# Quellcode fÃ¼r qiskit.extensions.hamiltonian_gate

```# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2020.
#
# obtain a copy of this license in the LICENSE.txt file in the root directory
#
# 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.

"""
Gate described by the time evolution of a Hermitian Hamiltonian operator.
"""

from numbers import Number
import numpy

from qiskit.circuit import Gate, QuantumCircuit, QuantumRegister, ParameterExpression
from qiskit.quantum_info.operators.predicates import matrix_equal
from qiskit.quantum_info.operators.predicates import is_hermitian_matrix
from qiskit.extensions.exceptions import ExtensionError
from qiskit.circuit.exceptions import CircuitError
from qiskit.utils.deprecation import deprecate_func

from .unitary import UnitaryGate

[Doku]class HamiltonianGate(Gate):
"""Class for representing evolution by a Hamiltonian operator as a gate.

This gate resolves to a :class:`.UnitaryGate` as :math:`U(t) = exp(-i t H)`,
which can be decomposed into basis gates if it is 2 qubits or less, or
simulated directly in Aer for more qubits. Note that you can also directly
use :meth:`.QuantumCircuit.hamiltonian`.
"""

def __init__(self, data, time, label=None):
"""Create a gate from a hamiltonian operator and evolution time parameter t

Args:
data (matrix or Operator): a hermitian operator.
time (float or ParameterExpression): time evolution parameter.
label (str): unitary name for backend [Default: None].

Raises:
ExtensionError: if input data is not an N-qubit unitary operator.
"""
if hasattr(data, "to_matrix"):
# If input is Gate subclass or some other class object that has
# a to_matrix method this will call that method.
data = data.to_matrix()
elif hasattr(data, "to_operator"):
# If input is a BaseOperator subclass this attempts to convert
# the object to an Operator so that we can extract the underlying
# numpy matrix from `Operator.data`.
data = data.to_operator().data
# Convert to numpy array in case not already an array
data = numpy.array(data, dtype=complex)
# Check input is unitary
if not is_hermitian_matrix(data):
raise ExtensionError("Input matrix is not Hermitian.")
if isinstance(time, Number) and time != numpy.real(time):
raise ExtensionError("Evolution time is not real.")
# Check input is N-qubit matrix
input_dim, output_dim = data.shape
num_qubits = int(numpy.log2(input_dim))
if input_dim != output_dim or 2**num_qubits != input_dim:
raise ExtensionError("Input matrix is not an N-qubit operator.")

# Store instruction params
super().__init__("hamiltonian", num_qubits, [data, time], label=label)

def __eq__(self, other):
if not isinstance(other, HamiltonianGate):
return False
if self.label != other.label:
return False
operators_eq = matrix_equal(self.params[0], other.params[0], ignore_phase=False)
times_eq = self.params[1] == other.params[1]
return operators_eq and times_eq

def __array__(self, dtype=None):
"""Return matrix for the unitary."""
# pylint: disable=unused-argument
import scipy.linalg

try:
return scipy.linalg.expm(-1j * self.params[0] * float(self.params[1]))
except TypeError as ex:
raise TypeError(
"Unable to generate Unitary matrix for "
"unbound t parameter {}".format(self.params[1])
) from ex

[Doku]    def inverse(self):
"""Return the adjoint of the unitary."""

[Doku]    def conjugate(self):
"""Return the conjugate of the Hamiltonian."""
return HamiltonianGate(numpy.conj(self.params[0]), -self.params[1])

"""Return the adjoint of the unitary."""
return HamiltonianGate(self.params[0], -self.params[1])

[Doku]    def transpose(self):
"""Return the transpose of the Hamiltonian."""
return HamiltonianGate(numpy.transpose(self.params[0]), self.params[1])

def _define(self):
"""Calculate a subcircuit that implements this unitary."""
q = QuantumRegister(self.num_qubits, "q")
qc = QuantumCircuit(q, name=self.name)
qc._append(UnitaryGate(self.to_matrix()), q[:], [])
self.definition = qc

[Doku]    @deprecate_func(
since="0.25.0",
)
def qasm(self):
"""Raise an error, as QASM is not defined for the HamiltonianGate."""
raise ExtensionError("HamiltonianGate has no OpenQASM 2 definition.")

[Doku]    def validate_parameter(self, parameter):
"""Hamiltonian parameter has to be an ndarray, operator or float."""
if isinstance(parameter, (float, int, numpy.ndarray)):
return parameter
elif isinstance(parameter, ParameterExpression) and len(parameter.parameters) == 0:
return float(parameter)
else:
raise CircuitError(f"invalid param type {type(parameter)} for gate {self.name}")

def hamiltonian(self, operator, time, qubits, label=None):
"""Apply hamiltonian evolution to qubits.

This gate resolves to a :class:`.UnitaryGate` as :math:`U(t) = exp(-i t H)`,
which can be decomposed into basis gates if it is 2 qubits or less, or
simulated directly in Aer for more qubits.

Args:
operator (matrix or Operator): a hermitian operator.
time (float or ParameterExpression): time evolution parameter.
qubits (Union[int, Tuple[int]]): The circuit qubits to apply the
transformation to.
label (str): unitary name for backend [Default: None].

Returns:
QuantumCircuit: The quantum circuit.

Raises:
ExtensionError: if input data is not an N-qubit unitary operator.
"""
if not isinstance(qubits, list):
qubits = [qubits]

return self.append(HamiltonianGate(data=operator, time=time, label=label), qubits, [])

QuantumCircuit.hamiltonian = hamiltonian
```