Quantum Computing Application in Flow Distribution using QUBO modeling

This is an attempt to solve flow distribution modeling using Qubo Modeling technique, so as to run the algorithm on a Quantum Computer.

Motivation

Note: The underlying problem can be solved using other traditional techniques. Here the objective is to introduce Qubo modeling to solve this problem, and also to make us appreciate the Energy minimisation objective using science, which is difficult to appreciate in case of other resource optimisation problems in Business or other domains. Refer the great work done in this space, in the link below and my motivation to attempt such a problem

Problem Definition

Referring to the fig above, you can see 2 circuits, blue and brown. Assumption is, you are sending 100 units of flow through the inlet, and objective is to find the flow distribution across the 2 circuits i.e. how much flow will go through each circuit — blue and brown circuit respectively.

Constraints

Flow in blue and brown circuit should add up to 100 units.

Total resistance of the circuit should be minimum. Pressure drop across the 2 circuits should be equal

Find 2 equations at the bottom of the above figure, which will help you to meet the above 2 criteria/constraints and also adding the effort for each scenario and solving to minimize the overall effort or energy or resistance will lead to the desired solution. Find a screen shot of the same below.

Closing Notes

I have restricted the solution to find the optimum using the above 16 scenarios, but in actual practice you can run on much more scenarios to get close to the actual solution.

Also the circuit chosen is very simple as the objective is to explain the concept. We can have a much complicated circuit such as Membrane Panel of Boilers or a circuit to design water distribution pipeline in cities or….

If you want to learn something, well, explain it

— Richard Feynman

Explorer | Teacher | AI Consultant, CXO Advisory | 18 Patents | 2 International Publications | www.linkedin.com/in/irahulkharat |