# braket.default_simulator.observables module¶

class braket.default_simulator.observables.Identity(targets: Optional[List[int]] = None)[source]

Identity observable

Note

This observable refers to the same mathematical object as the gate operation of the same name, but is meant to be used differently; the observable is viewed as a Hermitian operator to be measured, while the gate is viewed as a unitary operator to evolve the state of the system.

targets

The indices of the qubits the operation applies to.

Note: For an index to be a target of an observable, the observable must have a nontrivial (i.e. non-identity) action on that index. For example, a tensor product observable with a Z factor on qubit j acts trivially on j, so j would not be a target. This does not apply to gate operations.

Type: Tuple[int, ..]
measured_qubits

The indices of the qubits that are measured for this observable.

Unlike targets, this includes indices on which the observable acts trivially. For example, a tensor product observable made entirely of n Z factors will have n measured qubits.

Type: Tuple[int, ..]
eigenvalues

The eigenvalues of the observable ordered by computational basis state.

Type: np.ndarray
apply(state: numpy.ndarray) → numpy.ndarray[source]

Applies this observable to the given state.

Parameters: state (np.ndarray) – The state to apply the observable to. np.ndarray – The state after the observable has been applied.
fix_qubit(qubit: int) → braket.default_simulator.operation.Observable[source]

Creates a copy of it acting on the given qubit.

Only defined for observables that act on 1 qubit.

Parameters: qubit (int) – The target qubit of the new observable. Observable – A copy of this observable, acting on the new qubit.
diagonalizing_gates(num_qubits: Optional[int] = None) → Tuple[braket.default_simulator.operation.GateOperation, ...][source]

The gates that diagonalize the observable in the computational basis.

Parameters: num_qubits (int, optional) – The number of qubits the observable acts on. Only used if no target is specified, in which case a gate is created for each target qubit. This only makes sense for single-qubit observables. Tuple[GateOperation, …] – The gates that diagonalize the observable in the computational basis, if it is not already in the computational basis. If there is no explicit target, this method returns a tuple of gates acting on every qubit.
class braket.default_simulator.observables.Hadamard(targets: Optional[List[int]] = None)[source]

Bases: braket.default_simulator.observables._InvolutoryMatrixObservable

Note

This observable refers to the same mathematical object as the gate operation of the same name, but is meant to be used differently; the observable is viewed as a Hermitian operator to be measured, while the gate is viewed as a unitary operator to evolve the state of the system.

is_standard

Whether the observable is Pauli-like, that is, has eigenvalues of $$\pm 1$$.

Examples include the Pauli and Hadamard observables.

Type: bool
eigenvalues

The eigenvalues of the observable ordered by computational basis state.

Type: np.ndarray
fix_qubit(qubit: int) → braket.default_simulator.operation.Observable[source]

Creates a copy of it acting on the given qubit.

Only defined for observables that act on 1 qubit.

Parameters: qubit (int) – The target qubit of the new observable. Observable – A copy of this observable, acting on the new qubit.
diagonalizing_gates(num_qubits: Optional[int] = None) → Tuple[braket.default_simulator.operation.GateOperation, ...][source]

The gates that diagonalize the observable in the computational basis.

Parameters: num_qubits (int, optional) – The number of qubits the observable acts on. Only used if no target is specified, in which case a gate is created for each target qubit. This only makes sense for single-qubit observables. Tuple[GateOperation, …] – The gates that diagonalize the observable in the computational basis, if it is not already in the computational basis. If there is no explicit target, this method returns a tuple of gates acting on every qubit.
class braket.default_simulator.observables.PauliX(targets: Optional[List[int]] = None)[source]

Bases: braket.default_simulator.observables._InvolutoryMatrixObservable

Pauli-X observable

Note

This observable refers to the same mathematical object as the gate operation of the same name, but is meant to be used differently; the observable is viewed as a Hermitian operator to be measured, while the gate is viewed as a unitary operator to evolve the state of the system.

is_standard

Whether the observable is Pauli-like, that is, has eigenvalues of $$\pm 1$$.

Examples include the Pauli and Hadamard observables.

