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.
Highlights
Recent technological advances have led to a large number of implementations [1,2,3,4] of so-called Noisy Intermediate-Scale Quantum (NISQ) devices [5]
The fact that TQA initialization converges to a good minimum for the range of times T ∈ [Tm∗ in, Tm∗ ax], see Fig. 4, suggests that this algorithm has a high tolerance towards imperfections in determining the value of δt
In addition to practical NISQ algorithms, our finding suggest a previously unknown connection between the quantum approximate optimization algorithm (QAOA) at relatively small circuit depth and quantum annealing
Summary
Recent technological advances have led to a large number of implementations [1,2,3,4] of so-called Noisy Intermediate-Scale Quantum (NISQ) devices [5]. We explore the observation that Trotterization of unitary evolution in quantum annealing provides a particular choice of parameters for the QAOA [6] This leads us to introduce a one-parameter family of Trotterized quantum annealing (TQA) initializations for QAOA, controlled by the time step or, equivalently, total time used in adiabatic evolution. The central result of our work is the demonstration that TQA initialization for QAOA gives comparable performance to the search over an exponentially scaling number of random initializations To this end, we establish that TQA initialization leads to convergence of the QAOA to a nearly optimal minimum for a certain range of time steps, see Fig. 1(c) for visualization. More recent work proposed quantum annealing inspired initialization strategies for the so-called ‘bang-bang’ modification of the QAOA [21] that corresponds to large circuit depths.
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