A hybrid quantum-classical lattice kinetic scheme with tensor-train feedback for incompressible flows
Abstract
Nonlinear lattice kinetic simulation requires each updated distribution to supply the velocity and gradients that determine the next step. In a quantum-classical solver, reading out the full distribution incurs work proportional to the lattice size. We construct a tensor-train (TT) interface that retains reusable classical cores at the physical amplitude scale for a full-relaxation lattice kinetic scheme. The cores supply nonlinear coefficients and prepare each quantum input. Energy-scaled propagation and coordinate recovery encode the updated distribution, and alternating least-squares reconstruction converts signed Hadamard-test overlaps into output cores by restoring a known normalization factor. The next step starts from accepted cores without replaying previous quantum evolution. Under positive, unit-sum reference coefficients, positive lower and finite upper density bounds, and Lipschitz equilibrium sensitivity, perturbation bounds relate local defects to feedback errors. Resource bounds account for classical operations, circuit execution, sampling, and verification. Classical diagnostics expose why distribution accuracy alone is insufficient: in 80-step feedback on a 16×16 grid, rank cap 4 nearly eliminates the vortex despite a final distribution error below 1%, whereas rank cap 12 gives relative velocity error 1.03×10−3. Four-step binomial readout simulations show that tightening core sampling tolerance threefold raises the prescribed sufficient budget from 5.97×1012 to 5.37×1013 shots as the result approaches the fixed-rank, fixed-sweep exact-overlap trajectory. The interface therefore provides a way to connect quantum propagation to nonlinear feedback and to assess the separate demands of compression, velocity accuracy, and readout precision.
Related
- Finite-blocklength classical communication over the quantum erasure channel with and without classical feedback
- Entanglement-of-formation potentials for feedback-assisted classical communication and randomness distillation
- Certain Standard Young Tableaux of Non-Classical Shapes and Lattice Path Enumeration
- A Quantum Spectral Solver for Periodic Incompressible Stokes Flow
- Methods for Deriving Nonlinear Kinetic Equations from the Dynamics of Quantum Systems
BibTeX
@misc{guo2026hybrid,
title = {{A hybrid quantum-classical lattice kinetic scheme with tensor-train feedback for incompressible flows}},
author = {Yongwei Guo and Yuan Yu and Yue Yu and Yuting Zhou},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04500},
eprint = {2611.04500},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04500},
}
RIS
TY - UNPB
TI - A hybrid quantum-classical lattice kinetic scheme with tensor-train feedback for incompressible flows
AU - Yongwei Guo
AU - Yuan Yu
AU - Yue Yu
AU - Yuting Zhou
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04500
UR - https://arxiv.org/abs/2611.04500
AB - Nonlinear lattice kinetic simulation requires each updated distribution to supply the velocity and gradients that determine the next step. In a quantum-classical solver, reading out the full distribution incurs work proportional to the lattice size. We construct a tensor-train (TT) interface that retains reusable classical cores at the physical amplitude scale for a full-relaxation lattice kinetic scheme. The cores supply nonlinear coefficients and prepare each quantum input. Energy-scaled propagation and coordinate recovery encode the updated distribution, and alternating least-squares reconstruction converts signed Hadamard-test overlaps into output cores by restoring a known normalization factor. The next step starts from accepted cores without replaying previous quantum evolution. Under positive, unit-sum reference coefficients, positive lower and finite upper density bounds, and Lipschitz equilibrium sensitivity, perturbation bounds relate local defects to feedback errors. Resource bounds account for classical operations, circuit execution, sampling, and verification. Classical diagnostics expose why distribution accuracy alone is insufficient: in 80-step feedback on a 16×16 grid, rank cap 4 nearly eliminates the vortex despite a final distribution error below 1%, whereas rank cap 12 gives relative velocity error 1.03×10^−3. Four-step binomial readout simulations show that tightening core sampling tolerance threefold raises the prescribed sufficient budget from 5.97×10^12 to 5.37×10^13 shots as the result approaches the fixed-rank, fixed-sweep exact-overlap trajectory. The interface therefore provides a way to connect quantum propagation to nonlinear feedback and to assess the separate demands of compression, velocity accuracy, and readout precision.
ER -