Researchers Develop Machine Learning Framework for Wigner Function Reconstruction from Sparse Data

Researchers have created a new machine learning framework to efficiently reconstruct Wigner functions, tools used to describe continuous variable quantum systems, from limited data.

This addresses a key challenge; accurately characterising these systems typically requires many measurements as their complexity increases. The new approach uses machine learning to infer the Wigner function directly from sparse phase-space data, improving efficiency. Researchers from Shanghai Jiao Tong University, The University of Hong Kong, Nanyang Technological University, and Peking University have developed a new machine learning framework to efficiently reconstruct Wigner functions, tools used to describe continuous variable quantum systems, from limited data.

Accurately characterising these systems traditionally requires a substantial number of measurements as their complexity increases, but this new approach uses machine learning to infer the Wigner function directly from sparse phase-space data, improving efficiency. The team demonstrated the framework’s applicability using both simulated data and experiments performed on a circuit-QED system, a type of superconducting circuit analogous to an electronic circuit used to process information in a computer.

Reconstructing quantum states via sparse regression of Wigner function data

A new machine learning technique infers the complete Wigner function, a map showing the probability of finding a quantum particle at different positions and momenta, from a limited number of data points. These models, akin to finding patterns in incomplete information, scale logarithmically with the system’s dimension, dramatically reducing the measurement burden.

The framework focused on states exhibiting sparsity, meaning they have simple representations in either the Fock basis or coherent-state basis, including binomial and cat states. This approach offers a sharp reduction in measurement requirements compared to conventional techniques.

Logarithmic scaling of Wigner function reconstruction via machine learning for complex quantum

The machine learning framework reduces the number of measurements needed to resolve the Wigner function from the traditional d² to a logarithmic scaling of d², a substantial improvement for high-dimensional systems. Accurately mapping the Wigner function, a vital tool for understanding continuous variable quantum systems, previously demanded an impractical number of data points as system complexity increased, hindering detailed analysis of quantum states.

Reconstruction of Wigner functions across several error correction cycles allowed the model to identify the dominant error process with greater efficiency. For states exhibiting sparse representations, either in terms of Fock states or coherent states, the machine learning model required only a logarithmic number of measurements, where d represents the effective Hilbert-space dimension. While these results represent a major advancement in efficient quantum state characterisation, the current framework does not yet demonstrate scalability to extremely complex, highly entangled states or address the challenges of imperfect measurement apparatuses in real-world applications.

Researchers at Shanghai Jiao Tong University and collaborating institutions have unveiled a machine learning framework promising more efficient characterisation of continuous variable quantum systems, a vital step towards building practical quantum technologies. The team successfully reconstructed Wigner functions for GKP states, though the deep learning model’s generalizability to all continuous variable states remains an open question. Reconstructing Wigner functions, a way of visualising quantum states, from limited data is key for practical quantum computing.

This advance enables more detailed analysis of complex quantum states, in particular GKP states during quantum error correction, and identifies dominant error sources with improved efficiency. By employing machine learning, logarithmic scaling with system dimension was achieved for sparse states, a substantial reduction in required data compared to conventional methods. This overcomes a longstanding challenge in continuous variable quantum systems where detailed characterisation demands extensive measurement, and provides essential maps describing quantum states from limited data.

The researchers developed a machine learning framework that reconstructs Wigner functions, representing quantum states, directly from limited phase-space data. This is important because detailed characterisation of quantum states is crucial for developing practical quantum technologies, and this method reduces the amount of measurement needed. For states with sparse representations, the model’s measurement complexity scaled logarithmically with the Hilbert-space dimension, improving efficiency. The team demonstrated this framework using both simulated and experimental data from a circuit-QED system, including reconstructing Wigner functions of GKP code states during quantum error correction and identifying the dominant error process.