Quantum enhanced rare event discovery and sampling

2026-06-04

AI Summary

This work addresses the challenge of efficiently sampling rare events—such as financial crashes or cascading failures—which are difficult to capture using conventional methods due to their extremely low probability and lack of prior knowledge about their characteristics. The authors propose a novel quantum algorithm capable of automatically discovering and sampling such events without requiring any prior information. By integrating optimal quantum search with entropy rate analysis, the method achieves a quadratic speedup relative to the rarity threshold in heavy-tailed distributions and a polynomial speedup governed by the entropy rate structure in stationary stochastic processes. This approach substantially reduces data acquisition costs and represents the first demonstration of quantum sampling for rare events in the absence of prior knowledge.

Abstract

Financial crashes, cascading failures in infrastructure, and critical errors in AI systems are frequently triggered by events that occur with extremely small probability. Efficiently discovering and sampling events with probability below a threshold is therefore of critical interest. Yet this task is highly non-trivial using existing classical or quantum methods. Being rare, such events require an immense sampling overhead to collect sufficient data samples. Moreover, because the rare events are not known in advance, they cannot be flagged for amplification using standard techniques. Here, we introduce a quantum algorithm for rare-event discovery and sampling without first learning which events are rare. The algorithm achieves the optimal quantum scaling with the rarity threshold. We further demonstrate that this can achieve a quadratic speedup for heavy-tailed systems whose tail has nonvanishing total mass, and translates into a robust polynomial speedup for stationary stochastic processes, with the exponent determined by its entropy-rate structure.

Problem

• rare event
• quantum sampling
• probability threshold
• heavy-tailed systems
• stochastic processes

Innovation

• quantum algorithm
• rare event sampling
• quadratic speedup
• heavy-tailed distributions
• entropy-rate