# Quantum enhanced rare event discovery and sampling

arXiv: https://arxiv.org/abs/2606.06316 · HTML: https://mlsanity.com/paper/2606.06316/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 54 references that are in the map.
- First posted on arXiv 4 Jun 2026.

## Builds on (most cited first, 10 of 10)

- [A Baseline for Detecting Misclassified and Out-of-Distribution Examples in Neural Networks](https://mlsanity.com/paper/1610.02136/) (2016)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [A Comprehensive Survey on Rare Event Prediction](https://mlsanity.com/paper/2309.11356/) (2023)
- [Distributional property testing in a quantum world](https://mlsanity.com/paper/1902.00814/) (2019)
- [Nonlinear transformation of complex amplitudes via quantum singular value transformation](https://mlsanity.com/paper/2107.10764/) (2021)
- [Efficient phase-factor evaluation in quantum signal processing](https://mlsanity.com/paper/2002.11649/) (2020)
- [Wavefunction Flows: Efficient Quantum Simulation of Continuous Flow Models](https://mlsanity.com/paper/2510.08462/) (2025)
- [On distributionally robust extreme value analysis](https://mlsanity.com/paper/1601.06858/) (2016)
- [Accelerating Inference for Multilayer Neural Networks with Quantum Computers](https://mlsanity.com/paper/2510.07195/) (2025)

## Built on by (most cited first, 1 of 1)

- [Scalable quantum simulation of continuous-time generative models via tensor networks](https://mlsanity.com/paper/2608.21700/) (2026)

## Abstract (arXiv)

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.