# Optimal qubit assignment and routing via integer programming

arXiv: https://arxiv.org/abs/2106.06446 · HTML: https://mlsanity.com/paper/2106.06446/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Jun 2021.

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

- [Practical and efficient quantum circuit synthesis and transpiling with Reinforcement Learning](https://mlsanity.com/paper/2405.13196/) (2024)
- ['Eliv'agar: Efficient Quantum Circuit Search for Classification](https://mlsanity.com/paper/2401.09393/) (2024)
- [Quantum Circuit Synthesis and Compilation Optimization: Overview and Prospects](https://mlsanity.com/paper/2407.00736/) (2024)
- [AlphaRouter: Quantum Circuit Routing with Reinforcement Learning and Tree Search](https://mlsanity.com/paper/2410.05115/) (2024)
- [Attention-Based Deep Reinforcement Learning for Qubit Allocation in Modular Quantum Architectures](https://mlsanity.com/paper/2406.11452/) (2024)
- [AI-Powered Algorithm-Centric Quantum Processor Topology Design](https://mlsanity.com/paper/2412.13805/) (2024)
- [BIPNN: Learning to Solve Binary Integer Programming via Hypergraph Neural Networks](https://mlsanity.com/paper/2505.20997/) (2025)

## Abstract (arXiv)

We consider the problem of mapping a logical quantum circuit onto a given hardware with limited two-qubit connectivity. We model this problem as an integer linear program, using a network flow formulation with binary variables that includes the initial allocation of qubits and their routing. We consider several cost functions: an approximation of the fidelity of the circuit, its total depth, and a measure of cross-talk, all of which can be incorporated in the model. Numerical experiments on synthetic data and different hardware topologies indicate that the error rate and depth can be optimized simultaneously without significant loss. We test our algorithm on a large number of quantum volume circuits, optimizing for error rate and depth; our algorithm significantly reduces the number of CNOTs compared to Qiskit's default transpiler SABRE, and produces circuits that, when executed on hardware, exhibit higher fidelity.