cirq.PauliSum

Represents operator defined by linear combination of PauliStrings.

cirq.PauliSum(
    linear_dict: Optional[value.LinearDict[UnitPauliStringT]] = None
)

Since cirq.PauliStrings store their own coefficients, this class does not implement the cirq.LinearDict interface. Instead, you can add and subtract terms and then iterate over the resulting (simplified) expression.

Under the hood, this class is backed by a LinearDict with coefficient-less PauliStrings as keys. PauliStrings are reconstructed on-the-fly during iteration.

PauliSums can be constructed explicitly:

a, b = cirq.GridQubit.rect(1, 2)
psum = cirq.PauliSum.from_pauli_strings([
    cirq.PauliString(-1, cirq.X(a), cirq.Y(b)),
    cirq.PauliString(2, cirq.Z(a), cirq.Z(b)),
    cirq.PauliString(0.5, cirq.Y(a), cirq.Y(b))
])
print(psum)
-1.000*X(q(0, 0))*Y(q(0, 1))+2.000*Z(q(0, 0))*Z(q(0, 1))+0.500*Y(q(0, 0))*Y(q(0, 1))

or implicitly:

a, b = cirq.GridQubit.rect(1, 2)
psum = cirq.X(a) * cirq.X(b) + 3.0 * cirq.Y(a)
print(psum)
1.000*X(q(0, 0))*X(q(0, 1))+3.000*Y(q(0, 0))

basic arithmetic and expectation operations are supported as well:

a, b = cirq.GridQubit.rect(1, 2)
psum = cirq.X(a) * cirq.X(b) + 3.0 * cirq.Y(a)
two_psum = 2 * psum
four_psum = two_psum + two_psum
print(four_psum)
4.000*X(q(0, 0))*X(q(0, 1))+12.000*Y(q(0, 0))
 
expectation = four_psum.expectation_from_state_vector(
    np.array([0.707106, 0, 0, 0.707106], dtype=complex),
    qubit_map={a: 0, b: 1}
)
print(f'{expectation:.1f}')
4.0+0.0j

linear_dict Set of (cirq.Qid, cirq.Pauli) tuples to construct the sum from.

ValueError If structure of linear_dict contains tuples other than the form (cirq.Qid, cirq.Pauli).

qubits The sorted list of qubits used in this PauliSum.

Methods

copy

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copy() -> 'PauliSum'

Return a copy of this PauliSum.

Returns: A copy of this PauliSum.

expectation_from_density_matrix

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expectation_from_density_matrix(
    state: np.ndarray,
    qubit_map: Mapping[cirq.Qid, int],
    *,
    atol: float = 1e-07,
    check_preconditions: bool = True
) -> float

Evaluate the expectation of this PauliSum given a density matrix.

See PauliString.expectation_from_density_matrix.

Args
state An array representing a valid density matrix.
qubit_map A map from all qubits used in this PauliSum to the indices of the qubits that state is defined over.
atol Absolute numerical tolerance.
check_preconditions Whether to check that state represents a valid density matrix.

Returns
The expectation value of the input state.

Raises
NotImplementedError If any of the coefficients are imaginary, so that this is not Hermitian.
TypeError If the input state is not a complex type.
ValueError If the input vector is not the correct size or shape.

expectation_from_state_vector

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expectation_from_state_vector(
    state_vector: np.ndarray,
    qubit_map: Mapping[cirq.Qid, int],
    *,
    atol: float = 1e-07,
    check_preconditions: bool = True
) -> float

Evaluate the expectation of this PauliSum given a state vector.

See PauliString.expectation_from_state_vector.

Args
state_vector An array representing a valid state vector.
qubit_map A map from all qubits used in this PauliSum to the indices of the qubits that state_vector is defined over.
atol Absolute numerical tolerance.
check_preconditions Whether to check that state_vector represents a valid state vector.

Returns
The expectation value of the input state.

Raises
NotImplementedError If any of the coefficients are imaginary, so that this is not Hermitian.
TypeError If the input state is not a complex type.
ValueError If the input vector is not the correct size or shape.

from_boolean_expression

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@classmethod
from_boolean_expression(
    boolean_expr: Expr, qubit_map: Dict[str, 'cirq.Qid']
) -> 'PauliSum'

Builds the Hamiltonian representation of a Boolean expression.

This is based on "On the representation of Boolean and real functions as Hamiltonians for quantum computing" by Stuart Hadfield, https://arxiv.org/abs/1804.09130

Args
boolean_expr A Sympy expression containing symbols and Boolean operations
qubit_map map of string (boolean variable name) to qubit.

Return
The PauliSum that represents the Boolean expression.

Raises
ValueError If boolean_expr is of an unsupported type.

from_pauli_strings

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@classmethod
from_pauli_strings(
    terms: Union[PauliString, List[PauliString]]
) -> 'PauliSum'

Returns a PauliSum by combining cirq.PauliString terms.

Args
terms cirq.PauliString or List of cirq.PauliStrings to use inside of this PauliSum object.

Returns
PauliSum object representing the addition of all the cirq.PauliString terms in terms.

matrix

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matrix(
    qubits: Optional[Iterable[raw_types.Qid]] = None
) -> np.ndarray

Returns the matrix of this PauliSum in computational basis of qubits.

Args
qubits Ordered collection of qubits that determine the subspace in which the matrix representation of the Pauli sum is to be computed. If none is provided the default ordering of self.qubits is used. Qubits present in qubits but absent from self.qubits are acted on by the identity.

Returns
np.ndarray representing the matrix of this PauliSum expression.

Raises
TypeError if any of the gates in self does not provide a unitary.

with_qubits

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with_qubits(
    *new_qubits
) -> 'PauliSum'

Return a new PauliSum on new_qubits.

Args
*new_qubits cirq.Qid objects to replace existing qubit objects in this PauliSum.

Returns
PauliSum with new_qubits replacing the previous qubits.

Raises
ValueError If len(new_qubits) != len(self.qubits).

wrap

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@staticmethod
wrap(
    val: cirq.PauliSumLike
) -> 'PauliSum'

Convert a cirq.PauliSumLike object to a PauliSum

Attempts to convert an existing int, float, complex, cirq.PauliString, cirq.PauliSum or cirq.SingleQubitPauliStringGateOperation into a cirq.PauliSum object. For example:

my_psum = cirq.PauliSum.wrap(2.345)
my_psum
cirq.PauliSum(cirq.LinearDict({frozenset(): (2.345+0j)}))

Args
cirq.PauliSumLike to convert to PauliSum.

Returns
PauliSum representation of val.

__add__

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__add__(
    other
)

__bool__

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__bool__() -> bool

__eq__

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__eq__(
    other: _SupportsValueEquality
) -> bool

__iter__

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__iter__()

__len__

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__len__() -> int

__mul__

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__mul__(
    other: cirq.PauliSumLike
)

__ne__

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__ne__(
    other: _SupportsValueEquality
) -> bool

__neg__

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__neg__()

__pow__

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__pow__(
    exponent: int
)

__radd__

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__radd__(
    other
)

__rmul__

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__rmul__(
    other: cirq.PauliSumLike
)

__rsub__

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__rsub__(
    other
)

__sub__

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__sub__(
    other
)

__truediv__

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__truediv__(
    a: value.Scalar
)