aiqbench analysis
The study tests a variational quantum linear solver on IBM hardware for one implicit heat-conduction step. Error rises from 8.07% at N=4 to 20.14% at N=8, and increasing shot counts to N=16 does not reduce the mean field error, even though ideal sampling predicts a large improvement. For quantum-algorithm readers, this is a useful negative result: full-field readout of a nonuniform state appears limited by hardware noise beyond finite-shot sampling, which supports the authors' suggestion of targeting observables such as heat flux or stored energy.
Transient Heat Conduction on Quantum Hardware: Replicated Temperature-Field Reconstruction and Shot-Count Sensitivity with a Variational Quantum Linear Solver
arXiv:2610.24004v1 Announce Type: cross Abstract: Implicit discretizations of transient heat conduction repeatedly generate sparse linear systems, making diffusion problems a natural test bed for quantum linear solvers. This study evaluates how accurately a variational quantum linear solver (VQLS) recovers the temperature field produced by one backward-Euler step of one-dimensional conduction on IBM quantum hardware. A pre-specified confirmatory experiment compares N=4 interior temperatures encoded on two qubits with N=8 temperatures encoded on three qubits using ten paired hardware blocks; a separately defined N=16, four-qubit extension is evaluated in five independently scheduled exploratory blocks. Local VQLS optimization reduces relative temperature-field error to approximately 10^{-8} for all three cases, establishing an essentially exact ideal reference at this scale. On hardware, mean relative L2 temperature-field error is 8.07% for N=4 and 20.14% for N=8, a paired increase of 12.06 percentage points (95% CI, 10.71-13.42; exact paired sign-flip p=0.001953). The exploratory N=16 mean is 24.75+/-1.84%. A pre-specified N=16 shot-count follow-up then evaluates the same locked circuit at 2,048, 8,192, and 32,768 shots in six independently scheduled blocks. Mean field error remains 23.64%, 24.57%, and 24.37%, respectively; the 32,768-minus-2,048-shot contrast is +0.74 percentage points (95% CI, -0.65 to 2.12; p=0.281). In contrast, ideal multinomial sampling predicts a reduction from 2.68% to 0.75%. Higher shot counts reduce block-to-block variability but do not recover the mean cold-side temperature field. The results show that full-field readout of a strongly nonuniform thermal state is limited by more than ordinary finite-shot sampling under the tested hardware conditions, motivating observable-focused quantum formulations for heat flux, stored energy, and selected temperatures.
Abstract:Implicit discretizations of transient heat conduction repeatedly generate sparse linear systems, making diffusion problems a natural test bed for quantum linear solvers. This study evaluates how accurately a variational quantum linear solver (VQLS) recovers the temperature field produced by one backward-Euler step of one-dimensional conduction on IBM quantum hardware. A pre-specified confirmatory experiment compares N=4 interior temperatures encoded on two qubits with N=8 temperatures encoded on three qubits using ten paired hardware blocks; a separately defined N=16, four-qubit extension is evaluated in five independently scheduled exploratory blocks. Local VQLS optimization reduces relative temperature-field error to approximately 10^{-8} for all three cases, establishing an essentially exact ideal reference at this scale. On hardware, mean relative L2 temperature-field error is 8.07% for N=4 and 20.14% for N=8, a paired increase of 12.06 percentage points (95% CI, 10.71-13.42; exact paired sign-flip p=0.001953). The exploratory N=16 mean is 24.75+/-1.84%. A pre-specified N=16 shot-count follow-up then evaluates the same locked circuit at 2,048, 8,192, and 32,768 shots in six independently scheduled blocks. Mean field error remains 23.64%, 24.57%, and 24.37%, respectively; the 32,768-minus-2,048-shot contrast is +0.74 percentage points (95% CI, -0.65 to 2.12; p=0.281). In contrast, ideal multinomial sampling predicts a reduction from 2.68% to 0.75%. Higher shot counts reduce block-to-block variability but do not recover the mean cold-side temperature field. The results show that full-field readout of a strongly nonuniform thermal state is limited by more than ordinary finite-shot sampling under the tested hardware conditions, motivating observable-focused quantum formulations for heat flux, stored energy, and selected temperatures.
Computational Physics (physics.comp-ph); Quantum Physics (quant-ph)
arXiv:2610.24004 [physics.comp-ph]
(or arXiv:2610.24004v1 [physics.comp-ph] for this version)
https://doi.org/10.48550/arXiv.2610.24004 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 348 words