Spectral gap of Lee-Yang Hamiltonians

What the math gives to ML

The paper gives a constructive coupling condition for a broad class of 2-local qubit Hamiltonians under which adding a uniform Z-field produces a unique ground state and a system-size-independent gap of at least h/4. This can transfer to variational quantum neural networks: constrain trainable pairwise Hamiltonians so that imaginary-time or adiabatic state-preparation layers have a certified minimum relaxation rate, rather than relying on unconstrained couplings that may generate nearly degenerate states. The most direct use is a Lee-Yang-constrained quantum energy model or QNN whose ground-state preparation benefits from a provable suppression of excited-state contamination.