Simulation-Based Quantum System Inference with Neural Posterior Estimation

2026-09-28

AI Summary

This study addresses the computational intractability of likelihood functions in quantum system parameter inference caused by the exponential growth of Hilbert space. To overcome this, we propose a likelihood-free inference framework that shifts the computational cost to an upfront training phase. By integrating polynomial-complexity classical simulators, such as tensor networks, with neural density estimators like normalizing flows, the method directly learns the posterior distribution over parameters. Once trained, the model rapidly processes arbitrary new measurement data via a single forward pass. Experimental results demonstrate that this framework achieves accurate inference on 81-qubit circuits while significantly reducing data acquisition requirements. Ultimately, this approach accelerates the characterization of large-scale quantum systems.

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.

Problem

• quantum system inference
• parameter estimation
• intractable likelihood
• inverse problem

Innovation

• Simulation-Based Inference
• Likelihood-Free Inference
• Neural Posterior Estimation
• Normalizing Flows
• Quantum System Characterization