# Hamiltonian surgery: Cheeger-type gap inequalities for nonpositive (stoquastic), real, and Hermitian matrices

@inproceedings{Jarret2018HamiltonianSC, title={Hamiltonian surgery: Cheeger-type gap inequalities for nonpositive (stoquastic), real, and Hermitian matrices}, author={Michael Jarret}, year={2018} }

Cheeger inequalities bound the spectral gap $\gamma$ of a space by isoperimetric properties of that space and vice versa. In this paper, I derive Cheeger-type inequalities for nonpositive matrices (aka stoquastic Hamiltonians), real matrices, and Hermitian matrices. For matrices written $H = L+W$, where $L$ is either a combinatorial or normalized graph Laplacian, each bound holds independently of any information about $W$ other than its class and the weighted Cheeger constant induced by its… CONTINUE READING

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