qrunch.chemistry.orbital_optimizers.reduced_density_matrices

Module for reduced density matrix (RDM) calculators.

Functions

`project_reduced_density_matrix`(gamma_noisy, ...)	Project a noisy real 1-RDM to the space of valid 1-RDMs using spectral projection.
`project_to_capped_simplex`(eigenvalues, ...)	Project a vector onto the capped simplex.
`project_traceless_symmetric_matrix`(matrix_noisy)	Project a real symmetric matrix to the space of traceless symmetric matrices using a spectral shift.

Classes

`BosonReducedDensityMatrixCalculator`	Class for calculating restricted bosonic 1- and 2-particle reduced density matrices (RDMs).
`RestrictedReducedDensityMatrixCalculator`	Class for calculating restricted 1- and 2-particle reduced density matrices (RDMs).
`UnrestrictedReducedDensityMatrixCalculator`	Class for calculating unrestricted 1- and 2-particle reduced density matrices (RDMs).

class BosonReducedDensityMatrixCalculator

Bases: ReducedDensityMatrixCalculator

Class for calculating restricted bosonic 1- and 2-particle reduced density matrices (RDMs).

The boson RMD is restricted to half the number of qubits compared to the the fermionic RDMs. The restricted single excitation RMD consist of only alpha-alpha component. The restricted double excitation RDM consist of only alpha-alpha-alpha-alpha component

__init__(estimator: Estimator, mapper: Mapper | None = None, *, purify: bool = False) → None

Initialize a reduced density matrix calculator.

Parameters:

estimator (Estimator) – Estimator to use for estimating the RDMs.
mapper (Mapper | None) – mapper to use when mapping RDM operators.
purify (bool) – Purify the reduced density matrices.

Return type:

None

calculate(circuit: Circuit, shots: int | None = None) → RestrictedReducedDensityMatrices

Calculate the 1- and 2-particle RDMs.

Parameters:

circuit (Circuit) – Circuit to use as the ansatz for estimating the RDMs.
shots (int | None) – The number of shots to use in the estimation. Defaults to None.

Return type:

RestrictedReducedDensityMatrices

property estimator: Estimator: Return the estimator.

property mapper: Mapper: Return the mapper.

class RestrictedReducedDensityMatrixCalculator

Bases: ReducedDensityMatrixCalculator

Class for calculating restricted 1- and 2-particle reduced density matrices (RDMs).

The restricted single excitation RMD consist of only alpha-alpha component. The restricted double excitation RDM consist of only alpha-alpha-alpha-alpha component.

__init__(estimator: Estimator, mapper: Mapper | None = None) → None

Initialize a reduced density matrix calculator.

Parameters:

estimator (Estimator) – Estimator to use for estimating the RDMs.
mapper (Mapper | None) – mapper to use when mapping RDM operators.

Return type:

None

calculate(circuit: Circuit, shots: int | None = None) → RestrictedReducedDensityMatrices

Calculate the 1- and 2-particle RDMs.

Parameters:

circuit (Circuit) – Circuit to use as the ansatz for estimating the RDMs.
shots (int | None) – The number of shots to use in the estimation. Defaults to None.

Return type:

RestrictedReducedDensityMatrices

class UnrestrictedReducedDensityMatrixCalculator

Bases: ReducedDensityMatrixCalculator

Class for calculating unrestricted 1- and 2-particle reduced density matrices (RDMs).

The unrestricted 1-RMD consist of both alpha-alpha and beta-beta component. The unrestricted 2-RDM consist of alpha-alpha-alpha-alpha, beta-beta-beta-beta, and beta-alpha-beta-alpha (physics ordering).

__init__(estimator: Estimator, mapper: Mapper | None = None) → None

Initialize a reduced density matrix calculator.

Parameters:

estimator (Estimator) – Estimator to use for estimating the RDMs.
mapper (Mapper | None) – mapper to use when mapping RDM operators.

Return type:

None

calculate(circuit: Circuit, shots: int | None = None) → UnrestrictedReducedDensityMatrices

Calculate the 1- and 2-particle RDMs.

Parameters:

circuit (Circuit) – Circuit to use as the ansatz for estimating the RDMs.
shots (int | None) – The number of shots to use in the estimation. Defaults to None.

Return type:

UnrestrictedReducedDensityMatrices

project_reduced_density_matrix(gamma_noisy: ndarray[Any, dtype[float64]], electron_count: float) → ndarray[Any, dtype[float64]]

Project a noisy real 1-RDM to the space of valid 1-RDMs using spectral projection.

It is assumed that the real 1-RDM fulfills the following conditions: (1) Positive semidefiniteness (eigenvalues >= 0) (2) Eigenvalues must be below or equal to 1 (3) The trace must equal the electron count (4) The matrix is symmetric

This method uses spectral projection for speed: - Diagonalizes the matrix - Clips eigenvalues to [0, 1] - Rescales eigenvalues to match target trace - Reconstructs the matrix from adjusted spectrum

Parameters:

gamma_noisy (ndarray[Any, dtype[float64]]) – Symmetric real matrix with trace approximately equal to electron_count.
electron_count (float) – The desired trace of the projected density matrix.

Raises:

ValueError – If the matrix is not square or not symmetric.

Return type:

ndarray[Any, dtype[float64]]

project_to_capped_simplex(eigenvalues: ndarray[Any, dtype[float64]], target_sum: float, lower: float = 0.0, upper: float = 1.0) → ndarray[Any, dtype[float64]]

Project a vector onto the capped simplex.

Adjusts the entries of the input vector so that the sum equals the target value and each element is confined between the specified lower and upper bounds.

Parameters:

eigenvalues (ndarray[Any, dtype[float64]]) – A numpy array of values to project.
target_sum (float) – Desired sum of the output vector.
lower (float) – The minimum allowed value for each element.
upper (float) – The maximum allowed value for each element.

Return type:

ndarray[Any, dtype[float64]]

project_traceless_symmetric_matrix(matrix_noisy: ndarray[Any, dtype[float64]]) → ndarray[Any, dtype[float64]]

Project a real symmetric matrix to the space of traceless symmetric matrices using a spectral shift.

It is assumed that the input matrix is: (1) Symmetric (2) Real-valued (3) Trace may be non-zero (4) Eigenvalues may be positive or negative

The projection subtracts a scaled identity matrix to enforce tracelessness.

Parameters:: matrix_noisy (ndarray[Any, dtype[float64]]) – Real symmetric matrix to project.
Raises:: ValueError – If the input is not square or symmetric.
Return type:: ndarray[Any, dtype[float64]]