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Quantum Simulation

Symbolic Quantum State Representation and its Simulation

arXiv
Authors: Simon Sekavcnik, Janis Noetzel

Year

2026

Paper ID

28410

Status

Preprint

Abstract Read

~2 min

Abstract Words

91

Citations

N/A

Abstract

We introduce a symbolic operator framework for simulating quantum photonic systems that works directly with the canonical commutation relations and the Weyl algebra. Unlike existing Fock-space or Gaussian simulators, our method treats temporal wave packets and polarization modes in a continuous setting and does not rely on discretization or Hilbert-space truncation. Device operations are expressed as algebraic rewrite rules acting on creation and annihilation operators, allowing exact evolution of finite-photon states through linear optical networks. As an illustration, we reproduce Hong-Ou-Mandel interference for Gaussian pulses with controlled temporal and spectral mismatch.

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  • This paper contributes to the Quantum Simulation research area in the Quantum Articles archive.
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  • We introduce a symbolic operator framework for simulating quantum photonic systems that works directly with the canonical commutation relations and the Weyl algebra.

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References & Citation Signals

[1] DOI https://doi.org/arXiv:2603.11824 [2] arXiv https://arxiv.org/abs/2603.11824 [3] Publisher https://arxiv.org/abs/2603.11824

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