# CO-MAP: A Reinforcement Learning Approach to the Qubit Allocation Problem

arXiv: https://arxiv.org/abs/2605.13638 · HTML: https://mlsanity.com/paper/2605.13638/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Quantum reinforcement learning, one of 15 directions in Deep reinforcement learning methods.
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 13 May 2026.

## Placed in

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

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Layer Normalization](https://mlsanity.com/paper/1607.06450/) (2016)
- [Pointer Networks](https://mlsanity.com/paper/1506.03134/) (2015)
- [Variational Quantum Algorithms](https://mlsanity.com/paper/2012.09265/) (2020)
- [Attention, Learn to Solve Routing Problems!](https://mlsanity.com/paper/1803.08475/) (2018)
- [Machine Learning for Combinatorial Optimization: a Methodological Tour d'Horizon](https://mlsanity.com/paper/1811.06128/) (2018)
- [Neural Combinatorial Optimization with Reinforcement Learning](https://mlsanity.com/paper/1611.09940/) (2016)
- [Graph Normalizing Flows](https://mlsanity.com/paper/1905.13177/) (2019)
- [RL4CO: an Extensive Reinforcement Learning for Combinatorial Optimization Benchmark](https://mlsanity.com/paper/2306.17100/) (2023)
- [Winner Takes It All: Training Performant RL Populations for Combinatorial Optimization](https://mlsanity.com/paper/2210.03475/) (2022)
- [Graph Pointer Neural Networks](https://mlsanity.com/paper/2110.00973/) (2021)
- [Practical and efficient quantum circuit synthesis and transpiling with Reinforcement Learning](https://mlsanity.com/paper/2405.13196/) (2024)
- [Optimality Study of Existing Quantum Computing Layout Synthesis Tools](https://mlsanity.com/paper/2002.09783/) (2020)
- [An Open-Source, Industrial-Strength Optimizing Compiler for Quantum Programs](https://mlsanity.com/paper/2003.13961/) (2020)
- [Generating Compilers for Qubit Mapping and Routing](https://mlsanity.com/paper/2508.10781/) (2025)

## Abstract (arXiv)

A quantum compiler is a critical piece in the quantum computing pipeline since it allows an abstract quantum circuit to be run on a physical quantum computer. One extremely important subproblem in quantum compilation is the generation of a logical to physical qubit mapping. Typically in quantum compilers this step is either implemented as a random or a heuristic based assignment that aims to minimize additional (SWAP) gate overhead in the quantum circuit. In this paper, we present an alternative approach to solving the qubit mapping problem. Specifically, we formulate the qubit mapping problem with a combinatorial optimization (CO) objective. We then present a method to find a solution to the CO problem by training a reinforcement learning (RL) policy. We also propose a local search based post-processing algorithm to further reduce the overhead. Our results show a dramatic improvement over conventional techniques in reducing the number of SWAPs. On different real world datasets like MQTBench and Queko circuits, our trained policy achieves a 65-85% reduction in SWAP overhead when compared to existing quantum compilers.