Efficient large-scale quantum optimization via counterdiabatic ansatz

Quantum approximate optimization algorithm (QAOA) is one of the fundamental variational quantum algorithms, while a version of QAOA that includes counterdiabatic driving, termed digitized counterdiabatic QAOA (DC-QAOA), is generally considered to outperform QAOA for all system sizes when the circuit depth for the two algorithms are held equal. Nevertheless, DC-QAOA introduces more cnot gates per layer, so the overall circuit complexity is a tradeoff between the number of cnot gates per layer and the circuit depth and must be carefully assessed. In this paper, we conduct a comprehensive comparison of DC-QAOA and QAOA on maxcut problem with the total number of cnot gates held equal, and we focus on one implementation of counterdiabatic terms using nested commutators in DC-QAOA, termed as DC-QAOA(NC). We have found that DC-QAOA(NC) reduces the overall circuit complexity as compared to QAOA only for sufficiently large problems, and for maxcut problem the number of qubits must exceed 16 for DC-QAOA(NC) to outperform QAOA. Additionally, we benchmark DC-QAOA(NC) against QAOA on the Sherrington-Kirkpatrick model under realistic noise conditions, finding that DC-QAOA(NC) exhibits significantly improved robustness compared to QAOA, maintaining higher fidelity as the problem size scales. Notably, in a direct comparison between one-layer DC-QAOA(NC) and three-layer QAOA where both use the same number of cnot gates, we identify an exponential performance advantage for DC-QAOA(NC), further signifying its suitability for large-scale quantum optimization tasks. We have further shown that this advantage can be understood from the effective dimensions introduced by the counterdiabatic driving terms. Moreover, based on our finding that the optimal parameters generated by DC-QAOA(NC) strongly concentrate in the parameter space, we have devised an instance-sequential training method for DC-QAOA(NC) circuits, which, compared to traditional methods, offers performance improvement while using even fewer quantum resources. Our findings provide a more comprehensive understanding of the advantages of DC-QAOA circuits and an efficient training method based on their generalizability.

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