cirq.CliffordTableau

Tableau representation of a stabilizer state (based on Aaronson and Gottesman 2006).

Inherits From: StabilizerState, QuantumStateRepresentation

cirq.CliffordTableau(
    num_qubits,
    initial_state: int = 0,
    rs: Optional[np.ndarray] = None,
    xs: Optional[np.ndarray] = None,
    zs: Optional[np.ndarray] = None
)

The tableau stores the stabilizer generators of the state using three binary arrays: xs, zs, and rs.

Each row of the arrays represents a Pauli string, P, that is an eigenoperator of the state vector with eigenvalue one: P|psi> = |psi>.

can_represent_mixed_states Subclasses that can represent mixed states should override this.
rs

supports_factor Subclasses that allow factorization should override this.
xs

zs

Methods

apply_cx

View source

apply_cx(
    control_axis: int,
    target_axis: int,
    exponent: float = 1,
    global_shift: float = 0
)

Apply a CX operation to the state.

Args
control_axis The control axis of the operation.
target_axis The axis to which the operation should be applied.
exponent The exponent of the CX operation, must be an integer.
global_shift The global phase shift of the raw operation, prior to exponentiation. Typically the value in gate.global_shift.

Raises
ValueError If the exponent is not an integer.

apply_cz

View source

apply_cz(
    control_axis: int,
    target_axis: int,
    exponent: float = 1,
    global_shift: float = 0
)

Apply a CZ operation to the state.

Args
control_axis The control axis of the operation.
target_axis The axis to which the operation should be applied.
exponent The exponent of the CZ operation, must be an integer.
global_shift The global phase shift of the raw operation, prior to exponentiation. Typically the value in gate.global_shift.

Raises
ValueError If the exponent is not an integer.

apply_global_phase

View source

apply_global_phase(
    coefficient: linear_dict.Scalar
)

Apply a global phase to the state.

Args
coefficient The global phase to apply.

apply_h

View source

apply_h(
    axis: int, exponent: float = 1, global_shift: float = 0
)

Apply an H operation to the state.

Args
axis The axis to which the operation should be applied.
exponent The exponent of the H operation, must be an integer.
global_shift The global phase shift of the raw operation, prior to exponentiation. Typically the value in gate.global_shift.

Raises
ValueError If the exponent is not an integer.

apply_x

View source

apply_x(
    axis: int, exponent: float = 1, global_shift: float = 0
)

Apply an X operation to the state.

Args
axis The axis to which the operation should be applied.
exponent The exponent of the X operation, must be a half-integer.
global_shift The global phase shift of the raw operation, prior to exponentiation. Typically the value in gate.global_shift.

Raises
ValueError If the exponent is not half-integer.

apply_y

View source

apply_y(
    axis: int, exponent: float = 1, global_shift: float = 0
)

Apply an Y operation to the state.

Args
axis The axis to which the operation should be applied.
exponent The exponent of the Y operation, must be a half-integer.
global_shift The global phase shift of the raw operation, prior to exponentiation. Typically the value in gate.global_shift.

Raises
ValueError If the exponent is not half-integer.

apply_z

View source

apply_z(
    axis: int, exponent: float = 1, global_shift: float = 0
)

Apply a Z operation to the state.

Args
axis The axis to which the operation should be applied.
exponent The exponent of the Z operation, must be a half-integer.
global_shift The global phase shift of the raw operation, prior to exponentiation. Typically the value in gate.global_shift.

Raises
ValueError If the exponent is not half-integer.

copy

View source

copy(
    deep_copy_buffers: bool = True
) -> 'CliffordTableau'

Creates a copy of the object.

Args
deep_copy_buffers If True, buffers will also be deep-copied. Otherwise the copy will share a reference to the original object's buffers.

Returns
A copied instance.

destabilizers

View source

destabilizers() -> List['cirq.DensePauliString']

Returns the destabilizer generators of the state. These are n operators {S_1,S_2,...,S_n} such that along with the stabilizer generators above generate the full Pauli group on n qubits.

factor

View source

factor(
    axes: Sequence[int], *, validate=True, atol=1e-07
) -> Tuple[Self, Self]

Splits two state spaces after a measurement or reset.

inverse

View source

inverse() -> 'CliffordTableau'

Returns the inverse Clifford tableau of this tableau.

kron

View source

kron(
    other: Self
) -> Self

Joins two state spaces together.

matrix

View source

matrix() -> np.ndarray

Returns the 2n * 2n matrix representation of the Clifford tableau.

measure

View source

measure(
    axes: Sequence[int], seed: 'cirq.RANDOM_STATE_OR_SEED_LIKE' = None
) -> List[int]

Measures the state.

Args
axes The axes to measure.
seed The random number seed to use.

Returns
The measurements in order.

reindex

View source

reindex(
    axes: Sequence[int]
) -> Self

Physically reindexes the state by the new basis.

Args
axes The desired axis order.

Returns
The state with qubit order transposed and underlying representation updated.

sample

View source

sample(
    axes: Sequence[int],
    repetitions: int = 1,
    seed: 'cirq.RANDOM_STATE_OR_SEED_LIKE' = None
) -> np.ndarray

Samples the state. Subclasses can override with more performant method.

Args
axes The axes to sample.
repetitions The number of samples to make.
seed The random number seed to use.

Returns
The samples in order.

stabilizers

View source

stabilizers() -> List['cirq.DensePauliString']

Returns the stabilizer generators of the state. These are n operators {S_1,S_2,...,S_n} such that S_i |psi> = |psi>

then

View source

then(
    second: 'CliffordTableau'
) -> 'CliffordTableau'

Returns a composed CliffordTableau of this tableau and the second tableau.

Then composed tableau is equal to (up to global phase) the composed unitary operation of the two tableaux, i.e. equivalent to applying the unitary operation of this CliffordTableau then applying the second one.

Args
second The second CliffordTableau to compose with.

Returns
The composed CliffordTableau.

Raises
TypeError If the type of second is not CliffordTableau.
ValueError If the number of qubits in the second tableau mismatch with this tableau.

__eq__

View source

__eq__(
    other
)

Return self==value.

__matmul__

View source

__matmul__(
    second: 'CliffordTableau'
)