Quantum Approximation Complexity of Classical Optimization Problems

arXiv:2610.09584 · quant-ph, cs.CC · Submitted 2026-10-07 · Read on arXiv

quant-ph, cs.CC

Submitted: 2026-10-07

Updated: 2026-10-07

Terminology

• Accuracy — 25× in this paper · explained in 1 episode
• BQP — 21× in this paper · explained in 2 episodes
• Certified Maximum Order — 6× in this paper
• Optimal Polynomial Intersection — 5× in this paper
• Combinatorial Optimization — 4× in this paper · explained in 2 episodes
• Verifier — 3× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Adaptation — 1× in this paper · explained in 1 episode
• Adiabatic Evolution — 1× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Consistency — 1× in this paper · explained in 3 episodes
• Decode — 1× in this paper · explained in 2 episodes
• Decoded Quantum Interferometry (DQI) — 1× in this paper · explained in 2 episodes
• Pauli Correlation Encoding (PCE) — 1× in this paper · explained in 2 episodes

Sources

• Challenges and Opportunities in Quantum Optimization
• A Quantum Approximate Optimization Algorithm
• From the Quantum Approximate Optimization Algorithm to a Quantum Alternating Operator Ansatz
• A quantum walk assisted approximate algorithm for bounded NP optimisation problems
• Improving Quantum Approximate Optimization by Noise-Directed Adaptive Remapping
• Quantum Approximate Optimization via Noise-Directed Adaptive Warm-Starting
• Iterative warm-start optimization with quantum imaginary time evolution
• Towards large-scale quantum optimization solvers with few qubits
• Quantum Approximate Optimization Algorithm for MaxCut: A Fermionic View
• MAXCUT QAOA performance guarantees for p >1
• Complexity Barriers to State Preparation in Quantum Approximate Optimization
• An in-principle super-polynomial quantum advantage for approximating combinatorial optimization problems via computational learning theory
• Quantum advantage for combinatorial optimization problems, Simplified
• Analytical Approach to Parallel Repetition
• Optimization by Decoded Quantum Interferometry
• The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model
• Lower bounding the MaxCut of high girth 3-regular graphs using the QAOA
• A quantum algorithm for computing the Carmichael function
• Verifiable Quantum Advantage via Optimized DQI Circuits
• A nearly linear-time Decoded Quantum Interferometry algorithm for the Optimal Polynomial Intersection problem

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• A convergent hierarchy of spectral gap certificates for qubit Hamiltonians
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