Articles on Quantum Computing Quantum Finance

We talk to Chicago Quantum about picking stocks using a Quantum Computer and their new service

September 28, 2020

One of the first killer applications of quantum computing is optimization. No surprise that smart minds are looking at the intersection of Quantum and Finance. We spoke with Chicago Quantum who are driving innovation in Quantum Finance, by using the latest advances in Quantum technology to optimize stock portfolios.

QZ: Please tell us your genesis story How you began and why? Tell us a little about the team and their background.

Chicago Quantum began in December 2018 after a period of reflection. We attended the Chicago Quantum Exchange all-day sessions and began to understand the interest and potential of quantum computing to make a difference in academia, government, the IT supplier community, and for commercial enterprises. It could be the ‘next big thing’ and I decided to dedicate the next chapter of my career to quantum computing.

Our team is made up of academics, consultants and executives who share a passion for quantum computing, and who enjoy rolling up their sleeves and coding, working with clients, and learning. We are a diverse team with multiple backgrounds that work together. We have complementary skills and rely on each other.

QZ: Can you describe in one single sentence what Chicago Quantum does? Chicago Quantum picks stocks using quantum computing and classical algorithms and offers its expertise to consult commercial enterprise clients on quantum computing.

QZ: What is your company mission at Chicago Quantum? Our mission is to create meaningful employment for consultants in quantum computing while helping to promote economic productivity, social innovation, and security in the United States through the use of Quantum Computing.

QZ: You recently published work on portfolio optimization where you used a Quantum Computer to basically pick stocks. Can you explain what you did and why?

We focus on solving one specific problem. We select one stock portfolio based on analyzing the past year’s covariance and returns data using quantum computing and classical methods. We first run 40 stocks at one time, which is large but can be checked via brute force methods. We then run 60 stocks at one time, which is too large for brute force and requires advanced classical analytical methods to validate the quantum computer. Since those publications, we learn that the D-Wave Systems 2000Q (2017) quantum annealer can only run 64 stocks at one time, but the new system, the D-Wave Systems Advantage (2020) should be able to run more stocks.

We also push our classical algorithms, running 1,855 stocks in about an hour, and working to add a simulated bifurcator to our classical solver list. Our goal is to advance our classical methods to make quantum advantage as difficult to achieve as possible. We push the thinking on stock portfolio optimization using quantum and classical algorithms to enable a client application to pick stocks which is now live for client use on our website. What academics say is interesting is how we reformulate a decades-old method of selecting efficient stock portfolios to run on a quantum annealing computer.

QZ: Our understanding is that this is more a proof of principle, that there was no actual quantum advantage?

Algorithms deployed on a D-wave provided the basis for the underlying optimization using Quantum annealing.  We have not yet found quantum advantage when looking at the problem from the perspective of speed or quality of answers within a 64 stock scale. The quantum annealer is fast, but so are the classical methods. The answers are consistent as well, with the quantum annealer finding comparable answers based on the Chicago Quantum Net Score and acceptable answers based on the Sharpe Ratio. Since we published our last article pre-print, we increase the scale and speed of each classical algorithm. We also work to introduce a new classical solver, the simulated bifurcator, and to vary the order of the classical algorithms to further increase speed and scale. Our goal is to run all NYSE and NADSAQ-Q common stocks (about 3,200) at one time. If we can develop a quantum algorithm and method that can run 3,200 stocks, we can potentially find quantum advantage at this scale. Quantum advantage is in the eyes of the beholder. Our quantum annealer does find slightly different portfolios (e.g., 5 stocks vs. 3 stocks), and creates a group of attractive portfolios instead of one best portfolio, and this may create quantum advantage for some investors.

Comparing Portfolios picked from a Quantum Computer versus Classical
Comparing Portfolios picked from a Quantum Computer versus Classical

QZ: How does your work compare to classical portfolio optimization? It sounds like a combinatorics problem? Are there classical optimization routines which cut down the huge number of putative portfolios to go through or is it only brute force classically that you compare with?

During our 40 stock analysis, we compared the quantum algorithms against brute force, and a number of heuristic algorithms. We did this to validate the accuracy and precision of the quantum computer. It passed, and we could prove it classically via brute force. With 60 stocks, we rely on clever classical algorithms to quickly find acceptable and attractive portfolios, although maybe not the best portfolios, to compare to the quantum portfolios. Traditional portfolio optimization uses heuristic algorithms that also find these acceptable and attractive portfolios quickly. One difference is that Chicago Quantum is investing in writing proprietary code that may be different than those used by other data analytics firms and large quantitative trading firms. We all approach the problem using different methods, but all look to find acceptable answers quickly enough to take action in the real world markets.

QZ: Does this mean that we can select an even greater number of stocks to choose from for a portfolio?

