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.
The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: Worst Case Examples
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
abstract
The Quantum Approximate Optimization Algorithm can be applied to search problems on graphs with a cost function that is a sum of terms corresponding to the edges. When conjugating an edge term, the QAOA unitary at depth p produces an operator that depends only on the subgraph consisting of edges that are at most p away from the edge in question. On random d-regular graphs, with d fixed and with p a small constant time log n, these neighborhoods are almost all trees and so the performance of the QAOA is determined only by how it acts on an edge in the middle of tree. Both bipartite random d-regular graphs and general random d-regular graphs locally are trees so the QAOA's performance is the same on these two ensembles. Using this we can show that the QAOA with $(d-1)^{2p} < n^A$ for any $A<1$, can only achieve an approximation ratio of 1/2 for Max-Cut on bipartite random d-regular graphs for d large. For Maximum Independent Set, in the same setting, the best approximation ratio is a d-dependent constant that goes to 0 as d gets big.
representative citing papers
Global Annealing Monte Carlo with ML global moves plus local updates outperforms Simulated Annealing and is more robust than Population Annealing on 3D Ising spin glasses without hyperparameter tuning.
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.
Optimization-free Recursive QAOA solves the Binary Paint Shop Problem near-optimally with reduced quantum resources and robustness to parameter choice compared to standard QAOA.
Classical solvers solve random Ising models on heavy-hex graphs efficiently, with Gurobi showing linear or weakly quadratic scaling up to 100k variables and simulated annealing showing exponential time-to-solution without cubic terms.
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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Demonstrating Real Advantage of Machine-Learning-Enhanced Monte Carlo for Combinatorial Optimization
Global Annealing Monte Carlo with ML global moves plus local updates outperforms Simulated Annealing and is more robust than Population Annealing on 3D Ising spin glasses without hyperparameter tuning.
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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.
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Optimisation-Free Recursive QAOA for the Binary Paint Shop Problem
Optimization-free Recursive QAOA solves the Binary Paint Shop Problem near-optimally with reduced quantum resources and robustness to parameter choice compared to standard QAOA.
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Classical Combinatorial Optimization Scaling for Random Ising Models on 2D Heavy-Hex Graphs
Classical solvers solve random Ising models on heavy-hex graphs efficiently, with Gurobi showing linear or weakly quadratic scaling up to 100k variables and simulated annealing showing exponential time-to-solution without cubic terms.