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Code source de qiskit.opflow.primitive_ops.pauli_op

# This code is part of Qiskit.
#
# (C) Copyright IBM 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.

"""PauliOp Class """

from math import pi
from typing import Dict, List, Optional, Set, Union, cast

import numpy as np
from scipy.sparse import spmatrix

from qiskit import QuantumCircuit
from qiskit.circuit import Instruction, ParameterExpression
from qiskit.circuit.library import RXGate, RYGate, RZGate, XGate, YGate, ZGate
from qiskit.circuit.library.generalized_gates import PauliGate
from qiskit.opflow.exceptions import OpflowError
from qiskit.opflow.list_ops.summed_op import SummedOp
from qiskit.opflow.list_ops.tensored_op import TensoredOp
from qiskit.opflow.operator_base import OperatorBase
from qiskit.opflow.primitive_ops.primitive_op import PrimitiveOp
from qiskit.quantum_info import Pauli, SparsePauliOp, Statevector


[docs]class PauliOp(PrimitiveOp): """Class for Operators backed by Terra's ``Pauli`` module.""" primitive: Pauli def __init__(self, primitive: Pauli, coeff: Union[complex, ParameterExpression] = 1.0) -> None: """ Args: primitive: The Pauli which defines the behavior of the underlying function. coeff: A coefficient multiplying the primitive. Raises: TypeError: invalid parameters. """ if not isinstance(primitive, Pauli): raise TypeError(f"PauliOp can only be instantiated with Paulis, not {type(primitive)}") super().__init__(primitive, coeff=coeff)
[docs] def primitive_strings(self) -> Set[str]: return {"Pauli"}
@property def num_qubits(self) -> int: return len(self.primitive)
[docs] def add(self, other: OperatorBase) -> OperatorBase: if not self.num_qubits == other.num_qubits: raise ValueError( "Sum over operators with different numbers of qubits, {} and {}, is not well " "defined".format(self.num_qubits, other.num_qubits) ) if isinstance(other, PauliOp) and self.primitive == other.primitive: return PauliOp(self.primitive, coeff=self.coeff + other.coeff) # pylint: disable=cyclic-import from .pauli_sum_op import PauliSumOp if ( isinstance(other, PauliOp) and isinstance(self.coeff, (int, float, complex)) and isinstance(other.coeff, (int, float, complex)) ): return PauliSumOp( SparsePauliOp(self.primitive, coeffs=[self.coeff]) + SparsePauliOp(other.primitive, coeffs=[other.coeff]) ) if isinstance(other, PauliSumOp) and isinstance(self.coeff, (int, float, complex)): return PauliSumOp(SparsePauliOp(self.primitive, coeffs=[self.coeff])) + other return SummedOp([self, other])
[docs] def adjoint(self) -> "PauliOp": return PauliOp(self.primitive.adjoint(), coeff=self.coeff.conjugate())
[docs] def equals(self, other: OperatorBase) -> bool: if isinstance(other, PauliOp) and self.coeff == other.coeff: return self.primitive == other.primitive # pylint: disable=cyclic-import from .pauli_sum_op import PauliSumOp if isinstance(other, PauliSumOp): return other == self return False
def _expand_dim(self, num_qubits: int) -> "PauliOp": return PauliOp(Pauli("I" * num_qubits).expand(self.primitive), coeff=self.coeff)
[docs] def tensor(self, other: OperatorBase) -> OperatorBase: # Both Paulis if isinstance(other, PauliOp): return PauliOp(self.primitive.tensor(other.primitive), coeff=self.coeff * other.coeff) # pylint: disable=cyclic-import from .pauli_sum_op import PauliSumOp if isinstance(other, PauliSumOp): new_primitive = SparsePauliOp(self.primitive).tensor(other.primitive) return PauliSumOp(new_primitive, coeff=self.coeff * other.coeff) from .circuit_op import CircuitOp if isinstance(other, CircuitOp): return self.to_circuit_op().tensor(other) return TensoredOp([self, other])
