# Efficient Quantum Algorithms for Quantum Optimal Control

arXiv: https://arxiv.org/abs/2304.02613 · HTML: https://mlsanity.com/paper/2304.02613/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 52 references that are in the map.
- First posted on arXiv 5 Apr 2023.

## Builds on (most cited first, 9 of 9)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [A Short Note on Concentration Inequalities for Random Vectors with SubGaussian Norm](https://mlsanity.com/paper/1902.03736/) (2019)
- [Theory of overparametrization in quantum neural networks](https://mlsanity.com/paper/2109.11676/) (2021)
- [A Mean-Field Optimal Control Formulation of Deep Learning](https://mlsanity.com/paper/1807.01083/) (2018)
- [SGD Converges to Global Minimum in Deep Learning via Star-convex Path](https://mlsanity.com/paper/1901.00451/) (2019)
- [The power of block-encoded matrix powers: improved regression techniques via faster Hamiltonian simulation](https://mlsanity.com/paper/1804.01973/) (2018)
- [Time-dependent Hamiltonian simulation with L1-norm scaling](https://mlsanity.com/paper/1906.07115/) (2019)
- [Differentiable Analog Quantum Computing for Optimization and Control](https://mlsanity.com/paper/2210.15812/) (2022)

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

- [Differentiable Quantum Computing for Large-scale Linear Control](https://mlsanity.com/paper/2411.01391/) (2024)

## Abstract (arXiv)

In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time T, where the system is governed by a time-dependent Schr"odinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schr"odinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.