# The Problem of Dynamic Programming on a Quantum Computer

arXiv: https://arxiv.org/abs/1906.02229 · HTML: https://mlsanity.com/paper/1906.02229/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2019.

## Built on by (most cited first, 2 of 2)

- [A Survey on Quantum Reinforcement Learning](https://mlsanity.com/paper/2211.03464/) (2022)
- [Quantum policy gradient algorithms](https://mlsanity.com/paper/2212.09328/) (2022)

## Abstract (arXiv)

We discuss the problem of finite-horizon dynamic programming (DP) on a quantum computer. We introduce a query model for studying quantum and classical algorithms for solving DP problems, and provide example oracle constructions for the travelling salesperson problem, the minimum set-cover problem, and the edit distance problem. We formulate open questions regarding quadratic quantum speedups for DP and discuss their implications. We then prove lower bounds for the query complexity of quantum algorithms and classical randomized algorithms for DP, and show that no greater-than-quadratic speedup can be achieved for solving DP problems.