Quick note while writing an article

Sitting here writing our 2nd research article preprint to be published to arXiv by September 1, 2020.

A few key observations to share:
1.  We are getting very good at having D-Wave find valid, attractive answers.  During one run, I think it found the 'ideal' solution.  
2.  We struggle to get D-Wave to solve the problem when we have many assets.  This is due to the structure of the problem.  More assets means smaller variance and covariance terms for each stock.  Those small values are harder for an energy based analog system to find. By way of analogy, the D-Wave is like a rock climber and the wall has portions for each asset size.  At 20 assets, the hand-holds are large and easy to grab.  At 40 assets, they are more challenging.  Only an expert can grab hold.  At 60 assets, those hand-holds are maybe fingernail sized.  We may have to reformulate the problem at 80 assets again to make large portfolios easier to solve for.
3.  We have raised the bar by custom coding both a genetic algorithm and simulated annealer that solve the classical problem (finding one ideal solution per universe) in 10 - 20 seconds.  We also use a simulated annealer solver from D-Wave that solves the 60 asset problem in 11 seconds.
4.  We created a new way of using a random number generator to execute a Monte Carlo random strategy.  This one works really well.  We send a relatively small number of random portfolios to be scored, and we send them for each number of assets.  So, for 60 assets we query (N=1,2,3,4,.....56, 57, 58, 59) assets.  This helps us to see if the answer is at the tails (very small or very large portfolios) and we can then focus on those asset sizes.  In the case of our current sample, our random, fat-tailed Monte Carlo analysis finds the optimal answer in just over 220,000 trials.
We are eager to try 80 or more assets on the D-Wave quantum annealer.  Look for updates once we complete our current 60 asset paper.

Jeffrey Cohen, President, US Advanced Computing Infrastructure, Inc.
​August 7, 2020