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Spectral Certificates and Non-commutative Sum-of-Squares Lower Bounds for Hamiltonians
A central question in quantum many-body physics is estimating the ground energy of a $k$-local Hamiltonian system. In this work, we present a spectral technique for certifying a lower bound on the ground energy of a random $n$-qubit Hamiltonian system defined as the sum of signed $k$-local Pauli ope
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