# Quellcode fÃ¼r qiskit.transpiler.passes.optimization.optimize_1q_gates

```# This code is part of Qiskit.
#
# (C) Copyright IBM 2017, 2018.
#
# 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.

"""Optimize chains of single-qubit u1, u2, u3 gates by combining them into a single gate."""

from itertools import groupby

import numpy as np

from qiskit.transpiler.exceptions import TranspilerError
from qiskit.circuit.library.standard_gates.p import PhaseGate
from qiskit.circuit.library.standard_gates.u import UGate
from qiskit.circuit.library.standard_gates.u1 import U1Gate
from qiskit.circuit.library.standard_gates.u2 import U2Gate
from qiskit.circuit.library.standard_gates.u3 import U3Gate
from qiskit.circuit import ParameterExpression
from qiskit.circuit.gate import Gate
from qiskit.transpiler.basepasses import TransformationPass
from qiskit.quantum_info.synthesis import Quaternion
from qiskit._accelerate.optimize_1q_gates import compose_u3_rust

_CHOP_THRESHOLD = 1e-15

[Doku]class Optimize1qGates(TransformationPass):
"""Optimize chains of single-qubit u1, u2, u3 gates by combining them into a single gate."""

def __init__(self, basis=None, eps=1e-15, target=None):
"""Optimize1qGates initializer.

Args:
basis (list[str]): Basis gates to consider, e.g. `['u3', 'cx']`. For the effects
of this pass, the basis is the set intersection between the `basis` parameter and
the set `{'u1','u2','u3', 'u', 'p'}`.
eps (float): EPS to check against
target (Target): The :class:`~.Target` representing the target backend, if both
``basis`` and this are specified then this argument will take
precedence and ``basis`` will be ignored.
"""
super().__init__()
self.basis = set(basis) if basis else {"u1", "u2", "u3"}
self.eps = eps
self.target = target

[Doku]    def run(self, dag):
"""Run the Optimize1qGates pass on `dag`.

Args:
dag (DAGCircuit): the DAG to be optimized.

Returns:
DAGCircuit: the optimized DAG.

Raises:
TranspilerError: if YZY and ZYZ angles do not give same rotation matrix.
"""
use_u = "u" in self.basis
use_p = "p" in self.basis
runs = dag.collect_runs(["u1", "u2", "u3", "u", "p"])
runs = _split_runs_on_parameters(runs)
for run in runs:
run_qubits = None
if self.target is not None:
run_qubits = tuple(dag.find_bit(x).index for x in run[0].qargs)

if self.target.instruction_supported("p", run_qubits):
right_name = "p"
else:
right_name = "u1"
else:
if use_p:
right_name = "p"
else:
right_name = "u1"
right_parameters = (0, 0, 0)  # (theta, phi, lambda)
right_global_phase = 0
for current_node in run:
left_name = current_node.name
if (
getattr(current_node.op, "condition", None) is not None
or len(current_node.qargs) != 1
or left_name not in ["p", "u1", "u2", "u3", "u", "id"]
):
raise TranspilerError("internal error")
if left_name in ("u1", "p"):
left_parameters = (0, 0, current_node.op.params[0])
elif left_name == "u2":
left_parameters = (
np.pi / 2,
current_node.op.params[0],
current_node.op.params[1],
)
elif left_name in ("u3", "u"):
left_parameters = tuple(current_node.op.params)
else:
if use_p:
left_name = "p"
else:
left_name = "u1"  # replace id with u1
left_parameters = (0, 0, 0)
if (
current_node.op.definition is not None
and current_node.op.definition.global_phase
):
right_global_phase += current_node.op.definition.global_phase

