Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm

• URL: http://arxiv.org/abs/2206.03579v2
• Date: Tue, 25 Jul 2023 17:27:39 GMT
• Title: Sampling Frequency Thresholds for Quantum Advantage of Quantum Approximate Optimization Algorithm
• Authors: Danylo Lykov, Jonathan Wurtz, Cody Poole, Mark Saffman, Tom Noel, Yuri Alexeev
• Abstract summary: We compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers. We find that classical solvers are capable of producing high-quality approximate solutions in linear time complexity. Other problems, such as different graphs, weighted MaxCut, maximum independent set, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices.
• Score: 0.7046417074932257
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we compare the performance of the Quantum Approximate Optimization Algorithm (QAOA) with state-of-the-art classical solvers such as Gurobi and MQLib to solve the combinatorial optimization problem MaxCut on 3-regular graphs. The goal is to identify under which conditions QAOA can achieve "quantum advantage" over classical algorithms, in terms of both solution quality and time to solution. One might be able to achieve quantum advantage on hundreds of qubits and moderate depth $p$ by sampling the QAOA state at a frequency of order 10 kHz. We observe, however, that classical heuristic solvers are capable of producing high-quality approximate solutions in linear time complexity. In order to match this quality for $\textit{large}$ graph sizes $N$, a quantum device must support depth $p>11$. Otherwise, we demonstrate that the number of required samples grows exponentially with $N$, hindering the scalability of QAOA with $p\leq11$. These results put challenging bounds on achieving quantum advantage for QAOA MaxCut on 3-regular graphs. Other problems, such as different graphs, weighted MaxCut, maximum independent set, and 3-SAT, may be better suited for achieving quantum advantage on near-term quantum devices.

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