About the author:
Daniel is co-founder and CTO at Aqarios GmbH. He holds a M.Sc. in Computer Science from LMU Munich, and has published papers in reinforcement learning. He writes about technical topics in quantum computing.
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# Aesthetics of Scheduling QUBOs

This post is more of an appreciation post for quantum annealing and its aesthetics (and not much of a scientific one). We do lots of experiments at Aqarios involving a large number of different optimization problems and their QUBO representation. Most of them have one thing in common - the beautiful patterns of certain orders. We humans love patterns so so much. Patterns give us a sense of order. Since order gives predictability, which gives a sense of control, we all deep down love order.

For instance, check out this very interesting series of job shop scheduling QUBOs. From top to bottom, the QUBO sizes vary in 50, 100, 200 and 300.

I won't comment on the patterns itself, but the series is interesting - one can see how increasing the parameter T (which in job shop scheduling controls the strict upper time bound when all jobs should be finished) dilutes the contraints. The next series shows nurse scheduling QUBOs with the same size variation as in the job shop scheduling example.

I'd like to highlight the dilution again. Though, one most note, that the very distinct white diagonals stay in the same position. The last series is one that I find the most amazing. This is satellite scheduling, and especially the lower sizes show this beautiful pattern that reminds me of a light ray.

While this wasn't one of my usual scientific or business related posts, I still think it is nice to sometimes take a step back and just observe the beauty of nature and logic.

My deep thanks goes to our prolific QC expert Michael Lachner for generating those illustrations.

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