1Department of Physics, University of Washington, Seattle, WA 98195, USA
2InQubator for Quantum Simulation (IQuS), Department of Physics, University of Washington, Seattle, WA 98195, USA
3Dipartimento di Fisica, University of Trento, via Sommarive 14, I–38123, Povo, Trento, Italy
4Department of Computer Science, University of Toronto, Toronto, ON M5S 2E4, Canada
5Pacific Northwest National Laboratory, Richland, WA 99354, USA
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Abstract
Conventional methods of quantum simulation involve trade-offs that limit their applicability to specific contexts where their use is optimal. In particular, the interaction picture simulation has been found to provide substantial asymptotic advantages for some Hamiltonians, but incurs prohibitive constant factors and is incompatible with methods like qubitization. We provide a framework that allows different simulation methods to be hybridized and thereby improve performance for interaction picture simulations over known algorithms. These approaches show asymptotic improvements over the individual methods that comprise them and further make interaction picture simulation methods practical in the near term. Physical applications of these hybridized methods yield a gate complexity scaling as $log^2 Lambda$ in the electric cutoff $Lambda$ for the Schwinger Model and independent of the electron density for collective neutrino oscillations, outperforming the scaling for all current algorithms with these parameters. For the general problem of Hamiltonian simulation subject to dynamical constraints, these methods yield a query complexity independent of the penalty parameter $lambda$ used to impose an energy cost on time-evolution into an unphysical subspace.
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