# If there are any sympy objects coming from the gate convert
# to numpy.
try:
left_parameters = tuple(float(x) for x in left_parameters)
except TypeError:
# If left_parameters contained any unbound Parameters
pass

# Compose gates
name_tuple = (left_name, right_name)
if name_tuple in (("u1", "u1"), ("p", "p")):
# u1(lambda1) * u1(lambda2) = u1(lambda1 + lambda2)
right_parameters = (0, 0, right_parameters[2] + left_parameters[2])
elif name_tuple in (("u1", "u2"), ("p", "u2")):
# u1(lambda1) * u2(phi2, lambda2) = u2(phi2 + lambda1, lambda2)
right_parameters = (
np.pi / 2,
right_parameters[1] + left_parameters[2],
right_parameters[2],
)
elif name_tuple in (("u2", "u1"), ("u2", "p")):
# u2(phi1, lambda1) * u1(lambda2) = u2(phi1, lambda1 + lambda2)
right_name = "u2"
right_parameters = (
np.pi / 2,
left_parameters[1],
right_parameters[2] + left_parameters[2],
)
elif name_tuple in (("u1", "u3"), ("u1", "u"), ("p", "u3"), ("p", "u")):
# u1(lambda1) * u3(theta2, phi2, lambda2) =
#     u3(theta2, phi2 + lambda1, lambda2)
right_parameters = (
right_parameters[0],
right_parameters[1] + left_parameters[2],
right_parameters[2],
)
elif name_tuple in (("u3", "u1"), ("u", "u1"), ("u3", "p"), ("u", "p")):
# u3(theta1, phi1, lambda1) * u1(lambda2) =
#     u3(theta1, phi1, lambda1 + lambda2)
if use_u:
right_name = "u"
else:
right_name = "u3"
right_parameters = (
left_parameters[0],
left_parameters[1],
right_parameters[2] + left_parameters[2],
)
elif name_tuple == ("u2", "u2"):
# Using Ry(pi/2).Rz(2*lambda).Ry(pi/2) =
#    Rz(pi/2).Ry(pi-2*lambda).Rz(pi/2),
# u2(phi1, lambda1) * u2(phi2, lambda2) =
#    u3(pi - lambda1 - phi2, phi1 + pi/2, lambda2 + pi/2)
if use_u:
right_name = "u"
else:
right_name = "u3"
right_parameters = (
np.pi - left_parameters[2] - right_parameters[1],
left_parameters[1] + np.pi / 2,
right_parameters[2] + np.pi / 2,
)
elif name_tuple[1] == "nop":
right_name = left_name
right_parameters = left_parameters
else:
# For composing u3's or u2's with u3's, use
# u2(phi, lambda) = u3(pi/2, phi, lambda)
# together with the qiskit.mapper.compose_u3 method.
if use_u:
right_name = "u"
else:
right_name = "u3"
# Evaluate the symbolic expressions for efficiency
right_parameters = Optimize1qGates.compose_u3(
left_parameters[0],
left_parameters[1],
left_parameters[2],
right_parameters[0],
right_parameters[1],
right_parameters[2],
)
