aiqbench analysis
This paper argues that QAOA, a gate-based variational algorithm, and quantum annealing are closely related: QAOA circuit angles converge to universal annealing trajectories, and both act as cooling protocols for sampling from pseudo-Boltzmann distributions. For readers, the useful takeaway is a unified way to reason about how resources like circuit depth or annealing time translate into effective temperature and sampling quality, with the cooling-power scaling (coldest QAOA temperature roughly proportional to 1/p) giving a concrete benchmark. The results are theoretical and simulation-based, so they should be read as a framework for understanding near-term optimization hardware rather than evidence of practical advantage.
Universal resources for quantum approximate optimization algorithm and quantum annealing
arXiv:2506.03241v3 Announce Type: replace Abstract: The Quantum Approximate Optimization Algorithm (QAOA) is a variational ansatz that resembles the Trotterized dynamics of a Quantum Annealing (QA) protocol. This work formalizes this connection formally and empirically, showing the angles of a multilayer QAOA circuit converge to universal QA trajectories. Furthermore, the errors in both QAOA circuits and QA paths act as thermal excitations in pseudo-Boltzmann probability distributions whose temperature decreases with the invested resource -- i.e. integrated angles or total time -- and which in QAOA also contain a higher temperature arising from the Trotterization. This also means QAOA and QA are cooling protocols and simulators of partition functions whose target temperature can be tuned by rescaling the universal trajectory. The average cooling power of both methods exhibits favorable algebraic scalings with respect to the target temperature and problem size, whereby in QAOA the coldest temperature is inversely proportional to the number of layers, $T\sim 1/p$, and to the integrated angles -- or integrated interactions in QA.
Abstract:The Quantum Approximate Optimization Algorithm (QAOA) is a variational ansatz that resembles the Trotterized dynamics of a Quantum Annealing (QA) protocol. This work formalizes this connection formally and empirically, showing the angles of a multilayer QAOA circuit converge to universal QA trajectories. Furthermore, the errors in both QAOA circuits and QA paths act as thermal excitations in pseudo-Boltzmann probability distributions whose temperature decreases with the invested resource -- i.e. integrated angles or total time -- and which in QAOA also contain a higher temperature arising from the Trotterization. This also means QAOA and QA are cooling protocols and simulators of partition functions whose target temperature can be tuned by rescaling the universal trajectory. The average cooling power of both methods exhibits favorable algebraic scalings with respect to the target temperature and problem size, whereby in QAOA the coldest temperature is inversely proportional to the number of layers, $T\sim 1/p$, and to the integrated angles -- or integrated interactions in QA.
12 pages, 9 Figures. Title updated to reflect journal version
Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech)
arXiv:2506.03241 [quant-ph]
(or arXiv:2506.03241v3 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2506.03241 Focus to learn more arXiv-issued DOI via DataCite
Phys. Rev. Research 8, 013211 (2026)
https://doi.org/10.1103/hxv2-sbr7 Focus to learn more DOI(s) linking to related resources
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Full text under the publisher's open licence · 281 words
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