# A Rubik's Cube inspired approach to Clifford synthesis

arXiv: https://arxiv.org/abs/2307.08684 · HTML: https://mlsanity.com/paper/2307.08684/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 34 references that are in the map.
- First posted on arXiv 17 Jul 2023.

## Builds on (most cited first, 3 of 3)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Topological Quantum Compiling with Reinforcement Learning](https://mlsanity.com/paper/2004.04743/) (2020)
- [Improving Quantum Circuit Synthesis with Machine Learning](https://mlsanity.com/paper/2306.05622/) (2023)

## Abstract (arXiv)

The problem of decomposing an arbitrary Clifford element into a sequence of Clifford gates is known as Clifford synthesis. Drawing inspiration from similarities between this and the famous Rubik's Cube problem, we develop a machine learning approach for Clifford synthesis based on learning an approximation to the distance to the identity. This approach is probabilistic and computationally intensive. However, when a decomposition is successfully found, it often involves fewer gates than existing synthesis algorithms. Additionally, our approach is much more flexible than existing algorithms in that arbitrary gate sets, device topologies, and gate fidelities may incorporated, thus allowing for the approach to be tailored to a specific device.