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Quantum computers are increasing in size and quality, but are still verynoisy. Error mitigation extends the size of the quantum circuits that noisydevices can meaningfully execute. However, state-of-the-art error mitigationmethods are hard to implement and the limited qubit connectivity insuperconducting qubit devices restricts most applications to the hardware'snative topology. Here we show a quantum approximate optimization algorithm(QAOA) on non-planar random regular graphs with up to 40 nodes enabled by amachine learning-based error mitigation. We use a swap network with carefuldecision-variable-to-qubit mapping and a feed-forward neural network todemonstrate optimization of a depth-two QAOA on up to 40 qubits. We observe ameaningful parameter optimization for the largest graph which requires runningquantum circuits with 958 two-qubit gates. Our work emphasizes the need tomitigate samples, and not only expectation values, in quantum approximateoptimization. These results are a step towards executing quantum approximateoptimization at a scale that is not classically simulable. Reaching such systemsizes is key to properly understanding the true potential of heuristicalgorithms like QAOA.

Large-scale quantum approximate optimization on non-planar graphs with machine learning noise mitigation