2 results about "Conjugate transpose" patented technology

This invention discloses a multi-core computing method and apparatus for QR decomposition that integrates column-block TSQR and tile update. The method includes: for a large-scale matrix to be decomposed, horizontally dividing it into blocks based on the number of cores in the multi-core processor, and further dividing the large-scale matrix into multiple layers according to the tile update method; constructing a multi-stage pipeline with a binary tree structure, performing parallel triangular decomposition on the initial layers of the large-scale matrix through the multi-core processor to obtain the corresponding upper triangular matrix and orthogonal matrix; replacing the original layer block matrix with the upper triangular matrix, performing conjugate transpose on the orthogonal matrix to obtain the update matrix, and implementing parallel updates for the remaining layers through the multi-core processor; based on the reflection vector implicitly stored by the multi-core processor during the parallel triangular decomposition process, solving for the overall orthogonal matrix corresponding to the large-scale matrix, and simultaneously outputting the overall upper triangular matrix obtained after layer update. This invention can realize QR decomposition of large-scale matrices.

A computing device including one or more processing devices configured to receive classical shadow measurement results associated with a fermion wavefunction. The fermion wavefunction may describe a particle-number-conserving fermion system. The one or more processing devices may compute an estimated k-reduced density matrix (k-RDM), where k is a number of ladder operator pairs. Computing the estimated k-RDM may include computing, as terms of the estimated k-RDM, traces of respective products of a number operator of the particle-number-conserving fermion system, a single-particle basis rotation matrix dependent upon the classical shadow measurement result, elementary symmetric polynomials of Majorana bivectors, and a conjugate transpose of the single-particle basis rotation matrix. Computing each trace may include iteratively computing derivatives of a Pfaffian. The one or more processing devices may output the estimated k-RDM.