# GFlowNets for Hamiltonian decomposition in groups of compatible operators

arXiv: https://arxiv.org/abs/2410.16041 · HTML: https://mlsanity.com/paper/2410.16041/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 35 references that are in the map.
- First posted on arXiv 21 Oct 2024.

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

- [Flow Network based Generative Models for Non-Iterative Diverse Candidate Generation](https://mlsanity.com/paper/2106.04399/) (2021)
- [GFlowNet Foundations](https://mlsanity.com/paper/2111.09266/) (2021)
- [Trajectory balance: Improved credit assignment in GFlowNets](https://mlsanity.com/paper/2201.13259/) (2022)
- [Predicting Many Properties of a Quantum System from Very Few Measurements](https://mlsanity.com/paper/2002.08953/) (2020)
- [Generative Flow Networks for Discrete Probabilistic Modeling](https://mlsanity.com/paper/2202.01361/) (2022)
- [GFlowNets for AI-Driven Scientific Discovery](https://mlsanity.com/paper/2302.00615/) (2023)
- [Graph colouring algorithms](https://mlsanity.com/paper/1505.05825/) (2015)

## Built on by (most cited first, 2 of 2)

- [Derandomized shallow shadows: Efficient Pauli learning with bounded-depth circuits](https://mlsanity.com/paper/2412.18973/) (2024)
- [Generative Learning for Quantum Measurement Design](https://mlsanity.com/paper/2608.11396/) (2026)

## Abstract (arXiv)

Quantum computing presents a promising alternative for the direct simulation of quantum systems with the potential to explore chemical problems beyond the capabilities of classical methods. However, current quantum algorithms are constrained by hardware limitations and the increased number of measurements required to achieve chemical accuracy. To address the measurement challenge, techniques for grouping commuting and anti-commuting terms, driven by heuristics, have been developed to reduce the number of measurements needed in quantum algorithms on near-term quantum devices. In this work, we propose a probabilistic framework using GFlowNets to group fully (FC) or qubit-wise commuting (QWC) terms within a given Hamiltonian. The significance of this approach is demonstrated by the reduced number of measurements for the found groupings; 51% and 67% reduction factors respectively for FC and QWC partitionings with respect to greedy coloring algorithms, highlighting the potential of GFlowNets for future applications in the measurement problem. Furthermore, the flexibility of our algorithm extends its applicability to other resource optimization problems in Hamiltonian simulation, such as circuit design.