Transfer learning of optimal QAOA parameters in combinatorial
  optimization
Solving combinatorial optimization problems (COPs) is a promising application
of quantum computation, with the Quantum Approximate Optimization Algorithm
(QAOA) being one of the most studied quantum algorithms for solving them.
However, multiple factors make the parameter search of the QAOA a hard
optimization problem. In this work, we study transfer learning (TL), a
methodology to reuse pre-trained QAOA parameters of one problem instance into
different COP instances. To this end, we select small cases of the traveling
salesman problem (TSP), the bin packing problem (BPP), the knapsack problem
(KP), the weighted maximum cut (MaxCut) problem, the maximal independent set
(MIS) problem, and portfolio optimization (PO), and find optimal $\beta$ and
$\gamma$ parameters for $p$ layers. We compare how well the parameters found
for one problem adapt to the others. Among the different problems, BPP is the
one that produces the best transferable parameters, maintaining the probability
of finding the optimal solution above a quadratic speedup for problem sizes up
to 42 qubits and p = 10 layers. Using the BPP parameters, we perform
experiments on IonQ Harmony and Aria, Rigetti Aspen-M-3, and IBM Brisbane of
MIS instances for up to 18 qubits. The results indicate IonQ Aria yields the
best overlap with the ideal probability distribution. Additionally, we show
that cross-platform TL is possible using the D-Wave Advantage quantum annealer
with the parameters found for BPP. We show an improvement in performance
compared to the default protocols for MIS with up to 170 qubits. Our results
suggest that there are QAOA parameters that generalize well for different COPs
and annealing protocols.
J. A. Montanez-Barrera Dennis Willsch Kristel Michielsen