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This research demonstrates how aligning measurement bases with plasma flux surfaces eliminates anisotropy-induced error floors in quantum subspace solvers, a critical advancement for simulating magnetized plasmas on near-term devices. By leveraging a five-qubit quantum Fourier transform without time evolution, the method achieves high-precision results on both superconducting and trapped-ion hardware where standard computational bases fail. This work bridges theoretical bounds with experimental verification, offering a practical pathway to handle extreme anisotropy ratios ($10^8$–$10^{10}$) in fusion energy modeling.
Field-aligned measurement removes the anisotropy barrier of sample-based quantum subspace solvers for magnetized-plasma heat conduction
arXiv:2611.07102v1 Announce Type: new 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 $\chi_\parallel/\chi_\perp$ 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 $\|r_0\|_{L^+}(\chi_\parallel-\chi_\perp)^{-1/2}$, where the numerator does not depend on $\chi_\parallel$. 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 $\chi_\parallel^{-1/2}$, 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 $\chi_\parallel/\chi_\perp=10^9$, the computational basis gives an error of order unity for every shot budget, whereas a quantum Fourier transform on the poloidal register gives $1.3\times10^{-5}$. 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 $7.0\times10^{-6}$ with 768 shots, whereas the computational basis gives errors above 0.94 up to $1.2\times10^4$ shots. A trapped-ion processor shows the same behavior.
Authors:Doyeol (David)Ahn (1,2) ((1) Department of Electrical and Computer Engineering, University of Seoul, Dongdaemun-gu, Seoul, Republic of Korea, (2) Singularity Quantum Inc., Newport Beach, California, USA)
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 $\chi_\parallel/\chi_\perp$ 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 $\|r_0\|_{L^+}(\chi_\parallel-\chi_\perp)^{-1/2}$, where the numerator does not depend on $\chi_\parallel$. 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 $\chi_\parallel^{-1/2}$, 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 $\chi_\parallel/\chi_\perp=10^9$, the computational basis gives an error of order unity for every shot budget, whereas a quantum Fourier transform on the poloidal register gives $1.3\times10^{-5}$. 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 $7.0\times10^{-6}$ with 768 shots, whereas the computational basis gives errors above 0.94 up to $1.2\times10^4$ shots. A trapped-ion processor shows the same behavior.
Quantum Physics (quant-ph); Computational Physics (physics.comp-ph); Plasma Physics (physics.plasm-ph)
arXiv:2611.07102 [quant-ph]
(or arXiv:2611.07102v1 [quant-ph] for this version)
https://doi.org/10.48550/arXiv.2611.07102 arXiv-issued DOI via DataCite (pending registration)
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