aiqbench analysis
This research demonstrates a physics-aware ranking transformer that directly learns optimal Trotter orderings for Heisenberg Hamiltonians, bypassing the need for expensive candidate enumeration or simulated annealing. By incorporating commutator-biased attention and anticommutation-weighted losses, the model achieves high-fidelity predictions on systems up to 20 qubits while generalizing effectively across different lattice geometries. This approach significantly accelerates quantum simulation workflows by replacing heuristic search with a single forward pass prediction.
Learning Trotter Orderings for Heisenberg Hamiltonians with a Ranking Transformer
arXiv:2609.31977v1 Announce Type: new Abstract: Trotterization approximates quantum time evolution by sequentially applying Hamiltonian terms. Because noncommuting terms introduce ordering-dependent errors, selecting an optimal term ordering is a combinatorial problem over a factorial search space. Prior approaches rely on fixed heuristics or on selection among predefined structured orderings, both of which require simulating candidates before choosing among them. For 1D and 2D Heisenberg-style Hamiltonians, we instead learn the ordering directly with a physics-aware ranking transformer that assigns a scalar score to each Hamiltonian term and predicts an ordering by sorting these scores. Physical structure enters through commutator-biased attention and an anticommutation-weighted ranking loss, and the models are trained on simulated-annealing (SA) reference orderings. We train separate models for first- and second-order Trotterization, each jointly on chains up to 14 qubits and lattices up to 12 qubits, and evaluate them on unseen chains with 16-20 qubits and lattices with 16 and 20 qubits. Predicted orderings are evaluated by the median gap in simulation fidelity to the SA reference. At first order, the model reaches a pooled gap below 10^-4 on chains, 0.0144 and 0.0088 on triangular lattices, and 0.0948 and 0.0823 on rectangular lattices at 16 and 20 qubits; at second order, the gaps are 0.0114, 0.0364 and 0.0244, and 0.1348 and 0.1239. The prediction exceeds the SA reference on 34% of first-order and 8% of second-order chain instances and can match its fidelity even when the two sequences differ because commuting terms may be rearranged without changing the Trotter unitary. The learned models generalize to larger systems across all three geometries, performing best on chains and triangular lattices, and produce an ordering in one forward pass without candidate enumeration, simulated annealing, or fidelity evaluation.
Abstract:Trotterization approximates quantum time evolution by sequentially applying Hamiltonian terms. Because noncommuting terms introduce ordering-dependent errors, selecting an optimal term ordering is a combinatorial problem over a factorial search space. Prior approaches rely on fixed heuristics or on selection among predefined structured orderings, both of which require simulating candidates before choosing among them. For 1D and 2D Heisenberg-style Hamiltonians, we instead learn the ordering directly with a physics-aware ranking transformer that assigns a scalar score to each Hamiltonian term and predicts an ordering by sorting these scores. Physical structure enters through commutator-biased attention and an anticommutation-weighted ranking loss, and the models are trained on simulated-annealing (SA) reference orderings. We train separate models for first- and second-order Trotterization, each jointly on chains up to 14 qubits and lattices up to 12 qubits, and evaluate them on unseen chains with 16-20 qubits and lattices with 16 and 20 qubits. Predicted orderings are evaluated by the median gap in simulation fidelity to the SA reference. At first order, the model reaches a pooled gap below 10^-4 on chains, 0.0144 and 0.0088 on triangular lattices, and 0.0948 and 0.0823 on rectangular lattices at 16 and 20 qubits; at second order, the gaps are 0.0114, 0.0364 and 0.0244, and 0.1348 and 0.1239. The prediction exceeds the SA reference on 34% of first-order and 8% of second-order chain instances and can match its fidelity even when the two sequences differ because commuting terms may be rearranged without changing the Trotter unitary. The learned models generalize to larger systems across all three geometries, performing best on chains and triangular lattices, and produce an ordering in one forward pass without candidate enumeration, simulated annealing, or fidelity evaluation.
8 pages, 4 figures. Accepted at 2026 IEEE 2nd International Conference on Quantum Artificial Intelligence (QAI)
arXiv:2609.31977 [quant-ph]
(or arXiv:2609.31977v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2609.31977 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
Full text under the publisher's open licence · 386 words
Related coverage
Physics Guided Generative Optimization for Trotter Suzuki Decomposition
arXiv · Jun 8, 2026
Sparse Hamiltonians can be learned with slower quantum controls
Quantum Zeitgeist · Oct 16, 2026
Trotter error compensation with polylogarithmic precision and nested-commutator scaling without ancillas
arXiv · Jul 24, 2026
An efficient Hamiltonian-based quantum algorithm for characters of the symmetric group
arXiv · Oct 6, 2026