Exponentiation of Parametric Hamiltonians via Unitary interpolation
arxiv(2024)
摘要
The effort to generate matrix exponentials and associated differentials,
required to determine the time evolution of quantum systems, frequently
constrains the evaluation of problems in quantum control theory, variational
circuit compilation, or Monte-Carlo sampling. We introduce two ideas for the
time-efficient approximation of matrix exponentials of linear multi-parametric
Hamiltonians. We modify the Suzuki-Trotter product formula from an
approximation to an interpolation schemes to improve both accuracy and
computational time. This allows us to achieve high fidelities within a single
interpolation step, which can be computed directly from cached matrices. We
furthermore define the interpolation on a grid of system parameters, and show
that the infidelity of the interpolation converges with 4^th order
in the number of interpolation bins.
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