Investigating Implementation Challenges of Quantum Amplitude Amplification using a Traffic Signal Quadratic Unconstrained Binary Optimization Problem

Optimization plays a key role in many real-life applications, but computational limitations often force problem simplification or the use of suboptimal solutions, leading to diminished performance. When searching for a way to mitigate this, quantum amplitude amplification (QAA) is appealing because it offers both the potential to reduce computation time and yield optimal solutions under certain conditions. However, these conditions are unknown and often problem-dependent. Several important factors determine whether QAA is successful, including the number of QAA iterations and the value of the objective function scaling parameter. Currently, finding these values involves performing exhaustive classical QAA simulations and selecting the best outcome, which is not a viable strategy for real-life application of QAA. This work seeks to connect these unknown parameters to a realistic problem involving the optimization of vehicle traffic, formulated as a quadratic unconstrained binary optimization (QUBO) problem, to develop strategies for how QAA could be implemented. After outlining the QUBO traffic simulation, we discuss how trends and patterns in the parameter space can be exploited to allow us to find values that work well without classical precalculation. We also consider the efficient use of QAA iterations, and we show strategies of selecting parameters and implementing QAA in a way where the algorithm is successful over a range of traffic configurations.