arXiv subjects

Nhat-Quang Nguyen

Publications and source records attributed to Nhat-Quang Nguyen.

3 recordsLinked to original sources

arXiv2026

Reconstructing fluid velocity fields from sparse sensors using a variational quantum algorithm

Reconstructing fields governed by nonlinear partial differential equations (PDEs) from sparse measurements is a challenging task because the governing equations are strongly nonlinear and observations are available at only a few locations. Fluid velocity fields are a representative case. In this paper, we propose a variational quantum algorithm that reconstructs the solution over the entire spacetime domain at once. Rather than marching in time, the method encodes the full discrete spacetime solution in a single variational quantum state, so that all time points are optimized jointly. The cost function combines a sparse-measurement mismatch term with a physics-informed PDE violation term, letting data and the governing equation constrain the solution simultaneously. We demonstrate the method on the one-dimensional Burgers and Kuramoto--Sivashinsky equations using numerical simulations. The results suggest that variational quantum algorithms with a spacetime encoding scheme offer a compact framework for reconstructing nonlinear PDE dynamics.

quant-ph↗

arXiv2026

Efficient Quantum Simulation of Variable-Coefficient Transport with Continuous Source Injection

Quantum time-marching algorithms for transport PDEs often represent variable coefficients and forcing through register-expanding dilations, block-encoding oracles, or repeated postselection. We present an alternative algorithm for a forced variable-coefficient advection-diffusion equation in flow-inspired skew-symmetric form that incorporates spatially varying velocity, viscous dissipation, and persistent source injection with a peak logical requirement of $n_q+1$ qubits. A centered skew-symmetric discretization makes the advection operator strictly skew-Hermitian for arbitrary velocity profiles, enabling an ancilla-free unitary realization using a Gray-code Trotter sequence of controlled-$R_y$ rotations. Diffusion is applied in the Fourier basis through a uniformly controlled rotation on one postselected ancilla, which is measured, reset, and reused between the two diffusion half-steps, while the source is incorporated classically through second-order Strang splitting. Statevector simulations for $N=16$ and $32$ recover second-order temporal convergence against high-accuracy classical solutions, while Richardson extrapolation gives fourth-order accuracy and reduces kernel calls by factors of four to fourteen. Independent tests through $N=256$ confirm second-order spatial consistency. We further show that the per-step ancilla failure probability is proportional to the instantaneous viscous dissipation rate, making postselection cost self-regulating over a fifty-fold viscosity range. Stable evolution is demonstrated for $5\times10^4$ time steps without observable secular error growth, while Gray-code advection accounts for $71$--$95\%$ of transpiled controlled-NOT gates. The fixed-width kernel provides a qubit-efficient building block for near-term hardware studies, although classical readout and state re-preparation remain the main obstacles to coherent multistep evolution.

quant-ph↗

arXiv2024

Analytical exciton energies in monolayer transition-metal dichalcogenides

We derive an analytical expression for $s$-state exciton energies in monolayer transition-metal dichalcogenides (TMDCs): $E_{\text{ns}}=-{\text{Ry}}^*\times P_n/{(n-1/2+0.479\, r^*_0/κ)^2}$, $n=1,2,...$, where $r^*_0$ and $κ$ are the dimensionless screening length and dielectric constant of the surrounding medium; $\text{Ry}^*$ is an effective Rydberg energy scaled by the dielectric constant and exciton reduced mass; $P_n(r^*_0/κ)$ is a function of variables $n$ and $r^*_0/κ$. Its values are around 1.0 so we consider it a term that corrects the Rydberg energy. Despite the simple form, the suggested formula gives exciton energies with high precision compared to the exact numerical solutions that accurately describe recent experimental data for a large class of TMDC materials, including WSe$_2$, WS$_2$, MoSe$_2$, MoS$_2$, and MoTe$_2$. To achieve these results, we have developed a so-called regulated perturbation theory by combining the conventional perturbation method with several elements of the Feranchuk-Komarov operator method, including the Levi-Civita transformation, the algebraic calculation technique via the annihilation and creation operators, and the introduction of a free parameter to optimize the convergence rate of the perturbation series. This universal form of exciton energies could be helpful in various physical analyses, including retrieval of the material parameters such as reduced exciton mass and screening length from the available measured exciton energies.

cond-mat.mtrl-sci↗