Tyler D. Kharazi | Searcharxiv

arXiv2026

Quantum Simulations for Extreme Ultraviolet Photolithography

A key challenge of extreme ultraviolet (EUV) lithography in semiconductor fabrication is the line edge roughness or "blur" produced by the electron cascades following absorption of a high-energy photon. Here we present quantum algorithms to compute EUV absorption and photoelectron emission spectra, which are key to predicting blur. The first is a time-domain algorithm resolving absorption at a given frequency; the second is a first-quantized plane-wave algorithm computing the photoemission spectrum via real-time dynamics that treats bound and continuum states on equal footing. For a model photoresist monomer IMePh, 92 eV absorption requires $200$ logical qubits and $10^{9}$ non-Clifford gates per circuit with $10^3$ shots, while the photoemission spectrum needs $\geq 10^{14}$ gates, $10^4$ shots, and several thousand logical qubits. These results establish high-fidelity quantum simulations as a key component to parameterize the multi-scale macroscopic models required to overcome the electron blur bottleneck in semiconductor miniaturization.

quant-ph↗

arXiv2025

A Quantum Algorithm for the Finite Element Method

The finite element method (FEM) is a cornerstone numerical technique for solving partial differential equations (PDEs). Here, we present $\textbf{Qu-FEM}$, a fault-tolerant era quantum algorithm for the finite element method. In contrast to other quantum PDE solvers, Qu-FEM preserves the geometric flexibility of FEM by introducing two new primitives, the unit of interaction and the local-to-global indicator matrix, which enable the assembly of global finite element arrays with a constant-size linear combination of unitaries. We study the modified Poisson equation as an elliptic problem of interest, and provide explicit circuits for Qu-FEM in Cartesian domains. For problems with constant coefficients, our algorithm admits block-encodings of global arrays that require only $\tilde{\mathcal{O}}\left(d^2 p^2 n\right)$ Clifford+$T$ gates for $d$-dimensional, order-$p$ tensor product elements on grids with $2^n$ degrees of freedom in each dimension, where $n$ is the number of qubits representing the $N=2^n$ discrete grid points. For problems with spatially varying coefficients, we perform numerical integration directly on the quantum computer to assemble global arrays and force vectors. Dirichlet boundary conditions are enforced via the method of Lagrange multipliers, eliminating the need to modify the block-encodings that emerge from the assembly procedure. This work presents a framework for extending the geometric flexibility of quantum PDE solvers while preserving the possibility of a quantum advantage.

quant-ph↗