Related papers: Plane Wave Methods for Quantum Eigenvalue Problems…
We propose an adaptive planewave method for eigenvalue problems in electronic structure calculations. The method combines a priori convergence rates and accurate a posteriori error estimates into an effective way of updating the energy…
Incommensurate structures arise from stacking single layers of low-dimensional materials on top of one another with misalignment such as an in-plane twist in orientation. While these structures are of significant physical interest, they…
Motivated by the recently proposed parallel orbital-updating approach in real space method, we propose a parallel orbital-updating based plane-wave basis method for electronic structure calculations, for solving the corresponding eigenvalue…
The computation of electronic structure properties at the quantum level is a crucial aspect of modern physics research. However, conventional methods can be computationally demanding for larger, more complex systems. To address this issue,…
Variational algorithms for strongly correlated chemical and materials systems are one of the most promising applications of near-term quantum computers. We present an extension to the variational quantum eigensolver that approximates the…
This work considers numerical methods for the time-dependent Schr\"{o}dinger equation of incommensurate systems. By using a plane wave method for spatial discretization, the incommensurate problem is lifted to a higher dimension that…
Based on our recently proposed plane wave framework, we theoretically study the localized-extended transition in the one dimensional incommensurate systems with cosine type of potentials, which are in close connection to many recent…
Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…
Eigenvalue problems are critical to several fields of science and engineering. We present a novel unsupervised neural network for discovering eigenfunctions and eigenvalues for differential eigenvalue problems with solutions that…
In Kohn-Sham electronic structure computations, wave functions have singularities at nuclear positions. Because of these singularities, plane-wave expansions give a poor approximation of the eigenfunctions. In conjunction with the use of…
Large-scale eigenvalue problems pose a significant challenge to classical computers. While there are efficient quantum algorithms for unitary or Hermitian matrices, eigenvalue problems for non-normal matrices remain open in quantum…
We present a general quantum circuit design for finding eigenvalues of non-unitary matrices on quantum computers using the iterative phase estimation algorithm. In particular, we show how the method can be used for the simulation of…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
In this paper, we apply the effective potentials in the localization landscape theory (Filoche et al., 2012, Arnold et al., 2016) to study the spectral properties of the incommensurate systems. We uniquely develop a plane wave method for…
We present a semi-analytical approach to compute quasi-guided elastic wave modes in horizontally layered structures radiating into unbounded fluid or solid media. This problem is of relevance, e.g., for the simulation of guided ultrasound…
In solid-state physics, energies of crystals are usually computed with a plane-wave discretization of Kohn-Sham equations. However the presence of Coulomb singularities requires the use of large plane-wave cut-offs to produce accurate…
Quantum computers promise to efficiently solve important problems that are intractable on a conventional computer. For quantum systems, where the dimension of the problem space grows exponentially, finding the eigenvalues of certain…
Quantum algorithms are able to solve particular problems exponentially faster than conventional algorithms, when implemented on a quantum computer. However, all demonstrations to date have required already knowing the answer to construct…
We present a novel method for improving the quantum simulation of the ground state energy of molecules. We perform a pre-processing step classically, which reduces the dimensionality of the problem by generating a custom mapping which…
In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds.…