Gate-Level Quantum Simulation of Nonunitary Linear Dynamics with Hybrid Oscillator-Qubit Architecture
Abstract
We translate the one-mode unitary-dilation framework for nonunitary linear dynamics into a gate-level hybrid oscillator--qubit architecture. An ancillary oscillator encodes the kernel through state preparation and postselection, while a qubit register simulates the discretized system operator. The construction applies to time-independent dynamics u̇=−(L+iH)u, including discretized partial differential equations, and removes the 𝒪(log Ma) ancilla-qubit overhead of a discrete-variable (DV) Ma-term quadrature register. We bound the ideal state's squeezed-Fock coefficient-projection error, which decays superalgebraically in cutoff N for Schwartz-class kernels and at a stretched-exponential rate under stronger joint decay and smoothness assumptions. The finite squeezed-Fock state generically has stellar rank N−1, making N a measure of the oracle's non-Gaussian resource. For oscillator dimension NFock, a pth-order product formula reaches error εt in 𝒪(t1+1/pNFock(p+1)/(2p)εt−1/p) Trotter steps, up to generator-dependent commutator factors. A perturbation bound separates total scaled-map error from postselection probability. We benchmark Law--Eberly synthesis and assess variational SNAP+𝒟 state preparation on heat and advection--diffusion equations. At the prescribed DV sizing, the hybrid CV--DV route has smaller fixed-scale error in all ten instances, while the DV route accepts with fewer repetitions in every instance. These results quantify when a continuous qumode can replace a discretized ancilla register.
Versions
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BibTeX
@misc{das2026gatelevel,
title = {{Gate-Level Quantum Simulation of Nonunitary Linear Dynamics with Hybrid Oscillator-Qubit Architecture}},
author = {Elin Ranjan Das and Muqing Zheng and Rishab Dutta and Ang Li and Timothy Stavenger and Yuan Liu},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.10708},
eprint = {2605.10708},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.10708},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gate-Level Quantum Simulation of Nonunitary Linear Dynamics with Hybrid Oscillator-Qubit Architecture
AU - Elin Ranjan Das
AU - Muqing Zheng
AU - Rishab Dutta
AU - Ang Li
AU - Timothy Stavenger
AU - Yuan Liu
PY - 2026
DA - 2026/08/21
PB - arXiv
DO - 10.48550/arxiv.2605.10708
UR - https://arxiv.org/abs/2605.10708
AB - We translate the one-mode unitary-dilation framework for nonunitary linear dynamics into a gate-level hybrid oscillator--qubit architecture. An ancillary oscillator encodes the kernel through state preparation and postselection, while a qubit register simulates the discretized system operator. The construction applies to time-independent dynamics u̇=−(L+iH)u, including discretized partial differential equations, and removes the 𝒪(log M_a) ancilla-qubit overhead of a discrete-variable (DV) M_a-term quadrature register. We bound the ideal state's squeezed-Fock coefficient-projection error, which decays superalgebraically in cutoff N for Schwartz-class kernels and at a stretched-exponential rate under stronger joint decay and smoothness assumptions. The finite squeezed-Fock state generically has stellar rank N−1, making N a measure of the oracle's non-Gaussian resource. For oscillator dimension N_Fock, a pth-order product formula reaches error ε_t in 𝒪(t^1+1/pN_Fock^(p+1)/(2p)ε_t^−1/p) Trotter steps, up to generator-dependent commutator factors. A perturbation bound separates total scaled-map error from postselection probability. We benchmark Law--Eberly synthesis and assess variational SNAP+𝒟 state preparation on heat and advection--diffusion equations. At the prescribed DV sizing, the hybrid CV--DV route has smaller fixed-scale error in all ten instances, while the DV route accepts with fewer repetitions in every instance. These results quantify when a continuous qumode can replace a discretized ancilla register.
ER -