63 research outputs found
A domain-specific language and matrix-free stencil code for investigating electronic properties of Dirac and topological materials
We introduce PVSC-DTM (Parallel Vectorized Stencil Code for Dirac and
Topological Materials), a library and code generator based on a domain-specific
language tailored to implement the specific stencil-like algorithms that can
describe Dirac and topological materials such as graphene and topological
insulators in a matrix-free way. The generated hybrid-parallel (MPI+OpenMP)
code is fully vectorized using Single Instruction Multiple Data (SIMD)
extensions. It is significantly faster than matrix-based approaches on the node
level and performs in accordance with the roofline model. We demonstrate the
chip-level performance and distributed-memory scalability of basic building
blocks such as sparse matrix-(multiple-) vector multiplication on modern
multicore CPUs. As an application example, we use the PVSC-DTM scheme to (i)
explore the scattering of a Dirac wave on an array of gate-defined quantum
dots, to (ii) calculate a bunch of interior eigenvalues for strong topological
insulators, and to (iii) discuss the photoemission spectra of a disordered Weyl
semimetal.Comment: 16 pages, 2 tables, 11 figure
Shift-invert diagonalization of large many-body localizing spin chains
We provide a pedagogical review on the calculation of highly excited
eigenstates of disordered interacting quantum systems which can undergo a
many-body localization (MBL) transition, using shift-invert exact
diagonalization. We also provide an example code at
https://bitbucket.org/dluitz/sinvert_mbl/. Through a detailed analysis of the
simulational parameters of the random field Heisenberg spin chain, we provide a
practical guide on how to perform efficient computations. We present data for
mid-spectrum eigenstates of spin chains of sizes up to . This work is
also geared towards readers with interest in efficiency of parallel sparse
linear algebra techniques that will find a challenging application in the MBL
problem
Scalable Quantum Computation of Highly Excited Eigenstates with Spectral Transforms
We propose a natural application of Quantum Linear Systems Problem (QLSP)
solvers such as the HHL algorithm to efficiently prepare highly excited
interior eigenstates of physical Hamiltonians in a variational manner. This is
enabled by the efficient computation of inverse expectation values, taking
advantage of the QLSP solvers' exponentially better scaling in problem size
without concealing exponentially costly pre/post-processing steps that usually
accompanies it. We detail implementations of this scheme for both
fault-tolerant and near-term quantum computers, analyse their efficiency and
implementability, and discuss applications and simulation results in many-body
physics and quantum chemistry that demonstrate its superior effectiveness and
scalability over existing approaches.Comment: 16 pages, 6 figure
Application de la mécanique quantique à la résolution de problèmes de spectroscopie : développement de méthodes pour le calcul de propriétés d'états métastables
Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal
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