cirq.CliffordTableau

Tableau representation of a stabilizer state

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
)

(based on Aaronson and Gottesman 2006).

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>.

num_qubits The number of qubits in the system.
initial_state The computational basis representation of the state as a big endian int.

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

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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

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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

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apply_global_phase(
    coefficient: linear_dict.Scalar
)

Apply a global phase to the state.

Args
coefficient The global phase to apply.

apply_h

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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

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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

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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

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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

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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

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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

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

Splits two state spaces after a measurement or reset.

inverse

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inverse() -> 'CliffordTableau'

Returns the inverse Clifford tableau of this tableau.

kron

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kron(
    other: TSelf
) -> TSelf

Joins two state spaces together.

matrix

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matrix() -> np.ndarray

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

measure

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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

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

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

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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

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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

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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__

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__eq__(
    other
)

Return self==value.

__matmul__

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__matmul__(
    second: 'CliffordTableau'
)