See the Medium article here:

https://medium.com/@cohen.sourcing/what-happened-when-we-tried-to-run-72-stocks-on-the-quantum-annealer-d93bfdd6c94c

Will be updating this Medium Article as we learn more.  DM me for a 'friend' link with Medium.

Jeffrey Cohen, President, US Advanced Computing Infrastructure Inc.  August 20, 2020

Good news.  We submitted our article to arXiv yesterday.  Should publish Friday.  
arXiv:submit/3330970 [cs.DM] 19 Aug 2020 

What did we learn?
1.  Today's stock pickers can use either the D-Wave quantum annealer (2048 qubits), or classical methods to optimize a 60 stock universe (with 1 year of historical data). Our custom coded Genetic Algorithm found the 'ideal' portfolio in 7 seconds...and all take under a minute of computation time. 

2.  Our Chicago Quantum Net Score is a reformulation of the traditional Sharpe ratio and is used to pick efficient equity portfolios.  It seems to work well.  It quickly picks portfolios on the Efficient Frontier (return / risk).  It runs well on the D-Wave quantum annealer and in classical solvers too.

An efficient frontier is the top of a set of portfolios (highest return for each level of risk).  The upper points are either yellow, red or blue.
The yellow dots are the efficient frontier with our Monte Carlo analysis (fat-tailed, & discrete distribution around N/2).  We ran over 200K samples, and picked from every asset size.  It picked the 'ideal' portfolio.
The red dots are picked by the quantum computer.
The blue dots are picked by our genetic algorithm (random seed).

3.  We can successfully analyze 60 stocks at a time.  What might stop us from running 100 at once?
We find two challenges:
a) We are running out of room on the quantum computer (we use 1,700 qubits out of 2,048).
b) Our variance terms get very small when we choose larger portfolios (e.g., 55 stocks out of 60).  

The good news is that D-Wave has a new quantum annealer with over 5,000 qubits (more room to grow), and we continue to research and learn new methods for larger portfolios.

We will let you know when our article is available on arXiv in a comment to this post.

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

Hello and good morning,
On Monday August 3, 2020 we published the results of our first 'published' portfolios.  Our 'ideal' CQNS portfolio delivered 13% returns over the 3 week measurement period vs. 4% for the benchmark.

​As a reminder, we are selecting from a set of 60 liquid, US equities.  We created a Python script so we can test these 5 portfolios anytime.  

The best, optimal 60 asset portfolio according to CQNS was two stocks, AMP (Ameriprise) and APA (Apache).  Those two stocks returned 13% during the measurement period.  This compares favorably to the benchmarks of all 60 stocks, and the S&P 500 during the period.

Our two generalized portfolios produced by the quantum annealing computer, which were selected to pick the highest CQNS, with a high CQR, and the highest CQR, with a high CQNS, did not perform as well as the benchmark of 60 stocks they were chosen from.

As a disclosure, we have not taken positions in any of the portfolios mentioned in this research.  

Our goal is to complete our 60 asset engineering (*we have 8 items left), and publish another article (preprint) on arXiv in August 2020.  After that, we will scale up again to evaluate more assets at a time.

Jeffrey Cohen, founder of Chicago Quantum and President, US Advanced Computing Infrastructure, Inc.  August 4, 2020.  For more information, please see the detailed articles (in the buttons below):