# Optimal Layout Synthesis for Quantum Circuits as Classical Planning (full version)

arXiv: https://arxiv.org/abs/2304.12014 · HTML: https://mlsanity.com/paper/2304.12014/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 40 references that are in the map.
- First posted on arXiv 24 Apr 2023.

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

- [Qubit Mapping and Routing via MaxSAT](https://mlsanity.com/paper/2208.13679/) (2022)
- [Optimality Study of Existing Quantum Computing Layout Synthesis Tools](https://mlsanity.com/paper/2002.09783/) (2020)
- [Optimal Layout Synthesis for Quantum Computing](https://mlsanity.com/paper/2007.15671/) (2020)
- [Comparing and Integrating Constraint Programming and Temporal Planning for Quantum Circuit Compilation](https://mlsanity.com/paper/1803.06775/) (2018)
- [A Hardware-Aware Heuristic for the Qubit Mapping Problem in the NISQ Era](https://mlsanity.com/paper/2010.03397/) (2020)
- [Classical Planning as QBF without Grounding (extended version)](https://mlsanity.com/paper/2106.10138/) (2021)
- [Planning for Compilation of a Quantum Algorithm for Graph Coloring](https://mlsanity.com/paper/2002.10917/) (2020)

## Built on by (most cited first, 7 of 7)

- [Learning to rank quantum circuits for hardware-optimized performance enhancement](https://mlsanity.com/paper/2404.06535/) (2024)
- [Optimal Layout-Aware CNOT Circuit Synthesis with Qubit Permutation](https://mlsanity.com/paper/2408.04349/) (2024)
- [Optimal Layout Synthesis for Deep Quantum Circuits on NISQ Processors with 100+ Qubits](https://mlsanity.com/paper/2403.11598/) (2024)
- [CNOT-Optimal Clifford Synthesis as SAT](https://mlsanity.com/paper/2504.00634/) (2025)
- [Depth-Optimal Quantum Layout Synthesis as SAT](https://mlsanity.com/paper/2506.06752/) (2025)
- [Two Constraint Compilation Methods for Lifted Planning](https://mlsanity.com/paper/2511.10164/) (2025)
- [A 12-CNOT Double Qubit Excitation Gate](https://mlsanity.com/paper/2608.11733/) (2026)

## Abstract (arXiv)

In Layout Synthesis, the logical qubits of a quantum circuit are mapped to the physical qubits of a given quantum hardware platform, taking into account the connectivity of physical qubits. This involves inserting SWAP gates before an operation is applied on distant qubits. Optimal Layout Synthesis is crucial for practical Quantum Computing on current error-prone hardware: Minimizing the number of SWAP gates directly mitigates the error rates when running quantum circuits. In recent years, several approaches have been proposed for minimizing the required SWAP insertions. The proposed exact approaches can only scale to a small number of qubits. Proving that a number of swap insertions is optimal is much harder than producing near optimal mappings. In this paper, we provide two encodings for Optimal Layout Synthesis as a classical planning problem. We use optimal classical planners to synthesize the optimal layout for a standard set of benchmarks. Our results show the scalability of our approach compared to previous leading approaches. We can optimally map circuits with 9 qubits onto a 14 qubit platform, which could not be handled before by exact methods.