[docs] def permute(self, permutation: List[int]) -> "PauliOp": """Permutes the sequence of Pauli matrices. Args: permutation: A list defining where each Pauli should be permuted. The Pauli at index j of the primitive should be permuted to position permutation[j]. Returns: A new PauliOp representing the permuted operator. For operator (X ^ Y ^ Z) and indices=[1,2,4], it returns (X ^ I ^ Y ^ Z ^ I). Raises: OpflowError: if indices do not define a new index for each qubit. """ pauli_string = self.primitive.__str__() length = max(permutation) + 1 # size of list must be +1 larger then its max index new_pauli_list = ["I"] * length if len(permutation) != self.num_qubits: raise OpflowError( "List of indices to permute must have the same size as Pauli Operator" ) for i, index in enumerate(permutation): new_pauli_list[-index - 1] = pauli_string[-i - 1] return PauliOp(Pauli("".join(new_pauli_list)), self.coeff)
[docs] def compose( self, other: OperatorBase, permutation: Optional[List[int]] = None, front: bool = False ) -> OperatorBase: new_self, other = self._expand_shorter_operator_and_permute(other, permutation) new_self = cast(PauliOp, new_self) if front: return other.compose(new_self) # Both Paulis if isinstance(other, PauliOp): product = new_self.primitive.dot(other.primitive) return PrimitiveOp(product, coeff=new_self.coeff * other.coeff) # pylint: disable=cyclic-import from .pauli_sum_op import PauliSumOp if isinstance(other, PauliSumOp): return PauliSumOp( SparsePauliOp(new_self.primitive).dot(other.primitive), coeff=new_self.coeff * other.coeff, ) # pylint: disable=cyclic-import from ..state_fns.circuit_state_fn import CircuitStateFn from .circuit_op import CircuitOp if isinstance(other, (CircuitOp, CircuitStateFn)): return new_self.to_circuit_op().compose(other) return super(PauliOp, new_self).compose(other)
[docs] def to_matrix(self, massive: bool = False) -> np.ndarray: OperatorBase._check_massive("to_matrix", True, self.num_qubits, massive) return self.primitive.to_matrix() * self.coeff
[docs] def to_spmatrix(self) -> spmatrix: """Returns SciPy sparse matrix representation of the Operator. Returns: CSR sparse matrix representation of the Operator. Raises: ValueError: invalid parameters. """ return self.primitive.to_matrix(sparse=True) * self.coeff
def __str__(self) -> str: prim_str = str(self.primitive) if self.coeff == 1.0: return prim_str else: return f"{self.coeff} * {prim_str}"
[docs] def eval( self, front: Optional[ Union[str, Dict[str, complex], np.ndarray, OperatorBase, Statevector] ] = None, ) -> Union[OperatorBase, complex]: if front is None: return self.to_matrix_op() # pylint: disable=cyclic-import from ..list_ops.list_op import ListOp from ..state_fns.circuit_state_fn import CircuitStateFn from ..state_fns.dict_state_fn import DictStateFn from ..state_fns.state_fn import StateFn from .circuit_op import CircuitOp new_front = None # For now, always do this. If it's not performant, we can be more granular. if not isinstance(front, OperatorBase): front = StateFn(front, is_measurement=False) if isinstance(front, ListOp) and front.distributive: new_front = front.combo_fn( [self.eval(front.coeff * front_elem) for front_elem in front.oplist] ) else: if self.num_qubits != front.num_qubits: raise ValueError( "eval does not support operands with differing numbers of qubits, " "{} and {}, respectively.".format(self.num_qubits, front.num_qubits) ) if