Efficient Simulation of Hybrid Continuous- and Discrete-Variable Quantum Circuits via Gaussian Decompositions
Abstract
Hybrid quantum systems combining discrete-variable (DV) and continuous-variable (CV) subsystems arise across a broad range of physical platforms and enable quantum information processing beyond purely qubit-based designs. Their classical simulation, however, is challenging since computational costs of both CV and DV systems exponentially increase. In this paper, we introduce a simulation framework for CV--DV hybrid systems based on linear combination of Gaussian (LCoG) decomposition. We decompose the hybrid density matrix into blocks in a DV basis and represent each block as an LCoG expansion. Within the representation, Gaussian operations on the bosonic subsystem independently act on each Gaussian function. We derive analytic formulas describing how complex Gaussian functions transform under controlled Gaussian operations. We further extend the framework to controlled Gaussian channels with state-dependent Gaussian noise. The method avoids a Fock-space truncation for the CV subsystem, and the cost of updating each Gaussian term scales polynomially with the number of modes. The framework provides a general computational tool for analyzing hybrid quantum algorithms, quantum simulation protocols, and non-Gaussian state generation schemes. As an example, we simulate Gottesman--Kitaev--Preskill (GKP) state generation based on a cavity-QED system.
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BibTeX
@misc{tanji2026efficient,
title = {{Efficient Simulation of Hybrid Continuous- and Discrete-Variable Quantum Circuits via Gaussian Decompositions}},
author = {Kazufumi Tanji and Dot Belin Pio and Shohei Kiryu and Ulrik Lund Andersen and Masahiro Takeoka},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.34793},
eprint = {2609.34793},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.34793},
}
RIS
TY - UNPB
TI - Efficient Simulation of Hybrid Continuous- and Discrete-Variable Quantum Circuits via Gaussian Decompositions
AU - Kazufumi Tanji
AU - Dot Belin Pio
AU - Shohei Kiryu
AU - Ulrik Lund Andersen
AU - Masahiro Takeoka
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2609.34793
UR - https://arxiv.org/abs/2609.34793
AB - Hybrid quantum systems combining discrete-variable (DV) and continuous-variable (CV) subsystems arise across a broad range of physical platforms and enable quantum information processing beyond purely qubit-based designs. Their classical simulation, however, is challenging since computational costs of both CV and DV systems exponentially increase. In this paper, we introduce a simulation framework for CV--DV hybrid systems based on linear combination of Gaussian (LCoG) decomposition. We decompose the hybrid density matrix into blocks in a DV basis and represent each block as an LCoG expansion. Within the representation, Gaussian operations on the bosonic subsystem independently act on each Gaussian function. We derive analytic formulas describing how complex Gaussian functions transform under controlled Gaussian operations. We further extend the framework to controlled Gaussian channels with state-dependent Gaussian noise. The method avoids a Fock-space truncation for the CV subsystem, and the cost of updating each Gaussian term scales polynomially with the number of modes. The framework provides a general computational tool for analyzing hybrid quantum algorithms, quantum simulation protocols, and non-Gaussian state generation schemes. As an example, we simulate Gottesman--Kitaev--Preskill (GKP) state generation based on a cavity-QED system.
ER -