# Quarl: A Learning-Based Quantum Circuit Optimizer

arXiv: https://arxiv.org/abs/2307.10120 · HTML: https://mlsanity.com/paper/2307.10120/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 17 Jul 2023.

## Builds on (most cited first, 10 of 10)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Asynchronous Methods for Deep Reinforcement Learning](https://mlsanity.com/paper/1602.01783/) (2016)
- [Reinforcement learning for optimization of variational quantum circuit architectures](https://mlsanity.com/paper/2103.16089/) (2021)
- [Qubit Routing using Graph Neural Network aided Monte Carlo Tree Search](https://mlsanity.com/paper/2104.01992/) (2021)
- [A Verified Optimizer for Quantum Circuits](https://mlsanity.com/paper/1912.02250/) (2019)
- [Synthesizing Quantum-Circuit Optimizers](https://mlsanity.com/paper/2211.09691/) (2022)
- [Quanto: Optimizing Quantum Circuits with Automatic Generation of Circuit Identities](https://mlsanity.com/paper/2111.11387/) (2021)
- [Quartz: Superoptimization of Quantum Circuits (Extended Version)](https://mlsanity.com/paper/2204.09033/) (2022)

## Built on by (most cited first, 10 of 10)

- [A Primer on Quantum Machine Learning](https://mlsanity.com/paper/2511.15969/) (2025)
- [A Reinforcement Learning Environment for Directed Quantum Circuit Synthesis](https://mlsanity.com/paper/2401.07054/) (2024)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [Optimizing ZX-Diagrams with Deep Reinforcement Learning](https://mlsanity.com/paper/2311.18588/) (2023)
- [AltGraph: Redesigning Quantum Circuits Using Generative Graph Models for Efficient Optimization](https://mlsanity.com/paper/2403.12979/) (2024)
- [Automated Design and Optimization of Distributed Filtering Circuits via Reinforcement Learning](https://mlsanity.com/paper/2402.14236/) (2024)
- [Quantum Circuit Pre-Synthesis: Learning Local Edits to Reduce T-count](https://mlsanity.com/paper/2601.19738/) (2026)
- [Reinforcement Learning for Adaptive Composition of Quantum Circuit Optimisation Passes](https://mlsanity.com/paper/2601.21629/) (2026)
- [Transpiler Autotuning with Predictive Models for Quantum Circuit Optimization](https://mlsanity.com/paper/2607.29145/) (2026)
- [Bridge of Psi's: Quantum Circuit Optimization with Schr"odinger Bridges](https://mlsanity.com/paper/2609.25947/) (2026)

## Abstract (arXiv)

Optimizing quantum circuits is challenging due to the very large search space of functionally equivalent circuits and the necessity of applying transformations that temporarily decrease performance to achieve a final performance improvement. This paper presents Quarl, a learning-based quantum circuit optimizer. Applying reinforcement learning (RL) to quantum circuit optimization raises two main challenges: the large and varying action space and the non-uniform state representation. Quarl addresses these issues with a novel neural architecture and RL-training procedure. Our neural architecture decomposes the action space into two parts and leverages graph neural networks in its state representation, both of which are guided by the intuition that optimization decisions can be mostly guided by local reasoning while allowing global circuit-wide reasoning. Our evaluation shows that Quarl significantly outperforms existing circuit optimizers on almost all benchmark circuits. Surprisingly, Quarl can learn to perform rotation merging, a complex, non-local circuit optimization implemented as a separate pass in existing optimizers.