Solving partial differential equations on near-term quantum computers

Understand

In this work, we obtain the numerical temperature field to a thermally developing fluid flow inside parallel plates problem with a quantum computing method.

• The physical problem deals with the heat transfer of a steady state, hydrodinamically developed and thermally developing fluid flow inside two parallel plates channel subjected to a prescribed constant heat flux.
• Its solution is formulated numerically with Finite Differences method, where a sequence of linear systems must be solved in order to determine the complete temperature field.
• Such linear systems are written as discrete unconstrained optimization problems with floating points being approximated using binary variables and solved using near-term quantum heuristics.