Patent ID: 11894107
Assignee: INTERNATIONAL BUSINESS MACHINES CORPORATION
Field: Computer technology (Electrical engineering)
Classification: CPC G | IPC G

Claim 4:
5. The system of claim 1, wherein:
the generating the unitary matrix comprises generating a unitary n-by-n permutation matrix, R, that corresponds to the spatial point group symmetry operation, such that there exists a first matrix, {circumflex over (R)}, wherein {circumflex over (R)}ap {circumflex over (R)}†=Σq=1np|R|qaq for all 1≤p≤n, wherein n is a number of fermionic modes of the molecule, and wherein ap and aq are fermionic annihilation operators;
the generating the Hermitian matrix comprises generating the Hermitian matrix, G, wherein R=exp (iG) such that there exists a second matrix, Ĝ, wherein R=exp(iG), such that there exists a second matrix, Ĝ, wherein Ĝ=Σp,q=1np|G|qap†aq; and
the generating the diagonalized second quantization representation comprises:
generating a unitary n-by-n matrix, V, that diagonalizes G such that V†GV=Σp=1nλp|p) (p|, wherein λp is a real eigenvalue, such that there exists a third matrix, {circumflex over (V)}, wherein {circumflex over (V)}, wherein {circumflex over (V)}ap{circumflex over (V)}†=Σq=1np|V|qaq for all 1≤p≤n; and
generating as the diagonalized second quantization representation an operator S such that S={circumflex over (V)}{circumflex over (R)}{circumflex over (V)}†=exp({circumflex over (V)}Ĝ{circumflex over (V)}†)=Πp=1n exp (iλpap†ap).