Quantum-enhanced stochastic analysis - Chang, Derek Ding Cong (Nanyang Technological University, 2023)
The recent algorithm for quantum-enhanced analysis of discrete stochastic processes estimates expectation values of the random variables of a simulated process, achieving optimal sampling variance. In this paper, the algorithm was adapted to include a memory efficient unitary simulator acting step-wise. The construction of the unitary and its implementation on quantum circuits were demonstrated for the perturbed coin process. The algorithm was further expanded by implementing quantum amplitude estimation with maximum likelihood estimation post-processing. The required quantum circuit for this was also demonstrated. It was found that the original algorithm can be boosted with amplitude estimation to achieve lower estimation error. However, it requires a minimum query complexity and there is no clear quantum speedup in sampling convergence rate.