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

TL;DR

This paper demonstrates a machine learning-based error mitigation technique enabling the execution of quantum approximate optimization algorithms on non-planar graphs with up to 40 nodes, overcoming hardware connectivity limitations and noise issues.

Contribution

It introduces a novel combination of swap networks and neural network error mitigation to perform QAOA on larger, non-native topologies, advancing scalable quantum optimization.

Findings

Successful optimization of a depth-two QAOA on 40 qubits

Mitigation of noise allowing meaningful parameter tuning on large graphs

Demonstrated execution of circuits with 958 two-qubit gates

Abstract

Quantum computers are increasing in size and quality, but are still very noisy. Error mitigation extends the size of the quantum circuits that noisy devices can meaningfully execute. However, state-of-the-art error mitigation methods are hard to implement and the limited qubit connectivity in superconducting qubit devices restricts most applications to the hardware's native topology. Here we show a quantum approximate optimization algorithm (QAOA) on non-planar random regular graphs with up to 40 nodes enabled by a machine learning-based error mitigation. We use a swap network with careful decision-variable-to-qubit mapping and a feed-forward neural network to demonstrate optimization of a depth-two QAOA on up to 40 qubits. We observe a meaningful parameter optimization for the largest graph which requires running quantum circuits with 958 two-qubit gates. Our work emphasizes the need to mitigate samples, and not only expectation values, in quantum approximate optimization. These results are a step towards executing quantum approximate optimization at a scale that is not classically simulable. Reaching such system sizes is key to properly understanding the true potential of heuristic algorithms like QAOA.