# target¶

Graph.target(operator, filter_function_projector=None)

Create information about the target for system time evolution.

Nodes created with this function contain two types of information: the target gate for the system time evolution, and the projection operator that defines the subspace of interest for robustness.

Parameters
• operator (np.ndarray or Tensor) – The target gate $$U_\mathrm{target}$$. Must be a non-zero partial isometry.

• filter_function_projector (np.ndarray, optional) – The orthogonal projection matrix $$P$$ onto the subspace used for filter function calculations. If you provide a value then it must be Hermitian and idempotent. Defaults to the identity matrix.

Returns

The node containing the specified target information.

Return type

Target

infidelity_pwc()

Total infidelity of a system with a piecewise-constant Hamiltonian.

infidelity_stf()

Total infidelity of a system with a sampleable Hamiltonian.

Notes

The target gate $$U_\mathrm{target}$$ is a non-zero partial isometry, which means that it can be expressed in the form $$\sum_j \left|\psi_j\right>\left<\phi_j\right|$$, where $$\left\{\left|\psi_j\right>\right\}$$ and $$\left\{\left|\phi_j\right>\right\}$$ both form (non-empty) orthonormal, but not necessarily complete, sets. Such a target represents a target state $$\left|\psi_j\right>$$ for each initial state $$\left|\phi_j\right>$$. The resulting operational infidelity is 0 if and only if, up to global phase, each initial state $$\left|\phi_j\right>$$ maps exactly to the corresponding final state $$\left|\psi_j\right>$$.

The filter function projector $$P$$ is an orthogonal projection matrix, which means that it satisfies $$P=P^\dagger=P^2$$. The image of $$P$$ defines the set of initial states from which the calculated filter function measures robustness.

Examples

Define a target operation for the Pauli $$X$$ gate.

>>> target_operation = graph.target(operator=np.array([[0, 1], [1, 0]]))
>>> target_operation
<Target: operation_name="target", value_shape=(2, 2)>


See more examples in the How to optimize controls robust to strong noise sources user guide.