Guarantees on Warm-Started QAOA: Single-Round Approximation Ratios for 3-Regular MAXCUT and Higher-Round Scaling Limits ...

• Main Authors: Tate, Reuben, Eidenbenz, Stephan
• Format: Report
• Language: unknown
• Published: arXiv 2024
• Subjects: Quantum Physics quant-ph; Data Structures and Algorithms cs.DS; Emerging Technologies cs.ET; Combinatorics math.CO; Optimization and Control math.OC; FOS Physical sciences; FOS Computer and information sciences; FOS Mathematics; South Pole; South pole
• Online Access: https://dx.doi.org/10.48550/arxiv.2402.12631; https://arxiv.org/abs/2402.12631

We generalize Farhi et al.'s 0.6924-approximation result technique of the Max-Cut Quantum Approximate Optimization Algorithm (QAOA) on 3-regular graphs to obtain provable lower bounds on the approximation ratio for warm-started QAOA. Given an initialization angle $θ$, we consider warm-starts where the initial state is a product state where each qubit position is angle $θ$ away from either the north or south pole of the Bloch sphere; of the two possible qubit positions the position of each qubit is decided by some classically obtained cut encoded as a bitstring $b$. We illustrate through plots how the properties of $b$ and the initialization angle $θ$ influence the bound on the approximation ratios of warm-started QAOA. We consider various classical algorithms (and the cuts they produce which we use to generate the warm-start). Our results strongly suggest that there does not exist any choice of initialization angle that yields a (worst-case) approximation ratio that simultaneously beats standard QAOA and the ...