Quantum annealing initialization of the quantum approximate optimization algorithm

Stefan H. Sack and Maksym Serbyn

IST Austria, Am Campus 1, 3400 Klosterneuburg, Austria

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Abstract

The quantum approximate optimization algorithm (QAOA) is a prospective near-term quantum algorithm due to its modest circuit depth and promising benchmarks. However, an external parameter optimization required in QAOA could become a performance bottleneck. This motivates studies of the optimization landscape and search for heuristic ways of parameter initialization. In this work we visualize the optimization landscape of the QAOA applied to the MaxCut problem on random graphs, demonstrating that random initialization of the QAOA is prone to converging to local minima with sub-optimal performance. We introduce the initialization of QAOA parameters based on the Trotterized quantum annealing (TQA) protocol, parameterized by the Trotter time step. We find that the TQA initialization allows to circumvent the issue of false minima for a broad range of time steps, yielding the same performance as the best result out of an exponentially scaling number of random initializations. Moreover, we demonstrate that the optimal value of the time step coincides with the point of proliferation of Trotter errors in quantum annealing. Our results suggest practical ways of initializing QAOA protocols on near-term quantum devices and reveals new connections between QAOA and quantum annealing.

The Quantum Approximate Optimization Algorithm (QAOA) is among the most promising near-term algorithms due to its modest hardware requirements and promising benchmarks. In this algorithm, a quantum computer is used to implement a variational ansatz, which is optimized in a feedback loop with a classical computer to find an approximate solution for a discrete classical optimization problem. The optimization landscape is however characterized by an exponentially scaling number of local optima, which could lead to a potential performance bottleneck. To address this issue we propose a novel, efficient initialization technique of the QAOA based on Trotterized Quantum Annealing. Our initialization achieves, within a single optimization run, a performance comparable to the best out of an exponentially scaling number of random initializations. Our results open the door for more time-efficient practical implementations of the QAOA on NISQ devices and inspire future research that could lead to a better understanding of the inner workings of the QAOA.

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Cited by

[1] V. Akshay, D. Rabinovich, E. Campos, and J. Biamonte, "Parameter concentrations in quantum approximate optimization", Physical Review A 104 1, L010401 (2021).

[2] Jonathan Wurtz and Peter J. Love, "Counterdiabaticity and the quantum approximate optimization algorithm", arXiv:2106.15645.

[3] Vrinda Mehta, Fengping Jin, Hans De Raedt, and Kristel Michielsen, "Quantum Annealing with Trigger Hamiltonians: Application to 2-SAT and Nonstoquastic Problems", arXiv:2106.04864.

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