Yes, this means that we can quickly evaluate a staggering number of stocks at one time to find an attractive portfolio. As we gain greater speed and scale, we can evaluate common stocks but maybe also fixed income securities, shorter-term trading strategies, and new means of factor analysis. Another interesting benefit of the Chicago Quantum Net Score is the fact that we can tune this model to account for market conditions, and the number of stocks a client ideally wants to hold.

QZ: Could we see Hedge funds and finance companies using these techniques to create portfolios soon or even consumers? Perhaps you could create a cloud based service for end users? 

Yes, we have selected this first research topic because there are commercial firms and individual investors that would potentially benefit from this work. This is one more form of trading discipline, the way to determine if a portfolio of stocks is efficient when looking at past risk and reward levels. It finds portfolios with stocks that zig while others zag, to potentially avoid drastic declines in portfolio value. We provide a remote service offering available via our website where clients pay for the service, send us their tickers, and we run then classically and on a quantum computer. We then write them a custom report of how their stocks and the system behaved, and the stocks recommended by each algorithm. In some cases, the algorithms largely agree while in others the client begins to understand any complexity in the evaluation of their stocks.

QZ: JP Morgan and other banks have people working on Quantum Computing applications, is Quantum Computing the next wave in Quantitative finance?

We know there is interest from the discussions we have had, both from regulators and financial institutions. This is a future technology that becomes more relevant as quantum technologies continue to advance. For example, for an investment manager that chooses between 64 stocks at one time, a quantum annealing computer provides another method to check their picks. It takes a few minutes to run and helps find gaps and issues. The investment manager likely already runs quantitative models using discrete mathematics (our classical methods), and likely at the scale that we are approaching (3,200 stocks at one time). The value comes from the new methods of analyzing stocks that are developed to take advantage of quantum processors. This is why banks are investigating this new technology…to climb a steep learning curve in quantum computing. Our work helps accelerate that climb.

QZ: Is there any portability to other types of device other than D-wave? Could the work be adapted to gate based technologies?

Yes, in theory this work can run on any technology that can accept a QUBO, or a quadratic unconstrained binary optimization problem. These include the Fujitsu Digital Annealer, the Toshiba Simulated Bifurcator, and any number of simulated annealers.

Running this analysis on a gate-based quantum computer will require a completely new formulation. The number of gates available to us is a limiting factor. Gate computers are on our future roadmap.

Jefferey Cohen from Chicago Quantum
Jeff Cohen from Chicago Quantum

QZ: Can you explain what happens “under the hood”? In terms of algorithms, processes and tools. Can people recreate this easily or will they need paid access to a Quantum Computer? 

The models are run in a cycle with a certain order.

  1. We validate the stocks to ensure we have complete data, and they match our entry criteria.
  2. We calculate the scores for all of the stocks to set a baseline.
  3. We run Markov Chain Monte Carlo and genetic algorithms.
  4. We run simulated annealers and other solvers.
  5. We run quantum algorithms (this requires an account and access to actual quantum computers).
  6. We run our quantum algorithms through the genetic algorithm.
  7. We then print the results from each method and select a ‘winning’ portfolio.
  8. We then write up a management report of the analysis and highlight interesting characteristics of the stocks or analysis.

The client analysis can be run on a modern personal computer, while the back-end system requires a quantum computer. We continuously introduce new quantum and classical solvers into this cycle to improve both the speed and scale of our solution.

QZ: Are there any spins-off from portfolio optimization to other areas of finance. What will you look at next?

We continue to find equity portfolio optimization a rich space for our research. However, we will rely on a paying client to decide where we next apply our models and capabilities. In that case, we may not be able to disclose our next project. However, we will continue to publish our work in portfolio optimization.

QZ: What was most surprising about your work on portfolio optimization?

We were surprised that the D-Wave Systems 2000Q (2017) quantum annealer could only support 64 stocks at one time. We thought we could modify our problem and stretch the quantum capability much further. The other surprise for us was the ability to scale our problem classically, with no end or plateau in sight. Our ability to code and understand the latest in discrete mathematical theory is what holds us back.

QZ: What is next for Chicago Quantum?

Simply put, we are ready to engage with clients and grow our consulting team and capabilities. We can engage by the transaction, via our online stock picking service. We can also engage in a project or advisory capacity with clients.

On a technical level, we add the simulated bifurcator to our classical solver set, we evaluate other capabilities to run our QUBO, and we research how quantum walks on graphs applies to financial services.


A big thanks to Jeff Cohen for being so open with us about the work he is doing with Chicago Quantum. It’s been a pleasure to have an interesting chat about ways in which Quantum Computing can be readily applied to current problems.

Perhaps in the future we’ll be using Chicago Quantum to pick a portfolio of IPO’d Quantum Technology stocks for a Quantum stock portfolio.

You can read more about Chicago Quantum’s research and find more from the portfolio optimization website. You can also see Jeff talk more about CQ on their YouTube channel.

Chicago Quantum is working at the intersection of Quantum Technology and Finance and building software for portfolio optimization.