braket.default_simulator.observables module

class braket.default_simulator.observables.Identity(targets: list[int] | None = None)

Bases: Observable

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.

property targets: tuple[int, ...]

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, …]

property 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, …]

property eigenvalues: ndarray

The eigenvalues of the observable ordered by computational basis state.

Type:

np.ndarray

apply(state: ndarray) → ndarray

Applies this observable to the given state.

Parameters:

state (np.ndarray) – The state to apply the observable to.

Returns:

np.ndarray – The state after the observable has been applied.

fix_qubit(qubit: int) → Observable

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.

Returns:

Observable – A copy of this observable, acting on the new qubit.

diagonalizing_gates(num_qubits: int | None = None) → tuple[GateOperation, ...]

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.

Returns:

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: list[int] | None = None)

Bases: _InvolutoryMatrixObservable

Hadamard 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.

property is_standard: bool

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

Examples include the Pauli and Hadamard observables.

Type:

bool

property eigenvalues: ndarray

The eigenvalues of the observable ordered by computational basis state.

Type:

np.ndarray

fix_qubit(qubit: int) → Observable

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.

Returns:

Observable – A copy of this observable, acting on the new qubit.

diagonalizing_gates(num_qubits: int | None = None) → tuple[GateOperation, ...]

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.

Returns:

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: list[int] | None = None)

Bases: _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.

property is_standard: bool

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

Examples include the Pauli and Hadamard observables.

Type:

bool

property eigenvalues: ndarray

The eigenvalues of the observable ordered by computational basis state.

Type:

np.ndarray

fix_qubit(qubit: int) → Observable

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.

Returns:

Observable – A copy of this observable, acting on the new qubit.

diagonalizing_gates(num_qubits: int | None = None) → tuple[GateOperation, ...]

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.

Returns:

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: list[int] | None = None)

Bases: _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.

property is_standard: bool

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

Examples include the Pauli and Hadamard observables.

Type:

bool

property eigenvalues: ndarray

The eigenvalues of the observable ordered by computational basis state.

Type:

np.ndarray

fix_qubit(qubit: int) → Observable

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.

Returns:

Observable – A copy of this observable, acting on the new qubit.

diagonalizing_gates(num_qubits: int | None = None) → tuple[GateOperation, ...]

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.

Returns:

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: list[int] | None = None)

Bases: _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.

property targets: tuple[int, ...]

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, …]

property 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, …]

property is_standard: bool

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

Examples include the Pauli and Hadamard observables.

Type:

bool

property eigenvalues: ndarray

The eigenvalues of the observable ordered by computational basis state.

Type:

np.ndarray

fix_qubit(qubit: int) → Observable

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.

Returns:

Observable – A copy of this observable, acting on the new qubit.

diagonalizing_gates(num_qubits: int | None = None) → tuple[GateOperation, ...]

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.

Returns:

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: ndarray, targets: list[int] | None = None)

Bases: Observable

Arbitrary Hermitian observable

property matrix: ndarray

The Hermitian matrix defining the observable.

Type:

np.ndarray

property targets: tuple[int, ...]

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, …]

property eigenvalues: ndarray

The eigenvalues of the observable ordered by computational basis state.

Type:

np.ndarray

apply(state: ndarray) → ndarray

Applies this observable to the given state.

Parameters:

state (np.ndarray) – The state to apply the observable to.

Returns:

np.ndarray – The state after the observable has been applied.

fix_qubit(qubit: int) → Observable

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.

Returns:

Observable – A copy of this observable, acting on the new qubit.

diagonalizing_gates(num_qubits: int | None = None) → tuple[GateOperation, ...]

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.

Returns:

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[Observable])

Bases: Observable

Tensor product of multiple observables.

Parameters:

factors (list[Observable]) – The observables to combine together into a tensor product

property factors: tuple[Observable]

property targets: tuple[int, ...]

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, …]

property measured_qubits: tuple[int, ...]

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, …]

property eigenvalues: ndarray

The eigenvalues of the observable ordered by computational basis state.

Type:

np.ndarray

apply(state: ndarray) → ndarray

Applies this observable to the given state.

Parameters:

state (np.ndarray) – The state to apply the observable to.

Returns:

np.ndarray – The state after the observable has been applied.

fix_qubit(qubit: int) → Observable

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.

Returns:

Observable – A copy of this observable, acting on the new qubit.

diagonalizing_gates(num_qubits: int | None = None) → tuple[GateOperation, ...]

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.

Returns:

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.