Type: bool
eigenvalues

The eigenvalues of the observable ordered by computational basis state.

Type: np.ndarray
fix_qubit(qubit: int) → braket.default_simulator.operation.Observable[source]

Creates a copy of it acting on the given qubit.

Only defined for observables that act on 1 qubit.

Parameters: qubit (int) – The target qubit of the new observable. Observable – A copy of this observable, acting on the new qubit.
diagonalizing_gates(num_qubits: Optional[int] = None) → Tuple[braket.default_simulator.operation.GateOperation, ...][source]

The gates that diagonalize the observable in the computational basis.

Parameters: num_qubits (int, optional) – The number of qubits the observable acts on. Only used if no target is specified, in which case a gate is created for each target qubit. This only makes sense for single-qubit observables. Tuple[GateOperation, …] – The gates that diagonalize the observable in the computational basis, if it is not already in the computational basis. If there is no explicit target, this method returns a tuple of gates acting on every qubit.
class braket.default_simulator.observables.PauliY(targets: Optional[List[int]] = None)[source]

Bases: braket.default_simulator.observables._InvolutoryMatrixObservable

Pauli-Y observable

Note

This observable refers to the same mathematical object as the gate operation of the same name, but is meant to be used differently; the observable is viewed as a Hermitian operator to be measured, while the gate is viewed as a unitary operator to evolve the state of the system.

is_standard

Whether the observable is Pauli-like, that is, has eigenvalues of $$\pm 1$$.

Examples include the Pauli and Hadamard observables.

Type: bool
eigenvalues

The eigenvalues of the observable ordered by computational basis state.

Type: np.ndarray
fix_qubit(qubit: int) → braket.default_simulator.operation.Observable[source]

Creates a copy of it acting on the given qubit.

Only defined for observables that act on 1 qubit.

Parameters: qubit (int) – The target qubit of the new observable. Observable – A copy of this observable, acting on the new qubit.
diagonalizing_gates(num_qubits: Optional[int] = None) → Tuple[braket.default_simulator.operation.GateOperation, ...][source]

The gates that diagonalize the observable in the computational basis.

Parameters: num_qubits (int, optional) – The number of qubits the observable acts on. Only used if no target is specified, in which case a gate is created for each target qubit. This only makes sense for single-qubit observables. Tuple[GateOperation, …] – The gates that diagonalize the observable in the computational basis, if it is not already in the computational basis. If there is no explicit target, this method returns a tuple of gates acting on every qubit.
class braket.default_simulator.observables.PauliZ(targets: Optional[List[int]] = None)[source]

Bases: braket.default_simulator.observables._InvolutoryMatrixObservable

Pauli-Z observable

Note

This observable refers to the same mathematical object as the gate operation of the same name, but is meant to be used differently; the observable is viewed as a Hermitian operator to be measured, while the gate is viewed as a unitary operator to evolve the state of the system.

targets

The indices of the qubits the operation applies to.

Note: For an index to be a target of an observable, the observable must have a nontrivial (i.e. non-identity) action on that index. For example, a tensor product observable with a Z factor on qubit j acts trivially on j, so j would not be a target. This does not apply to gate operations.

Type: Tuple[int, ..]
measured_qubits

The indices of the qubits that are measured for this observable.

Unlike targets, this includes indices on which the observable acts trivially. For example, a tensor product observable made entirely of n Z factors will have n measured qubits.

Type: Tuple[int, ..]
is_standard

Whether the observable is Pauli-like, that is, has eigenvalues of $$\pm 1$$.

Examples include the Pauli and Hadamard observables.

Type: bool
eigenvalues

The eigenvalues of the observable ordered by computational basis state.

Type: np.ndarray
fix_qubit(qubit: int) → braket.default_simulator.operation.Observable[source]

Creates a copy of it acting on the given qubit.

Only defined for observables that act on 1 qubit.

Parameters: qubit (int) – The target qubit of the new observable. Observable – A copy of this observable, acting on the new qubit.
diagonalizing_gates(num_qubits: Optional[int] = None) → Tuple[braket.default_simulator.operation.GateOperation, ...][source]

The gates that diagonalize the observable in the computational basis.

