Simulation-Based Quantum System Inference with Neural Posterior Estimation
Abstract
Models of quantum systems faithfully map system parameters to observations, but the inverse problem of parameter inference from measurement data presents a fundamental challenge: computationally intractable likelihoods due to an exponentially large Hilbert space. Here, we introduce simulation-based quantum system inference, a unified, likelihood-free framework that learns parameter posteriors directly from classical simulation data. The central idea is to pair polynomial-cost classical simulators, such as Pauli propagation and tensor networks, with normalizing flows or other neural density estimators for accurate, reusable inference. A single model, trained once, maps any new measurement record to its posterior in one forward pass---turning per-experiment inference into a fixed, up-front cost. We numerically demonstrate the framework's versatility across Pauli noise learning, quantum error mitigation, quantum state tomography, and Hamiltonian learning, with examples involving 81-qubit shallow circuits and 735-parameter inference. In each case, the approach yields accurate estimates of identifiable parameters, while posterior uncertainty provides additional diagnostics of non-identifiability and indicates where further characterization is needed. Our framework reduces data-acquisition requirements in quantum experiments and accelerates parameter inference, providing a practical route to characterizing and improving large-scale quantum systems.
Related
- Simulation-Based Inference and Unbinned Asimov Construction with Hybrid Neural Density Estimation
- Impact of Multiple Non-Invasive Biosignals on Cardiovascular Biomarker Estimation via Simulation-Based Inference
- Quantum Simulation of a Hyperbolically Driven Quantum System with Superconducting Circuits
- Gate-Based Quantum Simulation of Finite-Temperature Open-System Dynamics: A Post-Processing Reconstruction Approach for Collision Models
- Trotterisation Thresholds and Dissipative Quantum Chaos in Open-System Digital Quantum Simulation
BibTeX
@misc{zou2026simulationbased,
title = {{Simulation-Based Quantum System Inference with Neural Posterior Estimation}},
author = {Hang Zou and Anton Frisk Kockum and Martin Rahm and Simon Olsson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34995},
eprint = {2609.34995},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34995},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Simulation-Based Quantum System Inference with Neural Posterior Estimation
AU - Hang Zou
AU - Anton Frisk Kockum
AU - Martin Rahm
AU - Simon Olsson
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34995
UR - https://arxiv.org/abs/2609.34995
AB - Models of quantum systems faithfully map system parameters to observations, but the inverse problem of parameter inference from measurement data presents a fundamental challenge: computationally intractable likelihoods due to an exponentially large Hilbert space. Here, we introduce simulation-based quantum system inference, a unified, likelihood-free framework that learns parameter posteriors directly from classical simulation data. The central idea is to pair polynomial-cost classical simulators, such as Pauli propagation and tensor networks, with normalizing flows or other neural density estimators for accurate, reusable inference. A single model, trained once, maps any new measurement record to its posterior in one forward pass---turning per-experiment inference into a fixed, up-front cost. We numerically demonstrate the framework's versatility across Pauli noise learning, quantum error mitigation, quantum state tomography, and Hamiltonian learning, with examples involving 81-qubit shallow circuits and 735-parameter inference. In each case, the approach yields accurate estimates of identifiable parameters, while posterior uncertainty provides additional diagnostics of non-identifiability and indicates where further characterization is needed. Our framework reduces data-acquisition requirements in quantum experiments and accelerates parameter inference, providing a practical route to characterizing and improving large-scale quantum systems.
ER -