Hybridized Methods for Quantum Simulation in the Interaction Picture

Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where use is optimal. In particular, the interaction picture has been found provide substantial asymptotic advantages for some Hamiltonians, but incurs prohibitive constant factors and incompatible with like qubitization. We a framework allows different be hybridized thereby improve performance simulations over known algorithms. These approaches show improvements individual comprise them further make practical in near term. Physical applications these yield gate complexity scaling aslog2⁡Λin electric cutoffΛfor Schwinger Model independent electron density collective neutrino oscillations, outperforming all current algorithms parameters. For general problem Hamiltonian subject dynamical constraints, query penalty parameterλused impose an energy cost on time-evolution into unphysical subspace.