The Expressive Power of Constrained QAOA: What You Might Have MISsed

arXiv:2609.18209 · quant-ph · Submitted 2026-09-16 · Read on arXiv

quant-ph

Submitted: 2026-09-16

Updated: 2026-09-16

Terminology

• Maximum Independent Set — 14× in this paper
• Hilbert Space — 13× in this paper · explained in 2 episodes
• Loss Function — 10× in this paper · explained in 2 episodes
• Quantum Approximate Optimization Algorithm — 6× in this paper
• Adjacency Matrix — 3× in this paper · explained in 1 episode
• Objective Function — 3× in this paper · explained in 2 episodes
• Quantum Circuits — 3× in this paper · explained in 2 episodes
• Trace — 3× in this paper · explained in 2 episodes
• Degeneracy — 2× in this paper · explained in 3 episodes
• Spectral Gap — 2× in this paper · explained in 5 episodes
• Adiabatic Evolution — 1× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Convergence Guarantees — 1× in this paper · explained in 3 episodes
• Phase Transitions — 1× in this paper · explained in 2 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes

Sources

• PennyLane: Automatic differentiation of hybrid quantum-classical computations
• Dynamical Lie Algebras Cannot Describe Shallow QAOA: Cragged Terrains, Barren Plateaus, and Empirical Hardness Models
• Independent sets and cuts in large-girth regular graphs
• A Quantum Approximate Optimization Algorithm
• Quantum Computation by Adiabatic Evolution
• Lower bounding the MaxCut of high girth 3-regular graphs using the QAOA
• The Quantum Approximate Optimization Algorithm Needs to See the Whole Graph: Worst Case Examples
• QAOA-MaxCut has barren plateaus for almost all graphs
• Reductions of QAOA Induced by Classical Symmetries: Theoretical Insights and Practical Implications
• Provable avoidance of barren plateaus for the Quantum Approximate Optimization Algorithm with Grover mixers

Related papers

• Reconquering Bell sampling on qudits: stabilizer learning and testing, quantum pseudorandomness bounds, and more
• Encrypted clones can leak: Classification of informative subsets in Quantum Encrypted Cloning
• Polynomial-time classical and quantum simulation of quantum impurity models
• Theory of quantum-enhanced interferometry with general Markovian light sources
• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
• Universal Bound and Phase Transition in Many-Body Fermionic Non-Gaussianity