The dynamics of a droplet on an inclined plane containing a chemical step, implying a heterogeneity in the wettability, have been widely studied because of their relevance to many applications. However, the modeling of such dynamics remains inaccurate due to the lack of implementation of contact angle hysteresis. In this work, we implement a chemical potential wetting boundary condition that includes hysteresis in a well-balanced lattice Boltzmann simulation to address that specific shortcoming. We investigate the behavior of droplet dynamics including this hysteresis force, and subsequently, also probe the effects of chemical step strength, inclination angle, and droplet volume on the droplet dynamics. We observe that the dynamics at the leading and the trailing edges of the droplet are significantly impacted by hysteresis effects and the chemical step strength. In addition, we conclude that for varying inclination angles, the hysteresis contribution is comparable to other contributing forces in the precise manipulation of the droplet.

Efficiently mapping quantum circuits onto hardware is integral for the quantum compilation process, wherein a circuit is modified in accordance with a quantum processor’s connectivity. Many techniques currently exist for solving this problem, wherein SWAP-gate overhead is usually prioritized as a cost metric. We reconstitute quantum circuit mapping using tools from quantum information theory, showing that a lower bound, which we dub the lightcone bound, emerges for a circuit executed on hardware. We also develop an initial placement algorithm based on graph similarity search, aiding us in optimally placing circuit qubits onto a device. 600 realistic benchmarks using the IBM Qiskit compiler and a brute-force method are then tested against the lightcone bound, with results unambiguously verifying the veracity of the bound, while permitting trustworthy estimations of minimal overhead in near-term realizations of quantum algorithms. This work constitutes the first use of quantum circuit uncomplexity to practically-relevant quantum computing.