# Why evalf()? This program:
#   OPENQASM 2.0;
#   include "qelib1.inc";
#   qreg q[2];
#   creg c[2];
#   u3(0.518016983430947*pi,1.37051598592907*pi,1.36816383603222*pi) q[0];
#   u3(1.69867232277986*pi,0.371448347747471*pi,0.461117217930936*pi) q[0];
#   u3(0.294319836336836*pi,0.450325871124225*pi,1.46804720442555*pi) q[0];
#   measure q -> c;
# took >630 seconds (did not complete) to optimize without
# calling evalf() at all, 19 seconds to optimize calling
# evalf() AFTER compose_u3, and 1 second to optimize
# calling evalf() BEFORE compose_u3.
# 1. Here down, when we simplify, we add f(theta) to lambda to
# correct the global phase when f(theta) is 2*pi. This isn't
# necessary but the other steps preserve the global phase, so
# we continue in that manner.
# 2. The final step will remove Z rotations by 2*pi.
# 3. Note that is_zero is true only if the expression is exactly
# zero. If the input expressions have already been evaluated
# then these final simplifications will not occur.
# TODO After we refactor, we should have separate passes for
# exact and approximate rewriting.

# Y rotation is 0 mod 2*pi, so the gate is a u1
if (
not isinstance(right_parameters[0], ParameterExpression)
and abs(np.mod(right_parameters[0], (2 * np.pi))) < self.eps
and right_name != "u1"
and right_name != "p"
):
if use_p:
right_name = "p"
else:
right_name = "u1"
right_parameters = (
0,
0,
right_parameters[1] + right_parameters[2] + right_parameters[0],
)
# Y rotation is pi/2 or -pi/2 mod 2*pi, so the gate is a u2
if right_name in ("u3", "u"):
if not isinstance(right_parameters[0], ParameterExpression):
# theta = pi/2 + 2*k*pi
right_angle = right_parameters[0] - np.pi / 2
if abs(right_angle) < self.eps:
right_angle = 0
if abs(np.mod((right_angle), 2 * np.pi)) < self.eps:
right_name = "u2"
right_parameters = (
np.pi / 2,
right_parameters[1],
right_parameters[2] + (right_parameters[0] - np.pi / 2),
)
# theta = -pi/2 + 2*k*pi
right_angle = right_parameters[0] + np.pi / 2
if abs(right_angle) < self.eps:
right_angle = 0
if abs(np.mod(right_angle, 2 * np.pi)) < self.eps:
right_name = "u2"
right_parameters = (
np.pi / 2,
right_parameters[1] + np.pi,
right_parameters[2] - np.pi + (right_parameters[0] + np.pi / 2),
)

# u1 and lambda is 0 mod 2*pi so gate is nop (up to a global phase)
if (
not isinstance(right_parameters[2], ParameterExpression)
and right_name in ("u1", "p")
and abs(np.mod(right_parameters[2], 2 * np.pi)) < self.eps
):
right_name = "nop"

if self.target is not None:
if right_name == "u2" and not self.target.instruction_supported("u2", run_qubits):
if self.target.instruction_supported("u", run_qubits):
right_name = "u"
else:
right_name = "u3"
if right_name in ("u1", "p") and not self.target.instruction_supported(
right_name, run_qubits
):
if self.target.instruction_supported("u", run_qubits):
right_name = "u"
else:
right_name = "u3"
else:
if right_name == "u2" and "u2" not in self.basis:
if use_u:
right_name = "u"
else:
right_name = "u3"
if right_name in ("u1", "p") and right_name not in self.basis:
if use_u:
right_name = "u"
else:
right_name = "u3"

new_op = Gate(name="", num_qubits=1, params=[])
if right_name == "u1":
new_op = U1Gate(right_parameters[2])
if right_name == "p":
new_op = PhaseGate(right_parameters[2])
if right_name == "u2":
new_op = U2Gate(right_parameters[1], right_parameters[2])
if right_name == "u":
if "u" in self.basis:
new_op = UGate(*right_parameters)
if right_name == "u3":
if "u3" in self.basis:
new_op = U3Gate(*right_parameters)
else:
raise TranspilerError("It was not possible to use the basis %s" % self.basis)

dag.global_phase += right_global_phase

if right_name != "nop":
dag.substitute_node(run[0], new_op, inplace=True)

# Delete the other nodes in the run
for current_node in run[1:]:
dag.remove_op_node(current_node)
if right_name == "nop":
dag.remove_op_node(run[0])

return dag

[Doku]    @staticmethod
def compose_u3(theta1, phi1, lambda1, theta2, phi2, lambda2):
"""Return a triple theta, phi, lambda for the product.

u3(theta, phi, lambda)
= u3(theta1, phi1, lambda1).u3(theta2, phi2, lambda2)
= Rz(phi1).Ry(theta1).Rz(lambda1+phi2).Ry(theta2).Rz(lambda2)
= Rz(phi1).Rz(phi').Ry(theta').Rz(lambda').Rz(lambda2)
= u3(theta', phi1 + phi', lambda2 + lambda')

Return theta, phi, lambda.
"""
(theta, phi, lamb) = compose_u3_rust(theta1, phi1, lambda1, theta2, phi2, lambda2)
return (theta, phi, lamb)

[Doku]    @staticmethod
def yzy_to_zyz(xi, theta1, theta2, eps=1e-9):  # pylint: disable=invalid-name
"""Express a Y.Z.Y single qubit gate as a Z.Y.Z gate.

Solve the equation

.. math::

Ry(theta1).Rz(xi).Ry(theta2) = Rz(phi).Ry(theta).Rz(lambda)

for theta, phi, and lambda.

Return a solution theta, phi, and lambda.
"""
quaternion_yzy = Quaternion.from_euler([theta1, xi, theta2], "yzy")
euler = quaternion_yzy.to_zyz()
quaternion_zyz = Quaternion.from_euler(euler, "zyz")
# output order different than rotation order
out_angles = (euler[1], euler[0], euler[2])
abs_inner = abs(quaternion_zyz.data.dot(quaternion_yzy.data))
if not np.allclose(abs_inner, 1, eps):
raise TranspilerError("YZY and ZYZ angles do not give same rotation matrix.")
out_angles = tuple(0 if np.abs(angle) < _CHOP_THRESHOLD else angle for angle in out_angles)
return out_angles

def _split_runs_on_parameters(runs):
"""Finds runs containing parameterized gates and splits them into sequential
runs excluding the parameterized gates.
"""

out = []
for run in runs:
# We exclude only u3 and u gate because for u1 and u2 we can really straightforward
# merge two gate with parameters.
# It would be great to combine all gate with parameters but this requires
# support parameters in qiskit.quantum_info.synthesis.Quaternion.
groups = groupby(run, lambda x: x.op.is_parameterized() and x.op.name in ("u3", "u"))

for group_is_parameterized, gates in groups:
if not group_is_parameterized:
out.append(list(gates))

return out
```