English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The sum-of-squares (SoS) hierarchy is a powerful technique based onsemi-definite programming that can be used for both classical and quantumoptimization problems. This hierarchy goes under several names; in particular,in quantum chemistry it is called the reduced density matrix (RDM) method. Weconsider the ability of this hierarchy to reproduce weak coupling perturbationtheory for three different kinds of systems: spin (or qubit) systems, bosonicsystems (the anharmonic oscillator), and fermionic systems with quarticinteractions. For such fermionic systems, we show that degree-$4$ SoS (called$2$-RDM in quantum chemsitry) does not reproduce second order perturbationtheory but degree-$6$ SoS ($3$-RDM) does (and we conjecture that it reproducesthird order perturbation theory). Indeed, we identify a fragment of degree-$6$SoS which can do this, which may be useful for practical quantum chemicalcalculations as it may be possible to implement this fragment with less costthan the full degree-$6$ SoS. Remarkably, this fragment is very similar to onestudied by Hastings and O'Donnell for the Sachdev-Ye-Kitaev (SYK) model.

Perturbation Theory and the Sum of Squares