 After considerable deliberation...we went ahead and became subscribers and clients to Value Line. Looking forward to learning how our stock picks compare to theirs.
Check back for more insights! Symmetric matrices, or upper-triangular matrices? How to build them and where to use them.4/16/2021 Good morning! It's Friday, April 16, 2021 and we have been working to improve our performance on the D-Wave Systems quantum and simulated annealer, as well as in their TABU multistart solver.
One of the challenges is to load your problem into a matrix, since that is the only way you have of feeding your problem into many of the quantum, or quantum-inspired solvers. A full, symmetrical matrix has the same values above and below the main diagonal. Huh? The main diagonal has the same row and column: (0,0) (1,1) (2,2) all the way to the end (n,n). The positions above it have columns that are higher than the rows, and they look like (0,1), (1,2), (3,100) to (n-1,n). So, if you print it out, it looks like the half the matrix is filled in with the values you want, and the bottom half is either blank, or zero. A symmetric matrix has values you want above and below the main diagonal, but they are the same values, just reversed. So, (0,1) has the same value as (1,0), and they straddle the diagonal at positions (0,0) and (1,1). To boost performance of our solvers, I stripped the wood down to the core...took off all the paint and resanded it. I have been rebuilding our matrices to fit each solver. In other words, recoding the whole exercise. The D-Wave Systems Advantage 1.1 requires an upper-triangular matrix. I used to feed a lower triangular matrix to the solver (duh!) and the solver would convert that matrix into a BQM, or a binary quadratic model that the solver could use. It should work better now. But what about the classical solvers (the simulated annealer and TABU sampler)? "I heard it from a friend, who, heard it from a friend, who..." Journey. Ok, I heard that Microsoft Azure Quantum works best with a full, symmetric matrix, so we are now working to feed those two solvers a full symmetric matrix. Now, there are other questions. The symmetric matrix has the same values as the upper triangular, and if the matrix calculations occur as I think they will, they will overcount and overstate the energy state of the solution. So, now we have to ensure we modify the values of the full matrix to get the same answer, the same energy levels. More work to do. If you have experience working with solvers and matrices, and want to help out, please drop me a line or give me a call. Oh, and to make matters even more challenging, the D-Wave Systems solvers require you to convert your matrix into a dictionary {(i,j): value} which poses its own challenges. Been working through those as well. Good luck today for those in the research side of the business, and those in the financial markets. Be safe out there, and have great success. BTW, I found out that Fred Glover invented / discovered the Tabu sampler, and have been reading one of his papers on it. I know Fred, he is a great guy, and works with a terrific team based at the University of Colorado helping clients solve analytical problems. Here is a link to his 1999 paper on Research Gate: https://www.researchgate.net/publication/220693571_Tabu_search_I Tabu search I, by Fred Glover and Manuel Laguna
These stocks are likely more similar to the stocks in NYSE American...smaller and more innovative.
Interested in adding these into the comparison? Please leave your answers in the comments below, or email Jeffrey Cohen at jeffrey@quantum-usaci.com. Thanks |
Jeff CohenStrategic IT Management Consultant with a strong interest in Quantum Computing. Consulting for 29 years and this looks as interesting as cloud computing was in 2010. Archives
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