arXiv subjects

Lucy T. Zhang

Publications and source records attributed to Lucy T. Zhang.

3 recordsLinked to original sources

arXiv2026

Quantum HHL Algorithm for Solving 1D Linear Advection Equation Using Explicit and Implicit Finite Difference Schemes

This study develops and implements a Harrow-Hassidim-Lloyd (HHL) quantum algorithm for solving a one-dimensional linear advection equation with periodic boundary conditions. The governing equation is first discretized using a classical finite difference (FD) scheme to obtain a linear system suitable for quantum solution. We present a newly designed, circuit-level implementation of HHL assembled from Qiskit circuit components and exploit the circulant structure of the periodic discretization matrices through Fourier-based matrix evolution. The HHL algorithm is benchmarked with three explicit schemes and one implicit scheme. The implicit scheme requires a nontrivial linear solve arising from the discretized PDE on progressively finer grids, whereas the explicit schemes provide different input fields for testing state preparation and reconstruction with identity coefficient matrices. HHL solution states are validated against direct classical solves in noiseless simulation. For hardware execution, the periodic matrix structure permits a Fourier implementation that applies reciprocal eigenvalues without phase estimation. Results on the IBM Rensselaer Nighthawk processor are compared at a shared final time. Noiseless reconstructed fields approach the transported profile on resolved grids, while substantial hardware errors remain for both explicit and implicit schemes. Crank-Nicolson remains exceptionally well-conditioned and utilizes similar circuit re sources to the explicit controls, proving that hardware degradation in our tests was not driven by poor matrix conditioning. Ultimately, this study shows new means for HHL algorithms to study quantum CFD problems involving advection equations with implicit time integrations, while demonstrating how state preparation and measurement affect the practical performance of quantum solvers on current devices.

physics.comp-ph↗

arXiv2026

Machine Learning-Enabled Time-Skipping Method: Theory and Perturbation-Based Verification

Simulating the time evolution of practical mechanics problems requires many time steps. This cost is further compounded by the iterative nature of implicit solvers. We present a cycle-based Machine Learning-enabled Time-skipping (MLT) method. In each cycle, several time steps are skipped, a machine learning (ML) prediction bridges the gap to initialize one solver step, and the physics-based solver then runs for several steps to correct any accumulated errors. Using the Implicit Function Theorem, we derive first-order estimates that characterize how ML prediction errors propagate. These estimates identify when errors remain bounded across cycles and guide the choice of cycle parameters, independent of model architecture. We verify these estimates on the Allen-Cahn equation and a forced variant using controlled synthetic perturbations that emulate ML errors. Wall-clock measurements confirm the theoretical speedup is realizable in practice. The MLT method provides a robust framework for accelerating time-marching in dynamic simulations.

physics.comp-ph↗

arXiv2026

Benchmarking One-Dimensional Quantum Lattice Boltzmann Methods on Quantum Hardware

Classical computational fluid dynamics (CFD) methods encounter significant computational bottlenecks in large systems and at high Reynolds number flows due to the rapid increase in degrees of freedom, even on flagship supercomputers. As quantum computers emerge, the Quantum Lattice Boltzmann Method (QLBM) has been proposed as a quantum-native alternative for solving fluid dynamics problems. However, until recently, nearly all studies have relied on classical quantum simulators rather than real quantum hardware. This study presents a benchmark of a one-dimensional QLBM implementation executed on three different IBM Quantum hardware. We design and test a quantum circuit for the advection-diffusion equation using amplitude encoding, a Bhatnagar-Gross-Krook (BGK)-type collision operator, and a streaming step with periodic boundary conditions. Our numerical experiments evaluate transpiled two-qubit gate count, total circuit depth, runtime, and accuracy metrics including maximum absolute error ($L_\infty$ norm) and root-mean-square error (RMSE). We find that the present collision and streaming operators dominate the overall cost and become the primary scalability bottleneck on current hardware. To mitigate the prohibitive cost of full quantum state tomography on hardware-based benchmarking exercises, we introduce a sampler-based measurement strategy that reconstructs macroscopic density fields directly from computational-basis measurements. This approach substantially reduces measurement overhead while preserving the expected advection-diffusion dynamics on hardware. These results provide a quantitative assessment of QLBM performance in the noisy intermediate-scale quantum (NISQ) regime and identify the principal algorithmic and experimental limitations that must be addressed for QLBM to become viable for fluid dynamics.

physics.comp-ph↗