Today's noisy intermediate-scale quantum (NISQ) machines offer few (10's/100's) of noisy qubits. Hence, gate-based circuits must be narrow (short width) and shallow (short depth). To utilize such machines, hybrid quantum-classical algorithms are being pursued. The flagship example is the variational quantum algorithm (VQA) where a quantum computer (QC) is used to prepare a parameterized quantum circuit ansatz (trial solution). Measurements are made by the QC to determined a cost function that encodes the solution to the problem. The parameter vector of the ansatz is then updated using a classical computer via standard optimization techniques. Examples of this include the variational quantum eigensolver (VQE) for quantum chemistry, quantum approximate optimization algorithm (QAOA) for combinatorial optimization, and variational quantum linear solver (VQLS) for linear algebra. In this study, we focus on VQLS for solving linear systems of algebraic equations Ax=b since it is a key subroutine in many Computational Fluid Dynamic (CFD) solvers. Specifically, to reduce noise associated with gate-based quantum circuits, a novel pulse-level ansatz (PANSATZ) is employed. Our previous work using VQE for quantum chemistry has shown significant reductions in circuit latency resulting in improved accuracy. Issues related to converting a CFD relevant problem, such as Burgers' equation, to a linear system and mapping the result to VQLS, as well as issues related to limitations associated with the accessibility of the quantum state solution are discussed.