dorsal/arxiv
View SchemaAn alternative implementation of the Lanczos algorithm for wave function propagation
| Authors | Quanlin Jie, Dunhuan Liu |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0601024 |
| URL | https://arxiv.org/abs/quant-ph/0601024 |
| DOI | 10.1088/0305-4470/39/7/013 |
Abstract
We reformulate the Lanczos algorithm for quantum wave function propagation in terms of variational principle. By including some basis states of previous time steps into the variational subspace, the resultant accuracy increases by several orders. Numerical errors of the alternative method accumulate much slower than that of the original Lanczos method. There is almost no extra numeric cost for the gaining of the accuracy, i.e., the accuracy increase needs no extra operations of the Hamiltonian acting on state vectors, which are the major numeric cost for wave function propagation. A wave packet moving in a 2-dimensional H\'enon-Heiles model serves as an illustration. This method is suitable for small time step propagation of quantum wave functions in large scale time dependent calculations where the operations of the Hamiltonian acting on state vectors are expensive.
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"date_created": "2026-03-02T18:02:24.204000Z",
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"abstract": "We reformulate the Lanczos algorithm for quantum wave function propagation in\nterms of variational principle. By including some basis states of previous time\nsteps into the variational subspace, the resultant accuracy increases by\nseveral orders. Numerical errors of the alternative method accumulate much\nslower than that of the original Lanczos method. There is almost no extra\nnumeric cost for the gaining of the accuracy, i.e., the accuracy increase needs\nno extra operations of the Hamiltonian acting on state vectors, which are the\nmajor numeric cost for wave function propagation. A wave packet moving in a\n2-dimensional H\\\u0027enon-Heiles model serves as an illustration. This method is\nsuitable for small time step propagation of quantum wave functions in large\nscale time dependent calculations where the operations of the Hamiltonian\nacting on state vectors are expensive.",
"arxiv_id": "quant-ph/0601024",
"authors": [
"Quanlin Jie",
"Dunhuan Liu"
],
"categories": [
"quant-ph",
"physics.comp-ph"
],
"doi": "10.1088/0305-4470/39/7/013",
"title": "An alternative implementation of the Lanczos algorithm for wave function propagation",
"url": "https://arxiv.org/abs/quant-ph/0601024"
},
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