**Accurate simulations of many flows **of scientific and engineering interest are among the most computationally demanding applications in scientific computing In the algorithms considered in the present work, **the flow state** is defined through a **multi-qubit [[Register]]** and the circuit-model approach to quantum computing is followed, i.e. **single- and multi-qubit gates** are acting to mofidy **the state of the quantum system**. For an n-qubit system, a 2^n state-vector of complex numbers results when modeled on a conventional computer. This exponential growth of the required memory to store the state vector has motivated the development of a quantum computer simulator suitable for parallel computation on distributed-memory computers, such that algorithms with a significant number of qubits (e.g. ≥ 30) can be solved without memory limitations.