Hybrid Quantum-Classical Pressure Solvers in CFD with Classiq’s VQLS

Timothy Edward Pearson, Alexandre Gallardo

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Overview

This project explores the use of Variational Quantum Linear Solvers (VQLS) for simplified CFD pressure solves. The implementation is done within the Classiq framework, leveraging its tools for constructing quantum circuits, variational ansatz, and block-encoded Hamiltonians. The focus is on replacing the classical Poisson linear solver with a quantum-enhanced solver, benchmarking its performance and accuracy on small, controlled systems.

We currently simulate small linear systems $Ax = b$, where A is represented as a combination of Pauli operators and b is a simple superposition vector.

For more details on the implementation and parameter optimization workflow, see [Classiq VQLS with LCU: Classical Part - Finding Optimal Parameters](https://docs.classiq.io/latest/explore/algorithms/vqls/lcu_vqls/vqls _with_lcu/#classical-part-finding-optimal-parameters).

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