Efficient representations of nonlinear dynamics for quantum algorithms

To enable future quantum computers to speed up large-scale nonlinear simulations, including plasma physics simulations, the intrinsic difficulty of approximating nonlinearity with only linear, unitary quantum circuits must be overcome. When targeting a quantum speedup with respect to the number of variables in a nonlinear simulation, the challenge becomes to construct quantum systems with dynamics that somehow approximate the nonlinear simulation while taking advantage of the exponential Hilbert space dimension of the quantum computer to use a relatively small number of quantum objects. The merits and limitations of particular representations shall be discussed. A common underlying issue is the breakdown of approximation accuracy when features of strongly nonlinear evolution such as chaos are present in the nonlinear simulation. One representation of nonlinearity based on an extension of bosonic mean-field theory can avoid a complete breakdown in accuracy in these scenarios, making it a promising candidate for achieving quantum speedups of nonlinear simulations.