Train-and-Scaling the Quantum Alternating Operator Ansatz to Solve Portfolio Diversification

Low depth quantum circuits have widely studied limitations that impact their usefulness to solve optimization problems while training high depth quantum circuits from identity or random initialization are likely to be plagued by vanishing gradients in training. We propose a method, Train-and-Scale, that finds high quality parameters at smaller problem instances and then scales the depth of the quantum circuits as the size of instances considered is scaled up concurrently with repeated retraining. We test our approach on solving the Maximum Independent Set formulation of the Portfolio Diversification problem for assets selected from the SP500 and training on families of subgraphs generated from size 6 to size 30. Our results show high average quality solutions (with an average approximation ratio below 0.4 and small sampling complexities to find the best solution) with a modest increase of p-depth as the instance sizes are scaled up (p=54 for n=30).