# Perturbation Theory and the Sum of Squares

@inproceedings{Hastings2022PerturbationTA, title={Perturbation Theory and the Sum of Squares}, author={Matthew B. Hastings}, year={2022} }

The sum-of-squares (SoS) hierarchy is a powerful technique based on semi-deﬁnite programming that can be used for both classical and quantum optimization problems. This hierarchy goes under several names; in particular, in quantum chemistry it is called the reduced density matrix (RDM) method. We consider the ability of this hierarchy to reproduce weak coupling perturbation theory for three diﬀerent kinds of systems: spin (or qubit) systems, bosonic systems (the anharmonic oscil-lator), and…

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