wigner-function-reconstruction

name

wigner-function-reconstruction

description

Wigner function reconstruction methodology for continuous-variable quantum system characterization. Combines provably efficient regression for sparse states (binomial codes, cat states) with deep learning for general states (GKP). Use when: (1) characterizing CV quantum systems, (2) reconstructing Wigner functions from sparse measurements, (3) identifying error processes in QEC cycles, (4) phase-space tomography, (5) reducing measurement overhead in quantum state characterization. Trigger words: wigner function, phase-space reconstruction, CV quantum characterization, GKP state tomography, sparse phase-space data.

Wigner Function Reconstruction

Core Insight

Wigner function learning characterizes continuous-variable (CV) quantum systems by inferring continuous phase-space functions from sparse pointwise measurements. Complexity scales logarithmically with Hilbert space dimension for sparse states.

Two-Regime Approach

Sparse States (Binomial, Cat States)

For states with sparse Fock-space or coherent-state representations:

• Use provably efficient regression models
• Measurement complexity: O(log(d)) where d = effective Hilbert dimension
• No deep learning needed — compressed sensing suffices

General States (GKP, Unknown States)

For states without sparse structure:

• Train deep learning model on sparse measurements
• Model generalizes to arbitrary phase-space resolution
• Key: learns to identify dominant error processes with fewer measurements than conventional estimation

Experimental Validation

Validated on circuit-QED experimental data:

• Reconstructs Wigner functions across multiple QEC rounds
• Identifies dominant error processes with significantly fewer measurements
• Works on both simulated and real experimental data

Pipeline

1. Data collection: Sparse pointwise measurements in phase space
2. State classification: Determine if state has sparse structure
3. Method selection:
   • Sparse → compressed sensing regression (O(log d) measurements)
   • General → trained deep learning model
4. Reconstruction: Generate continuous Wigner function
5. Error identification: Identify dominant error processes from reconstructed function

Scripts

See scripts/wigner_reconstruct.py for implementation.

References

• arXiv:2607.06232 - "Learning to Reconstruct Wigner Functions in Phase Space"
• GKP codes: Gottesman-Kitaev-Preskill error correction
• Circuit QED: superconducting qubit-cavity systems

Activation Keywords

• wigner function, phase-space reconstruction, CV quantum characterization
• GKP state tomography, sparse phase-space data
• quantum state reconstruction, continuous variable tomography