Parameters: num_qubits (int, optional) – The number of qubits the observable acts on. Only used if no target is specified, in which case a gate is created for each target qubit. This only makes sense for single-qubit observables. Tuple[GateOperation, …] – The gates that diagonalize the observable in the computational basis, if it is not already in the computational basis. If there is no explicit target, this method returns a tuple of gates acting on every qubit.
class braket.default_simulator.observables.Hermitian(matrix: numpy.ndarray, targets: Optional[List[int]] = None)[source]

Arbitrary Hermitian observable

matrix

The Hermitian matrix defining the observable.

Type: np.ndarray
targets

The indices of the qubits the operation applies to.

Note: For an index to be a target of an observable, the observable must have a nontrivial (i.e. non-identity) action on that index. For example, a tensor product observable with a Z factor on qubit j acts trivially on j, so j would not be a target. This does not apply to gate operations.

Type: Tuple[int, ..]
eigenvalues

The eigenvalues of the observable ordered by computational basis state.

Type: np.ndarray
apply(state: numpy.ndarray) → numpy.ndarray[source]

Applies this observable to the given state.

Parameters: state (np.ndarray) – The state to apply the observable to. np.ndarray – The state after the observable has been applied.
fix_qubit(qubit: int) → braket.default_simulator.operation.Observable[source]

Creates a copy of it acting on the given qubit.

Only defined for observables that act on 1 qubit.

Parameters: qubit (int) – The target qubit of the new observable. Observable – A copy of this observable, acting on the new qubit.
diagonalizing_gates(num_qubits: Optional[int] = None) → Tuple[braket.default_simulator.operation.GateOperation, ...][source]

The gates that diagonalize the observable in the computational basis.

Parameters: num_qubits (int, optional) – The number of qubits the observable acts on. Only used if no target is specified, in which case a gate is created for each target qubit. This only makes sense for single-qubit observables. Tuple[GateOperation, …] – The gates that diagonalize the observable in the computational basis, if it is not already in the computational basis. If there is no explicit target, this method returns a tuple of gates acting on every qubit.
class braket.default_simulator.observables.TensorProduct(factors: List[braket.default_simulator.operation.Observable])[source]

Tensor product of multiple observables.

Parameters: factors (List[Observable]) – The observables to combine together into a tensor product
factors
targets

The indices of the qubits the operation applies to.

Note: For an index to be a target of an observable, the observable must have a nontrivial (i.e. non-identity) action on that index. For example, a tensor product observable with a Z factor on qubit j acts trivially on j, so j would not be a target. This does not apply to gate operations.

Type: Tuple[int, ..]
measured_qubits

The indices of the qubits that are measured for this observable.

Unlike targets, this includes indices on which the observable acts trivially. For example, a tensor product observable made entirely of n Z factors will have n measured qubits.

Type: Tuple[int, ..]
eigenvalues

The eigenvalues of the observable ordered by computational basis state.

Type: np.ndarray
apply(state: numpy.ndarray) → numpy.ndarray[source]

Applies this observable to the given state.

Parameters: state (np.ndarray) – The state to apply the observable to. np.ndarray – The state after the observable has been applied.
fix_qubit(qubit: int) → braket.default_simulator.operation.Observable[source]

Creates a copy of it acting on the given qubit.

Only defined for observables that act on 1 qubit.

Parameters: qubit (int) – The target qubit of the new observable. Observable – A copy of this observable, acting on the new qubit.
diagonalizing_gates(num_qubits: Optional[int] = None) → Tuple[braket.default_simulator.operation.GateOperation, ...][source]

The gates that diagonalize the observable in the computational basis.

Parameters: num_qubits (int, optional) – The number of qubits the observable acts on. Only used if no target is specified, in which case a gate is created for each target qubit. This only makes sense for single-qubit observables. Tuple[GateOperation, …] – The gates that diagonalize the observable in the computational basis, if it is not already in the computational basis. If there is no explicit target, this method returns a tuple of gates acting on every qubit.