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Introduction to stochastic error correction methods

Dean Lee, Nathan Salwen, Mark Windoloski

arXiv:hep-lat/0010039Physics Letters BMar 1, 200127 citations

Good error-correcting codes based on very sparse matrices (vol 45, pg 339, 1999)

Djc MacKay

Jul 1, 20013 citations

Error Correcting Codes Based on Probabilistic Decoding and Sparse Matrices

Hironori Uchikawa

Mathematics for industryJan 1, 20140 citations

Quasi-sparse eigenvector diagonalization and stochastic error correction

Dean Lee

We briefly review the diagonalization of quantum Hamiltonians using the quasisparse eigenvector (QSE) method. We also introduce the technique of stochastic error correction, which systematically removes the truncation error of the QSE result by stochastically sampling the contribution of the remaining basis states. 1 Quasi-sparse eigenvector method Quasi-sparse eigenvector (QSE) diagonalization is a new computational method which finds approximate low-lying eigenvalues and eigenvectors for a general quantum field Hamiltonian H [1]. It handles the exponential increase in the dimension of Fock space by exploiting the sparsity of the Hamiltonian. The method is most effective when the splitting between low-lying eigenvalues is not too small compared to the size of the Hamiltonian off-diagonal entries. In such cases the low-lying eigenvectors are quasi-sparse, meaning that the vector is dominated by a small fraction of its largest components. The QSE algorithm is applied using the following steps: (1) Select a subset of orthonormal basis vectors {ei1, · · · , ein} and call theWe briefly review the diagonalization of quantum Hamiltonians using the quasisparse eigenvector (QSE) method. We also introduce the technique of stochastic error correction, which systematically removes the truncation error of the QSE result by stochastically sampling the contribution of the remaining basis states. 1 Quasi-sparse eigenvector method Quasi-sparse eigenvector (QSE) diagonalization is a new computational method which finds approximate low-lying eigenvalues and eigenvectors for a general quantum field Hamiltonian H [1]. It handles the exponential increase in the dimension of Fock space by exploiting the sparsity of the Hamiltonian. The method is most effective when the splitting between low-lying eigenvalues is not too small compared to the size of the Hamiltonian off-diagonal entries. In such cases the low-lying eigenvectors are quasi-sparse, meaning that the vector is dominated by a small fraction of its largest components. The QSE algorithm is applied using the following steps: (1) Select a subset of orthonormal basis vectors {ei1, · · · , ein} and call the

Jan 1, 20001 citation

Stochastic Diagonalization

Hans A. De Raedt, Kristel F. L. Michielsen

Springer proceedings in physicsJan 1, 19990 citations

Stochastic diagonalization

Hans A. De Raedt

Physics ReportsAug 1, 199352 citations

Quasi-sparse eigenvector diagonalization and stochastic error correction

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