Unitary Qubit Representation of Quantum and Classical Turbulence

A unitary qubit lattice algorithm, which scales almost perfectly to the full number of cores available (216000 cores on a CRAY XT5), is used to examine quantum turbulence and its interrelationship to classical turbulence with production runs on grids up to $5760^3$. The maximal grids achievable by conventional CFD for quantum turbulence is just $2048^3$, and artificial dissipation had to be introduced. Our unitary algorithms preserve the Hamiltonian structure of the Gross-Pitaevskii equation which describes quantum turbulence in a zero-temperature (BEC). As a result, parameter regimes have been uncovered which exhibit very short Poincare recurrence time, as well as a strong triple cascade structure in the kinetic energy spectrum, with small k-region obeying a Kolmogorov $k^{-5/3}$ spectrum The incompressible energy spectrum shows a $k^{-3}$ spectrum for large-k, but a Saffman-like $k^{-4}$ for smaller-k which is attributed to vorticity discontinuities. 2D and 3D turbulence is considered. These unitary qubit lattice algorithms are directly applicable to quantum computers.