MultiQubitFrame

class MultiQubitFrame(list_operators, *, shape=None)

Bases: BaseFrame[LabelMultiQubitT]

Class that collects all information that any frame of multiple qubits should specify.

This is a representation of an operator-valued vector space frame. The effects are specified as a list of Operator.

Note

This is a base class which collects functionality common to various subclasses. As an end-user you would not use this class directly. Check out povm_toolbox.quantum_info for more general information.

Initialize from explicit operators.

Parameters:

• list_operators (list[Operator]) – list that contains the explicit frame operators. The length of the list is the number of operators of the frame.

• shape (tuple[int, ...] | None) – the shape defining the indexing of operators in list_operators. If None, the default shape is (self.num_operators,).

Raises:

• ValueError – if the length of list_operators is not compatible with shape.

• ValueError – if the frame operators do not have a correct shape. They should all be hermitian and of the same dimension.

Attributes

dimension

The dimension of the Hilbert space on which the effects act.

informationally_complete

If the frame spans the entire Hilbert space.

num_operators

The number of effects of the frame.

operators

Return the list of frame operators.

pauli_operators

Convert the internal frame operators to Pauli form.

Warning

The conversion to Pauli form can be computationally intensive.

Returns:

The frame operators in Pauli form. Each frame operator is returned as a dictionary mapping Pauli labels to coefficients.

Raises:

QiskitError – when the frame operators could not be converted to Pauli form (e.g. when they are not N-qubit operators).

shape

Return the shape of the frame.

Inherited Attributes

num_subsystems

The number of subsystems which the frame operators act on.

For qubits, this is always ${\log }_2($dimension$)$.

Methods

analysis(hermitian_op, frame_op_idx=None)

Return the frame coefficients of hermitian_op.

This method implements the analysis operator $A$ of the frame $\{F_k{\}}_k$:

$$A:\mathcal{O}\mapsto \{\mathrm{Tr}\left[F_k\mathcal{O}\right]{\}}_k,$$

where $c_k=\mathrm{Tr}\left[F_k\mathcal{O}\right]$ are called the frame coefficients of the Hermitian operator $\mathcal{O}$.

Parameters:

• hermitian_op (SparsePauliOp | Operator) – a hermitian operator whose frame coefficients to compute.

• frame_op_idx (LabelMultiQubitT | set[LabelMultiQubitT] | None) – label or set of labels indicating which coefficients are queried. If None, all coefficients are queried.

Returns:

Frame coefficients, specified by frame_op_idx, of the Hermitian operator hermitian_op. If a specific coefficient was queried, a float is returned. If a specific set of coefficients was queried, a dictionary mapping labels to coefficients is returned. If all coefficients were queried, an array with all coefficients is returned.

Raises:

• TypeError – when the provided single or sequence of labels frame_op_idx does not have a valid type.

• ValueError – when the dimension of the provided hermitian_op does not match the dimension of the frame operators.

Return type:

float | dict[LabelMultiQubitT, float] | ndarray

classmethod from_vectors(frame_vectors)

Initialize a frame from non-normalized bloch vectors.

The non-normalized Bloch vectors are given by $|{\tilde{\psi }}_k⟩=\sqrt{{\gamma }_k}|{\psi }_k⟩$. The resulting frame operators are $F_k={\gamma }_k|{\psi }_k⟩⟨{\psi }_k|$ where ${\gamma }_k$ is the trace of the $k$’th frame operator.

Parameters:

frame_vectors (ndarray) – list of vectors $|\widetilde{{\psi }_k}⟩$. The length of the list corresponds to the number of operators of the frame. Each vector is of shape $(\dim ,)$ where $\dim$ is the dimension of the Hilbert space on which the frame acts.

Returns:

The frame corresponding to the vectors.

Return type:

Self