Quantum annealing initialization of the quantum approximate optimization algorithm

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.

Wasserstein Solution Quality and the Quantum Approximate Optimization Algorithm: A Portfolio Optimization Case Study

“…Given the large spread of η over different cold-start repeats of the optimization, it is clear that many local minima exist in the cost landscape, especially for soft constraints. This supports current research directions related to global minimization [91] and warm-starting [35,87]. Using the WD (W), we were able to provide insights into how quantum computational difficulty scales with increasing n and p having identified the existence of critical p-values where the solution quality of n and n ± 1 intersect.…”

“…Since the large spread in η suggests that random initialization is not a good approach (as has been suggested in other works [13,86]), we must look to other angle initialization schemes. Some recent approaches include: encoding the solution of the continuous relaxation of the problem into the initial state [35], using a quantum annealing inspired initialization [87], initializing the p + 1 ansätz with the level p angles [86], using optimal anzätze from similar problems [88] and machine learning approaches [89,90]. To further mitigate the influence of local minima, various techniques have been suggested including: standard basin hopping, coupling the cost landscape with a classical neural network [91] or using the quantum natural gradient [92,93].…”

Quantum annealing with trigger Hamiltonians: Application to 2-satisfiability and nonstoquastic problems

“…This mechanism is also observed in the quantum approximate optimization algorithm (QAOA) with intermediate p levels for MaxCut problems if the optimal parameters are interpreted as the scheme for quantum annealing [44]. In general, using the scheme for quantum annealing as the initialization parameters for the QAOA can be advantageous for its performance [45,46] and, similarly, using the optimal parameters from the QAOA as the annealing scheme for quantum annealing can enhance the success probability for short annealing times.…”

Quantum Alternating Operator Ansatz (QAOA) Phase Diagrams and Applications for Quantum Chemistry

“…A more detailed comparison of the methods would require finding optimal adiabatic and optimal QAOA schedules. In the context of optimization there is a close connection between optimal QAOA parameters and smooth adiabatic schedules [10,28,35,36], showing conditions under which optimal schedules exist composed of "bang-bang" and "annealing" regimes, as well as the connection to counteradiabatic effects for suppressing excitations [37]. Cases where there are relatively few free parameters may be especially amenable to generalizations of our phase diagram approach.…”

“…. , p. Similar linear schedules are frequently used for QAOA in optimization settings [18,21,[25][26][27][28].…”