Quantum Amplitude Estimation for Investment Risk

Quantum amplitude estimation is the algorithm quantitative-finance research keeps proposing for pricing derivatives and stress-testing portfolios: instead of drawing millions of independent samples to estimate the probability of a rare event — say, a portfolio loss crossing a Value-at-Risk threshold — it rotates a quantum state by a fixed angle per oracle call and reads the rotation back with phase estimation, converging as 1/M instead of Monte Carlo's 1/√N. This simulator renders that Grover rotation as a literal 3D spiral: each step climbs one level and sweeps the state vector around a circle whose "good" wedge is sized to the true event probability you set, while a parallel classical Monte Carlo run accumulates real Bernoulli draws so you can watch both error bars shrink side by side and read off exactly how many classical samples it would take to match the quantum estimator's current precision.