# Circuit Transformations for Quantum Architectures

arXiv: https://arxiv.org/abs/1902.09102 · HTML: https://mlsanity.com/paper/1902.09102/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Feb 2019.

## Built on by (most cited first, 6 of 6)

- [Qubit Routing using Graph Neural Network aided Monte Carlo Tree Search](https://mlsanity.com/paper/2104.01992/) (2021)
- [Challenges for Reinforcement Learning in Quantum Circuit Design](https://mlsanity.com/paper/2312.11337/) (2023)
- [TensorRL-QAS: Reinforcement learning with tensor networks for improved quantum architecture search](https://mlsanity.com/paper/2505.09371/) (2025)
- [Graph-Based Bayesian Optimization for Quantum Circuit Architecture Search with Uncertainty Calibrated Surrogates](https://mlsanity.com/paper/2512.09586/) (2025)
- [Computing Graph Edit Distance with Algorithms on Quantum Devices](https://mlsanity.com/paper/2111.10183/) (2021)
- [AI Methods for Permutation Circuit Synthesis Across Generic Topologies](https://mlsanity.com/paper/2509.16020/) (2025)

## Abstract (arXiv)

Quantum computer architectures impose restrictions on qubit interactions. We propose efficient circuit transformations that modify a given quantum circuit to fit an architecture, allowing for any initial and final mapping of circuit qubits to architecture qubits. To achieve this, we first consider the qubit movement subproblem and use the routing via matchings framework to prove tighter bounds on parallel routing. In practice, we only need to perform partial permutations, so we generalize routing via matchings to that setting. We give new routing procedures for common architecture graphs and for the generalized hierarchical product of graphs, which produces subgraphs of the Cartesian product. Secondly, for serial routing, we consider the token swapping framework and extend a 4-approximation algorithm for general graphs to support partial permutations. We apply these routing procedures to give several circuit transformations, using various heuristic qubit placement subroutines. We implement these transformations in software and compare their performance for large quantum circuits on grid and modular architectures, identifying strategies that work well in practice.