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“Current Feasibility of Quantum Computing Algorithms for Direct Numerical Simulation”
Presented by DANIEL VELEZ
(Adviser: Prof. Gretar Tryggvason)
Recent advances in quantum computing, such as demonstrated quantum supremacy by Google for a quantum problem, indicate the potential for polynomial to exponential improvement over the best classical algorithms for solving systems of linear equations. In this study, we investigated two well-known quantum computing algorithms for solving systems of linear equations: the Harrow, Hassidim, and Lloyd (HHL) algorithm, and the Variational Quantum Linear Solver (VQLS) algorithm. Apart from current hardware limitations, by applying these algorithms to linear systems of equations representing real, physical phenomena, we have determined that inherent aspects of both the HHL and VQLS algorithm currently prevent efficient usage. In particular, the HHL algorithm, which is primarily based on the Quantum Phase Estimation algorithm is error bounded by the condition number of the matrices involved, which grows exponentially as the domain resolution approaches usable values. For non-trivial linear systems, the VQLS algorithm may require an approximately exponential increase in computational complexity to minimize the associated classical cost function.
“Interpretation of Measurements in Separated High-Speed Boundary Layers”
Presented by BRETT TILLMAN
(Adviser: Prof. Tamer Zaki)
Research interest in hypersonic flight has increased dramatically during the past decade due to its importance to space and national security applications. In this flow regime, flight vehicles are subjected to extreme conditions and the integrity of the vehicle is highly dependent on the state of very thin boundary layers which are sensitive to environmental disturbances in flight. Unfortunately, these disturbances are constantly changing and extremely difficult to measure in a wind tunnel or during a flight test in real time. While direct numerical simulations can be used to predict the flow response to a known disturbance, they must be augmented with data assimilation techniques in order to determine the environmental disturbances from limited measurements. Our recent work on ensemble-variational (EnVar) data assimilation demonstrated that we can accurately decode the signals of wall-pressure sensors in transitional boundary layers at Mach 4.5 and predict the entire flow field (Buchta & Zaki, J. Fluid Mechanics 2021). However, it is not clear whether shocks that interact with the boundary layer causing local separation can undermine the prediction accuracy. As a first step, we examine the impact of the shock on the dynamics of the instability waves in a boundary layer developing along a 5-degree compression ramp at Mach 4.5. The resulting compression shock leads to mild separation that modulates the oncoming instability waves. Future work will contrast the interpretability of sensors upstream and downstream of separation onset and examine in detail the domain of dependence of the sensors.