Papers, ranked by score

Ordered by a blend of empirical rigor (60%) and math complexity (40%).

Optimal randomized multilevel Monte Carlo for repeatedly nested expectations

The estimation of repeatedly nested expectations is a challenging task that arises in many real-world systems. However, existing methods generally suffer from high computational costs when the number of nestings becomes large. Fix any non-negative integer $D$ for the total number of nestings. Standa

Lab Rats Math 8.5 Rigor 3 ·  January 10, 2023

Connecting Quantum Computing with Classical Stochastic Simulation

This tutorial paper introduces quantum approaches to Monte Carlo computation with applications in computational finance. We outline the basics of quantum computing using Grover’s algorithm for unstructured search to build intuition. We then move slowly to amplitude estimation problems and applicatio

Lab Rats Math 6.5 Rigor 4 ·  September 23, 2025

Optimal Quantum Speedups for Repeatedly Nested Expectation Estimation

We study the estimation of repeatedly nested expectations (RNEs) with a constant horizon (number of nestings) using quantum computing. We propose a quantum algorithm that achieves $\varepsilon$-error with cost $\tilde O(\varepsilon^{-1})$, up to logarithmic factors. Standard lower bounds show this s

Lab Rats Math 9 Rigor 1.5 ·  February 8, 2026

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