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QuadraticSum

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NameDescription
QuadraticSum(const ComplexMatrix matrix) -> FermionOperatorThe QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}
QuadraticSum(const Operator operator) -> FermionOperatorThe QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}
QuadraticSum(const RealMatrix matrix) -> FermionOperatorThe QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}
QuadraticSum(const RealSparseMatrix matrix) -> FermionOperatorThe QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}
QuadraticSum(const ComplexSparseMatrix matrix) -> FermionOperatorThe QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}
QuadraticSum(const Operator operator, as_real options) -> FermionOperatorThe QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}
QuadraticSum(const Operator operator, as_complex options) -> FermionOperatorThe QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}

QuadraticSum(const ComplexMatrix matrix) -> FermionOperator​

The QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}

Parameters​

  • matrix: The Bogoliubov-de-Gennes matrix of a quadratic fermionic Hamiltonian.

QuadraticSum(const Operator operator) -> FermionOperator​

The QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}

Parameters​

  • operator: A sum of fermionic operators corresponding to either pairing or hopping terms.

QuadraticSum(const RealMatrix matrix) -> FermionOperator​

The QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}

Parameters​

  • matrix: The Bogoliubov-de-Gennes matrix of a quadratic fermionic Hamiltonian.

QuadraticSum(const RealSparseMatrix matrix) -> FermionOperator​

The QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}

Parameters​

  • matrix: The Bogoliubov-de-Gennes matrix of a quadratic fermionic Hamiltonian.

QuadraticSum(const ComplexSparseMatrix matrix) -> FermionOperator​

The QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}

Parameters​

  • matrix: The Bogoliubov-de-Gennes matrix of a quadratic fermionic Hamiltonian.

QuadraticSum(const Operator operator, as_real options) -> FermionOperator​

The QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}

Parameters​

  • operator: A sum of fermionic operators corresponding to either pairing or hopping terms.
  • options: Options used to specify the type of the stored coefficients. Options currently include as_real and as_complex

QuadraticSum(const Operator operator, as_complex options) -> FermionOperator​

The QuadraticSum operator is parametrized by a sparse matrix S(i,j)S(i,j) of size 2L×2L2L \times 2L . The operator represents the sum ∑i,jSi,j+,−fi†fj+Si,j−,+fifj†+Si,j+,+fi†fj†+Si,j−,−fifj\sum_{i,j}S_{i,j}^{+,-}f_i^{\dagger}f_j + S_{i,j}^{-,+}f_if_j^{\dagger} + S_{i,j}^{+,+}f_i^{\dagger}f_j^{\dagger} + S_{i,j}^{-,-}f_if_j with S=(S+,−,S+,+S−,−,S−,+)S =\begin{pmatrix}S^{+,-}, S^{+,+} \\ S^{-,-}, S^{-,+} \end{pmatrix}

Parameters​

  • operator: A sum of fermionic operators corresponding to either pairing or hopping terms.
  • options: Options used to specify the type of the stored coefficients. Options currently include as_real and as_complex