# Pauli Network Circuit Synthesis with Reinforcement Learning

arXiv: https://arxiv.org/abs/2503.14448 · HTML: https://mlsanity.com/paper/2503.14448/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Quantum reinforcement learning, one of 15 directions in Deep reinforcement learning methods.
- Builds on 7 of its 26 references that are in the map.
- First posted on arXiv 18 Mar 2025.

## Placed in

- Deep reinforcement learning methods / [Quantum reinforcement learning](https://mlsanity.com/deeprl/quantum-reinforcement-learning/)

## Builds on (most cited first, 7 of 7)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Curriculum Learning for Reinforcement Learning Domains: A Framework and Survey](https://mlsanity.com/paper/2003.04960/) (2020)
- [Practical and efficient quantum circuit synthesis and transpiling with Reinforcement Learning](https://mlsanity.com/paper/2405.13196/) (2024)
- [Best Approximate Quantum Compiling Problems](https://mlsanity.com/paper/2106.05649/) (2021)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [Relaxed Peephole Optimization: A Novel Compiler Optimization for Quantum Circuits](https://mlsanity.com/paper/2012.07711/) (2020)
- [Synthesizing efficient circuits for Hamiltonian simulation](https://mlsanity.com/paper/2209.03478/) (2022)

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

- [Optimizing the non-Clifford-count in unitary synthesis using Reinforcement Learning](https://mlsanity.com/paper/2509.21709/) (2025)
- [AI Methods for Permutation Circuit Synthesis Across Generic Topologies](https://mlsanity.com/paper/2509.16020/) (2025)

## Abstract (arXiv)

We introduce a Reinforcement Learning (RL)-based method for re-synthesis of quantum circuits containing arbitrary Pauli rotations alongside Clifford operations. By collapsing each sub-block to a compact representation and then synthesizing it step-by-step through a learned heuristic, we obtain circuits that are both shorter and compliant with hardware connectivity constraints. We find that the method is fast enough and good enough to work as an optimization procedure: in direct comparisons on 6-qubit random Pauli Networks against state-of-the-art heuristic methods, our RL approach yields over 2x reduction in two-qubit gate count, while executing in under 10 milliseconds per circuit. We further integrate the method into a collect-and-re-synthesize pipeline, applied as a Qiskit transpiler pass, where we observe average improvements of 20% in two-qubit gate count and depth, reaching up to 60% for many instances, across the Benchpress benchmark. These results highlight the potential of RL-driven synthesis to significantly improve circuit quality in realistic, large-scale quantum transpilation workloads.