Field-aligned measurement removes the anisotropy barrier of sample-based quantum subspace solvers for magnetized-plasma heat conduction
Abstract
Sample-based quantum subspace methods construct a small subspace from measured basis states and solve the target problem classically within it. We study these methods for heat conduction in magnetized plasmas, where the anisotropy χ∥/χ⊥ reaches 108 to 1010. We prove two results for the energy-norm Galerkin solution. First, if the measurement basis is aligned with the flux surfaces and the subspace contains the poloidal-mode-zero block, the error is bounded by |r0|L+(χ∥−χ⊥)−1/2, where the numerator does not depend on χ∥. The bound is sharp, so the accuracy improves as the anisotropy grows. Second, in the computational basis, a subspace that misses a single node of a flux surface suppresses the flux-function component there as χ∥−1/2, which gives an error floor when the limiting solution is nonzero on that surface. We verify both results on a shaped cross-section and on a KSTAR-like Miller equilibrium with ten qubits. At χ∥/χ⊥=109, the computational basis gives an error of order unity for every shot budget, whereas a quantum Fourier transform on the poloidal register gives 1.3×10−5. The same barrier limits sample-based quantum diagonalization. The aligned measurement needs no time evolution, so the circuit is only state preparation and a five-qubit quantum Fourier transform. On a ten-qubit superconducting processor, the aligned basis gives a median error of 7.0×10−6 with 768 shots, whereas the computational basis gives errors above 0.94 up to 1.2×104 shots. A trapped-ion processor shows the same behavior.
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BibTeX
@misc{doyeol2026fieldaligned,
title = {{Field-aligned measurement removes the anisotropy barrier of sample-based quantum subspace solvers for magnetized-plasma heat conduction}},
author = {Doyeol and Ahn},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07102},
eprint = {2611.07102},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07102},
}
RIS
TY - UNPB
TI - Field-aligned measurement removes the anisotropy barrier of sample-based quantum subspace solvers for magnetized-plasma heat conduction
AU - Doyeol
AU - Ahn
PY - 2026
DA - 2026/11/04
PB - arXiv
DO - 10.48550/arxiv.2611.07102
UR - https://arxiv.org/abs/2611.07102
AB - Sample-based quantum subspace methods construct a small subspace from measured basis states and solve the target problem classically within it. We study these methods for heat conduction in magnetized plasmas, where the anisotropy χ_∥/χ_⊥ reaches 10^8 to 10^10. We prove two results for the energy-norm Galerkin solution. First, if the measurement basis is aligned with the flux surfaces and the subspace contains the poloidal-mode-zero block, the error is bounded by |r_0|_L^+(χ_∥−χ_⊥)^−1/2, where the numerator does not depend on χ_∥. The bound is sharp, so the accuracy improves as the anisotropy grows. Second, in the computational basis, a subspace that misses a single node of a flux surface suppresses the flux-function component there as χ_∥^−1/2, which gives an error floor when the limiting solution is nonzero on that surface. We verify both results on a shaped cross-section and on a KSTAR-like Miller equilibrium with ten qubits. At χ_∥/χ_⊥=10^9, the computational basis gives an error of order unity for every shot budget, whereas a quantum Fourier transform on the poloidal register gives 1.3×10^−5. The same barrier limits sample-based quantum diagonalization. The aligned measurement needs no time evolution, so the circuit is only state preparation and a five-qubit quantum Fourier transform. On a ten-qubit superconducting processor, the aligned basis gives a median error of 7.0×10^−6 with 768 shots, whereas the computational basis gives errors above 0.94 up to 1.2×10^4 shots. A trapped-ion processor shows the same behavior.
ER -