Theoretical approximation ratios for Warm-Started QAOA on 3-regular max-cut instances at depth p=1

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 a tilt angle θ, we consider warm-starts where the initial st...

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Bibliographic Details
Published in:Theoretical computer science Vol. 1059; p. 115571
Main Authors: Tate, Reuben, Eidenbenz, Stephan
Format: Journal Article
Language:English
Published: Elsevier B.V 04.01.2026
Subjects:
Combinatorial optimization
Max-Cut
Quantum approximate optimization algorithm
Quantum computing
Quantum computing
Quantum approximate optimization algorithm
Combinatorial optimization
Max-Cut
ISSN:0304-3975
Online Access:Get full text
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Summary: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 a tilt 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 tilt 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 tilt angle that yields a (worst-case) approximation ratio that simultaneously beats standard QAOA and the classical algorithm used to create the warm-start. Additionally, we show that at θ=60∘, warm-started QAOA is able to (effectively) recover the cut used to generate the warm-start, thus suggesting that in practice, this value could be a promising starting angle to explore alternate solutions in a heuristic fashion.
ISSN:0304-3975
DOI:10.1016/j.tcs.2025.115571