Adaptive Reconstruction of Bosonic Quantum States

2026-08-03

AI Summary

Characterizing bosonic quantum states is challenging due to the vast Hilbert space and the high cost of tomography, and existing methods fail to handle state estimation under physically equivalent transformations such as phase-space translations and rotations. This work proposes an adaptive reconstruction approach that integrates physics-informed parametric modeling, Bayesian inference, bootstrapping, and active learning to iteratively select the most informative phase-space sampling points. With only a small number of measurements, the method simultaneously estimates the fidelity of an entire family of physically equivalent states and reconstructs the Wigner function. It achieves, for the first time, efficient and robust fidelity estimation of Schrödinger cat states with amplitudes α ∈ [1, 3] in minutes—significantly outperforming conventional Wigner sampling—and has been successfully integrated into a closed-loop quantum optimal control experiment for autonomous optimization.

Abstract

Bosonic quantum systems provide a hardware-efficient platform for quantum information processing but remain challenging to characterise due to their large Hilbert space and the high measurement cost of state tomography. Existing approaches estimate the fidelity with respect to a single target state, making them unsuitable for applications in which physically equivalent states differ by phase space translations, rotations, or other transformations. Here, we introduce an adaptive reconstruction technique that estimates the fidelity with respect to a family of bosonic states while reconstructing the underlying Wigner function from a small number of measurements. The method combines a physics-informed parametric model with Bayesian inference, bootstrap, and active learning to iteratively select the most informative phase space sampling points. We implement the approach on a circuit quantum electrodynamics platform and benchmark it on Schrödinger cat states with amplitudes $α\in[1,3]$. The reconstruction yields reproducible fidelity estimates within a few minutes, remains robust to substantial displacements and rotations in phase space despite using a mismatched prior, and is sensitive to subtle state imperfections. We further compare the adaptive strategy with existing Wigner function sampling protocols experimentally, demonstrating the advantage of adaptive sampling for measurement-efficient fidelity estimation with respect to a family of cat states. Finally, we incorporate the reconstructed fidelity into the figure of merit used in a proof-of-principle closed-loop quantum optimal control experiment, demonstrating the applicability of the method to autonomous optimisation of bosonic quantum states.

Problem

• bosonic quantum states
• quantum state tomography
• fidelity estimation
• phase space transformations
• Wigner function

Innovation

• adaptive reconstruction
• bosonic quantum states
• Wigner function
• Bayesian inference
• active learning