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Effective Mode Approximation for Probabilistic Verification of Collective Hamiltonians in Large Continuous-Variable
José R Rosas-Bustos1,2,3,4, Jesse Van Griensven Thé1,2,3,4, Roydon Andrew Fraser1,3,4
1Department of MME, University of Waterloo, Waterloo, ON N2L 3G1, Canada.
Entropy (Basel, Switzerland)
|May 26, 2026
Summary
The Effective Mode Approximation (EMA) verifies collective quantum dynamics in large systems using collective measurements. This framework efficiently characterizes quantum behavior without full Hamiltonian reconstruction, proving useful for scalable quantum hardware.
Area of Science:
- Quantum Physics
- Quantum Information Science
- Optical Systems
Background:
- Characterizing collective dynamics in large continuous-variable (CV) quantum systems is challenging.
- Full mode-resolved Hamiltonian reconstruction is often impractical due to system size and measurement constraints.
Purpose of the Study:
- To introduce and validate the Effective Mode Approximation (EMA) framework.
- To demonstrate EMA's utility in verifying collective Hamiltonian dynamics from experimental measurements.
- To assess EMA's scalability and effectiveness in large CV quantum systems.
Main Methods:
- Developed the Effective Mode Approximation (EMA) framework.
- Utilized time-resolved homodyne sampling in Gaussian simulations.
- Simulated ring-coupled multi-qu-mode optical systems with varying numbers of modes (N=8, 16, 32, 64).
- Employed one-tone and two-tone sinusoidal models selected via the Akaike Information Criterion (AIC).
Main Results:
- EMA successfully mapped observed dynamics onto a collective mode.
- Summed quadrature trajectories were consistent with an effective harmonic description.
- A stable dominant collective frequency was recovered across system sizes.
- Residuals remained centered near zero, indicating model accuracy.
- EMA verified dominant collective behavior with a fixed number of effective parameters.
Conclusions:
- EMA provides a verification-oriented framework for collective dynamics in large CV quantum systems.
- EMA is a low-overhead tool for validating collective behavior under realistic measurement constraints.
- The framework is suitable for scalable CV hardware where full reconstruction is impractical.
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