isinstance(front, DictStateFn): new_dict: Dict[str, complex] = {} corrected_x_bits = self.primitive.x[::-1] corrected_z_bits = self.primitive.z[::-1] for bstr, v in front.primitive.items(): bitstr = np.fromiter(bstr, dtype=int).astype(bool) new_b_str = np.logical_xor(bitstr, corrected_x_bits) new_str = "".join(map(str, 1 * new_b_str)) z_factor = np.product(1 - 2 * np.logical_and(bitstr, corrected_z_bits)) y_factor = np.product( np.sqrt(1 - 2 * np.logical_and(corrected_x_bits, corrected_z_bits) + 0j) ) new_dict[new_str] = (v * z_factor * y_factor) + new_dict.get(new_str, 0) # The coefficient consists of: # 1. the coefficient of *this* PauliOp (self) # 2. the coefficient of the evaluated DictStateFn (front) # 3. AND acquires the phase of the internal primitive. This is necessary to # ensure that (X @ Z) and (-iY) return the same result. new_front = StateFn( new_dict, coeff=self.coeff * front.coeff * (-1j) ** self.primitive.phase ) elif isinstance(front, StateFn) and front.is_measurement: raise ValueError("Operator composed with a measurement is undefined.") # Composable types with PauliOp elif isinstance(front, (PauliOp, CircuitOp, CircuitStateFn)): new_front = self.compose(front) # Covers VectorStateFn and OperatorStateFn elif isinstance(front, StateFn): new_front = self.to_matrix_op().eval(front.to_matrix_op()) return new_front
[docs] def exp_i(self) -> OperatorBase: """Return a ``CircuitOp`` equivalent to e^-iH for this operator H.""" # if only one qubit is significant, we can perform the evolution corrected_x = self.primitive.x[::-1] corrected_z = self.primitive.z[::-1] sig_qubits = np.logical_or(corrected_x, corrected_z) if np.sum(sig_qubits) == 0: # e^I is just a global phase, but we can keep track of it! Should we? # For now, just return identity return PauliOp(self.primitive) if np.sum(sig_qubits) == 1: sig_qubit_index = sig_qubits.tolist().index(True) coeff = ( np.real(self.coeff) if not isinstance(self.coeff, ParameterExpression) else self.coeff ) from .circuit_op import CircuitOp # Y rotation if corrected_x[sig_qubit_index] and corrected_z[sig_qubit_index]: rot_op = CircuitOp(RYGate(2 * coeff)) # Z rotation elif corrected_z[sig_qubit_index]: rot_op = CircuitOp(RZGate(2 * coeff)) # X rotation elif corrected_x[sig_qubit_index]: rot_op = CircuitOp(RXGate(2 * coeff)) # pylint: disable=cyclic-import from ..operator_globals import I left_pad = I.tensorpower(sig_qubit_index) right_pad = I.tensorpower(self.num_qubits - sig_qubit_index - 1) # Need to use overloaded operators here in case left_pad == I^0 return left_pad ^ rot_op ^ right_pad else: from ..evolutions.evolved_op import EvolvedOp return EvolvedOp(self)
[docs] def to_circuit(self) -> QuantumCircuit: pauli = self.primitive.to_label()[-self.num_qubits :] phase = self.primitive.phase qc = QuantumCircuit(self.num_qubits) if pauli == "I" * self.num_qubits: qc.global_phase = -phase * pi / 2 return qc if self.num_qubits == 1: if pauli != "I": gate = {"X": XGate, "Y": YGate, "Z": ZGate}[pauli] qc.append(gate(), [0]) else: gate = PauliGate(pauli) qc.append(gate, range(self.num_qubits)) if not phase: return qc qc.global_phase = -phase * pi / 2 return qc
[docs] def to_instruction(self) -> Instruction: # TODO should we just do the following because performance of adding and deleting IGates # doesn't matter? # (Reduce removes extra IGates). # return PrimitiveOp(self.primitive.to_instruction(), coeff=self.coeff).reduce() return self.primitive.to_instruction()
[docs] def to_pauli_op(self, massive: bool = False) -> "PauliOp": return self