# Differentiable Quantum Programming with Unbounded Loops

arXiv: https://arxiv.org/abs/2211.04507 · HTML: https://mlsanity.com/paper/2211.04507/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 72 references that are in the map.
- First posted on arXiv 8 Nov 2022.

## Builds on (most cited first, 16 of 16)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [An overview of gradient descent optimization algorithms](https://mlsanity.com/paper/1609.04747/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Parameterized quantum circuits as machine learning models](https://mlsanity.com/paper/1906.07682/) (2019)
- [Efficient Learning for Deep Quantum Neural Networks](https://mlsanity.com/paper/1902.10445/) (2019)
- [Stochastic gradient descent for hybrid quantum-classical optimization](https://mlsanity.com/paper/1910.01155/) (2019)
- [Learning to Transduce with Unbounded Memory](https://mlsanity.com/paper/1506.02516/) (2015)
- [Differentiable Programs with Neural Libraries](https://mlsanity.com/paper/1611.02109/) (2016)
- [Demystifying Differentiable Programming: Shift/Reset the Penultimate Backpropagator](https://mlsanity.com/paper/1803.10228/) (2018)
- [Correctness of Automatic Differentiation via Diffeologies and Categorical Gluing](https://mlsanity.com/paper/2001.02209/) (2020)
- [A Simple Differentiable Programming Language](https://mlsanity.com/paper/1911.04523/) (2019)
- [λS: Computable Semantics for Differentiable Programming with Higher-Order Functions and Datatypes](https://mlsanity.com/paper/2007.08017/) (2020)
- [Q#: Enabling scalable quantum computing and development with a high-level domain-specific language](https://mlsanity.com/paper/1803.00652/) (2018)
- [Towards Verified Stochastic Variational Inference for Probabilistic Programs](https://mlsanity.com/paper/1907.08827/) (2019)
- [Automatic Differentiation in PCF](https://mlsanity.com/paper/2011.03335/) (2020)
- [On the Principles of Differentiable Quantum Programming Languages](https://mlsanity.com/paper/2004.01122/) (2020)

## Abstract (arXiv)

The emergence of variational quantum applications has led to the development of automatic differentiation techniques in quantum computing. Recently, Zhu et al. (PLDI 2020) have formulated differentiable quantum programming with bounded loops, providing a framework for scalable gradient calculation by quantum means for training quantum variational applications. However, promising parameterized quantum applications, e.g., quantum walk and unitary implementation, cannot be trained in the existing framework due to the natural involvement of unbounded loops. To fill in the gap, we provide the first differentiable quantum programming framework with unbounded loops, including a newly designed differentiation rule, code transformation, and their correctness proof. Technically, we introduce a randomized estimator for derivatives to deal with the infinite sum in the differentiation of unbounded loops, whose applicability in classical and probabilistic programming is also discussed. We implement our framework with Python and Q#, and demonstrate a reasonable sample efficiency. Through extensive case studies, we showcase an exciting application of our framework in automatically identifying close-to-optimal parameters for several parameterized quantum applications.