# Differentiable Analog Quantum Computing for Optimization and Control

arXiv: https://arxiv.org/abs/2210.15812 · HTML: https://mlsanity.com/paper/2210.15812/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 73 references that are in the map.
- First posted on arXiv 28 Oct 2022.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [Stable Architectures for Deep Neural Networks](https://mlsanity.com/paper/1705.03341/) (2017)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [DiffTaichi: Differentiable Programming for Physical Simulation](https://mlsanity.com/paper/1910.00935/) (2019)
- [Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers](https://mlsanity.com/paper/2007.00016/) (2020)
- [Beyond Finite Layer Neural Networks: Bridging Deep Architectures and Numerical Differential Equations](https://mlsanity.com/paper/1710.10121/) (2017)
- [Dissecting Neural ODEs](https://mlsanity.com/paper/2002.08071/) (2020)
- [Learning to Control PDEs with Differentiable Physics](https://mlsanity.com/paper/2001.07457/) (2020)
- [A Differentiable Physics Engine for Deep Learning in Robotics](https://mlsanity.com/paper/1611.01652/) (2016)
- [gradSim: Differentiable simulation for system identification and visuomotor control](https://mlsanity.com/paper/2104.02646/) (2021)
- [Scalable Differentiable Physics for Learning and Control](https://mlsanity.com/paper/2007.02168/) (2020)
- [DiSECt: A Differentiable Simulation Engine for Autonomous Robotic Cutting](https://mlsanity.com/paper/2105.12244/) (2021)
- [DiffPD: Differentiable Projective Dynamics](https://mlsanity.com/paper/2101.05917/) (2021)
- [Fast and Feature-Complete Differentiable Physics for Articulated Rigid Bodies with Contact](https://mlsanity.com/paper/2103.16021/) (2021)
- [Efficient Differentiable Simulation of Articulated Bodies](https://mlsanity.com/paper/2109.07719/) (2021)
- [Differentiable Simulation of Soft Multi-body Systems](https://mlsanity.com/paper/2205.01758/) (2022)
- [DiffAqua: A Differentiable Computational Design Pipeline for Soft Underwater Swimmers with Shape Interpolation](https://mlsanity.com/paper/2104.00837/) (2021)
- [Resource-Efficient Quantum Computing by Breaking Abstractions](https://mlsanity.com/paper/2011.00028/) (2020)
- [On the Principles of Differentiable Quantum Programming Languages](https://mlsanity.com/paper/2004.01122/) (2020)
- [A Theory of Trotter Error](https://mlsanity.com/paper/1912.08854/) (2019)

## Built on by (most cited first, 4 of 4)

- [QuACK: Accelerating Gradient-Based Quantum Optimization with Koopman Operator Learning](https://mlsanity.com/paper/2211.01365/) (2022)
- [Efficient Quantum Algorithms for Quantum Optimal Control](https://mlsanity.com/paper/2304.02613/) (2023)
- [ResQ: A Novel Framework to Implement Residual Neural Networks on Analog Rydberg Atom Quantum Computers](https://mlsanity.com/paper/2506.21537/) (2025)
- [Differentiable Quantum Computing for Large-scale Linear Control](https://mlsanity.com/paper/2411.01391/) (2024)

## Abstract (arXiv)

We formulate the first differentiable analog quantum computing framework with a specific parameterization design at the analog signal (pulse) level to better exploit near-term quantum devices via variational methods. We further propose a scalable approach to estimate the gradients of quantum dynamics using a forward pass with Monte Carlo sampling, which leads to a quantum stochastic gradient descent algorithm for scalable gradient-based training in our framework. Applying our framework to quantum optimization and control, we observe a significant advantage of differentiable analog quantum computing against SOTAs based on parameterized digital quantum circuits by orders of magnitude.