Approximate stochastic localization plus conductance transfers yield a weak Poincaré inequality for the SK model at β < 1/2, enabling efficient Glauber sampling from a warm start.
MAXCUT QAOA performance guarantees for p >1
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abstract
We obtain worst case performance guarantees for $p=2$ and $3$ QAOA for MAXCUT on uniform 3-regular graphs. Previous work by Farhi et al obtained a lower bound on the approximation ratio of $0.692$ for $p=1$. We find a lower bound of $0.7559$ for $p=2$, where worst case graphs are those with no cycles $\leq 5$. This bound holds for any 3 regular graph evaluated at particular fixed parameters. We conjecture a hierarchy for all $p$, where worst case graphs have with no cycles $\leq 2p+1$. Under this conjecture, the approximation ratio is at least $0.7924$ for all 3 regular graphs and $p=3$. In addition, using a simple indistinguishability argument we find an upper bound on the worst case approximation ratio for all $p$, which indicates classes of graphs for which there can be no quantum advantage for at least $p<6$.
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CONDITIONAL 2representative citing papers
Systematic numerical study of QAOA parameter transfer on heavy-hex Ising models with local cubic terms shows transferred angles from small instances yield improving expectation values up to 49 layers on instances up to 156 qubits, with hardware runs confirming gains up to p=10.
citing papers explorer
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Weak Poincar\'e Inequalities via Approximate Stochastic Localization: Application to Sampling the Sherrington-Kirkpatrick Model
Approximate stochastic localization plus conductance transfers yield a weak Poincaré inequality for the SK model at β < 1/2, enabling efficient Glauber sampling from a warm start.
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Evaluating the Limits of QAOA Parameter Transfer at High-Rounds on Sparse Ising Models With Geometrically Local Cubic Terms
Systematic numerical study of QAOA parameter transfer on heavy-hex Ising models with local cubic terms shows transferred angles from small instances yield improving expectation values up to 49 layers on instances up to 156 qubits, with hardware runs confirming gains up to p=10.