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Quantum Simulation

Representation theory of inhomogeneous Gaussian unitaries

arXiv
Authors: Jingqi Sun, Joshua Combes, Lucas Hackl

Year

2026

Paper ID

237

Status

Preprint

Abstract Read

~2 min

Abstract Words

94

Citations

N/A

Abstract

Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing. Their structures correspond to symplectic (bosons) and orthogonal (fermions) groups, but physical realizations give rise to their respective double covers, introducing phase and sign ambiguities. The homogeneous (quadratic-only) case has been resolved through a parameterization constructed in a recent work [arXiv:2409.11628]. We extend the previous framework to inhomogeneous Gaussian unitaries parameterized by (M,z,Ψ). The Baker-Campbel-Hausdorff formula allows us then to factor any Gaussian unitary into a squeezing and a displacement transformation, from which we derive the group multiplication law.

Why This Paper Matters

  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
  • It adds a 2026 reference point for readers tracking recent quantum research.
  • Gaussian unitaries, generated by quadratic Hamiltonians, are fundamental in quantum optics and continuous-variable computing.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2602.08611 [2] arXiv https://arxiv.org/abs/2602.08611 [3] Publisher https://arxiv.org/abs/2602.08611

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