We prove exponentially slow thermalization for the quantum random energy model (QREM) under Davies dynamics. The QREM is the $n$-qubit Hamiltonian $H=\Gamma T+U$, where $U$ assigns independent Gaussian energies with variance equal to the system size to computational-basis configurations and $T$ is the transverse field...
Understanding when quantum many-body systems rapidly converge to thermal equilibrium is a central problem in quantum statistical mechanics. While spatial locality provides powerful tools for systems with an underlying geometry, fully connected models require estimates that accommodate interactions between every pair of...
This work proves that, for sufficiently large circuit width, the nonlinear gradient flow is quantitatively approximated by a linearized NTK model, with explicit bounds depending on the number of qubits, circuit depth, circuit light-cone geometry, and the dimension of the domain of the solution to the PDE.
A. M. Hernandez, Giacomo De Palma· 0 citations
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