A structure-aware transformer trained on 3-14 qubit systems predicts Trotter orderings for 16-20 qubit 1D Heisenberg Hamiltonians with a mean fidelity gap of 0.00115 to the best of 24 candidates.
An Analysis of Commutation-Based Trotter Ordering Strategies on Heisenberg-Style Hamiltonians
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abstract
Trotterization is a technique that allows one to approximate a time evolution of a Hamiltonian by repeatedly evolving the individual terms of the Hamiltonian one-at-a-time for small time durations. Bounds on the error of this approximation exist; however, they are typically loose and moreover, it is known that the true error can be greatly influenced by the order in which the terms of the Hamiltonian are evolved. In this work, we consider various ordering strategies that exploit the commutation structure of the Hamiltonian, in addition to a few other baseline ordering strategies. These commutation-based strategies involve dividing the terms of the Hamiltonian into groups where all the terms within each group commute with one another. These groupings can be obtained by using graph coloring techniques on what we call the "commutation graph" of the Hamiltonian. We prove various results regarding the structure and properties of such commutation graphs for certain classes of Hamiltonians. We also empirically calculate the (true) Trotter error using these ordering strategies on various 1D and 2D Heisenberg-style systems.
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Structure-Aware Transformers for Learning Near-Optimal Trotter Orderings with System-Size Generalization in 1D Heisenberg Hamiltonians
A structure-aware transformer trained on 3-14 qubit systems predicts Trotter orderings for 16-20 qubit 1D Heisenberg Hamiltonians with a mean fidelity gap of 0.00115 to the best of 24 candidates.