Qubit (qiskit_addon_sqd.qubit)

Functions for handling quantum samples.

solve_qubit(bitstring_matrix, hamiltonian, *, verbose=False, **scipy_kwargs)

Find the energies and eigenstates of a Hamiltonian projected into a subspace.

The subspace is defined by a collection of computational basis states which are specified by the bitstrings (rows) in the bitstring_matrix.

This function calls scipy.sparse.linalg.eigsh for the diagonalization.

Parameters:

• bitstring_matrix (ndarray) – A 2D array of bool representations of bit values such that each row represents a single bitstring. This set of bitstrings specifies the subspace into which the hamiltonian will be projected and diagonalized.

• hamiltonian (SparsePauliOp) – A Hamiltonian specified as a Pauli operator.

• verbose (bool) – Whether to print the stage of the subroutine.

• **scipy_kwargs –

  Keyword arguments to be passed to scipy.sparse.linalg.eigsh.

Returns:

• 1D array with the eigenvalues

• 2D array with the eigenvectors. Each column represents an eigenvector.

Raises:

ValueError – Bitstrings (rows) in bitstring_matrix must have length < 64.

Return type:

tuple[ndarray, ndarray]

project_operator_to_subspace(bitstring_matrix, hamiltonian, *, verbose=False)

Project a Pauli operator onto a Hilbert subspace defined by the computational basis states (rows) in bitstring_matrix.

The output sparse matrix, A, represents an NxN matrix s.t. N is the number of rows in bitstring_matrix. The rows of A represent the input configurations, and the columns represent the connected component associated with the configuration in the corresponding row. The non-zero elements of the matrix represent the complex amplitudes associated with the connected components.

Note

The bitstrings in the bitstring_matrix must be unique and sorted in ascending order according to their unsigned integer representation. Otherwise the projection will return wrong results. This function does not explicitly check for uniqueness and order because this can be rather time consuming. See qiskit_addon_sqd.qubit.sort_and_remove_duplicates() for a simple way to ensure your bitstring matrix is well-formatted.

Note

This function relies on jax to efficiently perform some calculations. jax converts the bit arrays to int64_t, which means the bit arrays in bitstring_matrix may not have length greater than 63.

Parameters:

• bitstring_matrix (ndarray) – A 2D array of bool representations of bit values such that each row represents a single bitstring. This set of bitstrings specifies the subspace into which the hamiltonian will be projected and diagonalized.

• hamiltonian (SparsePauliOp) – A Pauli operator to project onto a Hilbert subspace defined by bitstring_matrix.

• verbose (bool) – Whether to print the stage of the subroutine.

Returns:

A scipy.sparse.coo_matrix representing the operator projected in the subspace. The rows represent the input configurations, and the columns represent the connected component associated with the configuration in the corresponding row. The non-zero elements of the matrix represent the complex amplitudes associated with the pairs of connected components.

Raises:

ValueError – Bitstrings (rows) in bitstring_matrix must have length < 64.

Return type:

spmatrix

sort_and_remove_duplicates(bitstring_matrix)

Sort a bitstring matrix and remove duplicate entries.

The lowest bitstring values will be placed in the lowest-indexed rows.

Parameters:

bitstring_matrix (ndarray) – A 2D array of bool representations of bit values such that each row represents a single bitstring.

Returns:

Sorted version of bitstring_matrix without repeated rows.

Return type:

ndarray

matrix_elements_from_pauli(bitstring_matrix, pauli)

Find the sparse matrix elements of a Pauli operator in the subspace defined by the bitstrings.

The sparse matrix, A, defined by the outputs represents an NxN matrix s.t. N is the number of rows in bitstring_matrix. The rows of A represent the input configurations, and the columns represent the connected component associated with the configuration in the corresponding row. The output arrays define the sparse matrix, A, as follows:

A[rows[k], cols[k]] = amplutides[k].

Note

The bitstrings in the bitstring_matrix must be unique and sorted in ascending order according to their unsigned integer representation. Otherwise the projection will return wrong results. This function does not explicitly check for uniqueness and order because this can be rather time consuming. See qiskit_addon_sqd.qubit.sort_and_remove_duplicates() for a simple way to ensure your bitstring matrix is well-formatted.

Note

This function relies on jax to efficiently perform some calculations. jax converts the bit arrays to int64_t, which means the bit arrays in bitstring_matrix may not have length greater than 63.

Parameters:

• bitstring_matrix (ndarray) – A 2D array of bool representations of bit values such that each row represents a single bitstring. The bitstrings in the matrix must be sorted according to their unsigned integer representations. Otherwise the projection will return wrong results.

• pauli (Pauli) – A Pauli operator for which to find connected elements

Returns:

• The complex amplitudes corresponding to the nonzero matrix elements

• The row indices corresponding to non-zero matrix elements

• The column indices corresponding to non-zero matrix elements

Raises:

ValueError – Bitstrings (rows) in bitstring_matrix must have length < 64.

Return type:

tuple[ndarray, ndarray, ndarray]