New stock picks using the Chicago Quantum Net Score (classical methods)

Updated: September 16, 2020 with market results

This story is for those who want to see how we pick stocks…and what stocks we pick. On Friday, August 28, 2020, we evaluated 64 US liquid equities. We ran them through these classical methods:

1. Monte Carlo (94 seconds, fat-tailed method, custom code)

2. Genetic Algorithm (24 seconds, 80 generations, 80 parents, custom code)

3. Simulated Annealer (50 seconds, custom code)

4. D-Wave Quantum Annealer (1 run, ~1 millisecond of programing / compute time)

Our three ‘custom coded’ classical methods all picked the same four or five stocks out of 64. So, here we share our second public portfolio using our Chicago Quantum Net Score (CQNS) method:

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System output for selected classical methods
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System output for D-Wave Quantum Annealer method

The way to read the chart below is to compare the results of 930K Monte Carlo samples, the Genetic Algorithm runs, and the quantum annealing runs. The red dots come close to the efficient frontier, but in fact it was a blue dot that was selected for this portfolio.

It is important to note that this quantum annealing run took 100 micro seconds plus programming time, which comes to approximately a few milliseconds against 24 seconds for the genetic algorithm.

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System output comparing Monte Carlo, Genetic Algorithm (intermediate & final), and Quantum Annealer solutions

We have the best answer from our Genetic Algorithm, as defined by the smallest (or most negative) CQNS score of -0.002009. We also have three of those stocks selected by the D-Wave quantum annealer.

We have one additional stock (Twitter) selected by the Simulated Annealer and the D-Wave QA, and three additional stocks selected by the D-Wave QA. However, those stocks brought the quality of the solution down, and will be ignored.

In the end, the Genetic Algorithm found the best solution, and will define the portfolio selected this time.

Our CQNS portfolio is AXP, CHTR, QFIN, and WBT

64 stock dataset: [‘ADBE’, ‘IBM’, ‘ORCL’, ‘AXP’, ‘BA’, ‘BABA’, ‘BAC’, ‘BRK-B’, ‘BX’, ‘CCK’, ‘CHNG’, ‘CHTR’, ‘CNC’, ‘CLR’, ‘CNX’, ‘CPRT’, ‘DHR’, ‘DIS’, ‘DK’, ‘EL’, ‘ESTC’, ‘FB’, ‘FSLY’, ‘GE’, ‘GILD’, ‘GOLD’, ‘GOOG’, ‘GSK’, ‘HLT’, ‘INTC’, ‘JD’, ‘JNJ’, ‘LB’, ‘LNG’, ‘MSFT’, ‘MO’, ‘AZN’, ‘NIO’, ‘NVDA’, ‘NWL’, ‘PAYX’, ‘PFE’, ‘PK’, ‘QFIN’, ‘RACE’, ‘REGN’, ‘ROP’, ‘ROST’, ‘SBUX’, ‘SERV’, ‘SHW’, ‘SNE’, ‘MRO’, ‘SNY’, ‘STMP’, ‘TAK’, ‘TSLA’, ‘UAL’, ‘UBER’, ‘VALE’, ‘VIPS’, ‘W’, ‘WBT’, ‘TWTR’]

We will track this stock portfolio and update this Medium Article with results over time.

A few things changed from the last portfolio selected by Chicago Quantum.

  1. Due to the recent run-up of the stock market, we raised the power factor in the CQNS (alpha + 1 in our first paper), from 3 to 4. This more evenly balances the risk and return of the portfolios, and increases portfolio size.
  2. We incorporated a ceiling on individual stock index returns for the historical data. We set that ceiling to 17.5% per annum return.
  3. We do not incorporate three of the D-Wave solvers (D-Wave Simulated Annealer, D-Wave Hybrid Sampler, and D-Wave TABU Sampler) in the go-forward solution.
  4. We increased our stocks analyzed to 64 from 60. This required us to create three ways to embed the problem on the D-Wave quantum annealer. We were able to run using ‘EmbeddingComposite’, ‘LazyFixedEmbeddingComposite’ and ‘FixedEmbeddingComposite.’ This gives us greater control over the embedding of the problem on the qubits.

Market Results on September 16, 2020

We checked the market performance of these 64 stocks against our CQNS portfolio, and the S&P 500. Our CQNS portfolio declined more in a declining market. The benchmark of 64 stocks was down 2.80% vs. a drop of 3.36% for the CQNS portfolio of 4 stocks. In conclusion, we can build quantitative models and run them classically and on quantum computers. We still have analysis and research ahead of us to create the goose that lays golden eggs (although we continue to try).

A few things to note.

We are not taking positions in, nor trading in these stocks. We are still in Research and Development mode. This formulation is subject to change without notice.

For more information, please check our research at Research Gate, email us at, or visit us at

Jeffrey Cohen, President of US Advanced Computing Infrastructure, Inc., & founder of Chicago Quantum (SM). We use quantum algorithms & our quantum platform

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