103}, 115301 (2009), arXiv 1606.07190 (2016)