For Hamiltonian families with known generators and hidden parameters, the exact query cost of implementing the inverse is determined by spectral sumset relations and representation-theoretic reduction, yielding polynomial or constant bounds for several many-body families.
Heisenberg models and Schur--Weyl duality
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abstract
We present a detailed analysis of certain quantum spin systems with inhomogeneous (non-random) mean-field interactions. Examples include, but are not limited to, the interchange- and spin singlet projection interactions on complete bipartite graphs. Using two instances of the representation theoretic framework of Schur--Weyl duality, we can explicitly compute the free energy and other thermodynamic limits in the models we consider. This allows us to describe the phase-transition, the ground-state phase diagram, and the expected structure of extremal states.
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quant-ph 1years
2026 1verdicts
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Algebraic Speedups for Exact Inversion of Hamiltonian Evolutions
For Hamiltonian families with known generators and hidden parameters, the exact query cost of implementing the inverse is determined by spectral sumset relations and representation-theoretic reduction, yielding polynomial or constant bounds for several many-body families.