# Recursive Methods for Synthesizing Permutations on Limited-Connectivity Quantum Computers

arXiv: https://arxiv.org/abs/2207.06199 · HTML: https://mlsanity.com/paper/2207.06199/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jul 2022.

## Built on by (most cited first, 1 of 1)

- [Optimizing the non-Clifford-count in unitary synthesis using Reinforcement Learning](https://mlsanity.com/paper/2509.21709/) (2025)

## Abstract (arXiv)

We describe a family of recursive methods for the synthesis of qubit permutations on quantum computers with limited qubit connectivity. Two objectives are of importance: circuit size and depth. In each case we combine a scalable heuristic with a non-scalable, yet exact, synthesis. Our algorithms are applicable to generic connectivity constraints, scale favorably, and achieve close-to-optimal performance in many cases. We demonstrate the utility of these algorithms by optimizing the compilation of Quantum Volume circuits, and to disprove an old conjecture on reversals being the hardest permutation on a path.