# Quantum algorithms: A survey of applications and end-to-end complexities

**Authors:** Alexander M. Dalzell, Sam McArdle, Mario Berta, Przemyslaw Bienias, Chi-Fang Chen, András Gilyén, Connor T. Hann, Michael J. Kastoryano, Emil T. Khabiboulline, Aleksander Kubica, Grant Salton, Samson Wang, Fernando G. S. L. Brandão  
**arXiv:** [2310.03011](https://arxiv.org/abs/2310.03011)  
**Date:** 2023-10-04  
**Summary page:** https://www.summarizepaper.com/en/arxiv-id/2310.03011v1/

## Key points

- Survey explores potential applications of quantum algorithms in various fields
- Fields include quantum chemistry, many-body physics, optimization, finance, and machine learning
- Challenges and opportunities highlighted in each application area
- Comparison of quantum solutions to classical methods and complexity-theoretic limitations
- Modular structure facilitates navigation with bibliography and hyperlinks
- Importance of incorporating quantum error correction and fault tolerance in implementing algorithms
- Assessing benefits of quantum computing can be challenging due to technical details
- Comprehensive survey provides detailed analysis of potential applications with technical caveats
- Resource for researchers and practitioners interested in understanding capabilities and limitations of quantum computing.

## Summary

This survey explores the potential applications of quantum algorithms and their underlying algorithmic primitives in various fields such as quantum chemistry, many-body physics, optimization, finance, and machine learning. The authors highlight the challenges and opportunities in each application area by defining the problems being solved, specifying the input-output model, instantiating all "oracles," and considering hidden costs. They also compare quantum solutions to state-of-the-art classical methods and complexity-theoretic limitations to evaluate possible quantum speedups. The survey is structured in a modular, wiki-like fashion to facilitate navigation. Each section discusses a specific primitive or application area independently and includes a bibliography of references as well as embedded hyperlinks that direct readers to other relevant sections. This structure mirrors complex quantum algorithms that involve multiple layers of abstraction and allows for quick evaluation of how altering subroutines impacts end-to-end complexities. The authors emphasize the importance of incorporating methods for quantum error correction and fault tolerance when implementing overall quantum algorithms on hardware. They acknowledge that assessing the extent to which a particular application benefits from quantum computing can be challenging due to intricate technical details about the underlying primitives and their complexities. Overall, this comprehensive survey provides a detailed analysis of potential applications for quantum algorithms while considering technical caveats and subtleties. It serves as an invaluable resource for researchers and practitioners interested in understanding the capabilities and limitations of quantum computing in various domains.