Source code for qiskit.transpiler.passes.scheduling.dynamical_decoupling
# This code is part of Qiskit.
#
# (C) Copyright IBM 2021.
#
# 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.
"""Dynamical Decoupling insertion pass."""
import itertools
import numpy as np
from qiskit.circuit.delay import Delay
from qiskit.circuit.reset import Reset
from qiskit.circuit.library.standard_gates import IGate, UGate, U3Gate
from qiskit.quantum_info.operators.predicates import matrix_equal
from qiskit.quantum_info.synthesis import OneQubitEulerDecomposer
from qiskit.transpiler.passes.optimization import Optimize1qGates
from qiskit.transpiler.basepasses import TransformationPass
from qiskit.transpiler.exceptions import TranspilerError
[docs]class DynamicalDecoupling(TransformationPass):
"""Dynamical decoupling insertion pass.
This pass works on a scheduled, physical circuit. It scans the circuit for
idle periods of time (i.e. those containing delay instructions) and inserts
a DD sequence of gates in those spots. These gates amount to the identity,
so do not alter the logical action of the circuit, but have the effect of
mitigating decoherence in those idle periods.
As a special case, the pass allows a length-1 sequence (e.g. [XGate()]).
In this case the DD insertion happens only when the gate inverse can be
absorbed into a neighboring gate in the circuit (so we would still be
replacing Delay with something that is equivalent to the identity).
This can be used, for instance, as a Hahn echo.
This pass ensures that the inserted sequence preserves the circuit exactly
(including global phase).
.. jupyter-execute::
import numpy as np
from qiskit.circuit import QuantumCircuit
from qiskit.circuit.library import XGate
from qiskit.transpiler import PassManager, InstructionDurations
from qiskit.transpiler.passes import ALAPSchedule, DynamicalDecoupling
from qiskit.visualization import timeline_drawer
circ = QuantumCircuit(4)
circ.h(0)
circ.cx(0, 1)
circ.cx(1, 2)
circ.cx(2, 3)
circ.measure_all()
durations = InstructionDurations(
[("h", 0, 50), ("cx", [0, 1], 700), ("reset", None, 10),
("cx", [1, 2], 200), ("cx", [2, 3], 300),
("x", None, 50), ("measure", None, 1000)]
)
.. jupyter-execute::
# balanced X-X sequence on all qubits
dd_sequence = [XGate(), XGate()]
pm = PassManager([ALAPSchedule(durations),
DynamicalDecoupling(durations, dd_sequence)])
circ_dd = pm.run(circ)
timeline_drawer(circ_dd)
.. jupyter-execute::
# Uhrig sequence on qubit 0
n = 8
dd_sequence = [XGate()] * n
def uhrig_pulse_location(k):
return np.sin(np.pi * (k + 1) / (2 * n + 2)) ** 2
spacing = []
for k in range(n):
spacing.append(uhrig_pulse_location(k) - sum(spacing))
spacing.append(1 - sum(spacing))
pm = PassManager(
[
ALAPSchedule(durations),
DynamicalDecoupling(durations, dd_sequence, qubits=[0], spacing=spacing),
]
)
circ_dd = pm.run(circ)
timeline_drawer(circ_dd)
"""
def __init__(self, durations, dd_sequence, qubits=None, spacing=None, skip_reset_qubits=True):
"""Dynamical decoupling initializer.
Args:
durations (InstructionDurations): Durations of instructions to be
used in scheduling.
dd_sequence (list[Gate]): sequence of gates to apply in idle spots.
qubits (list[int]): physical qubits on which to apply DD.
If None, all qubits will undergo DD (when possible).
spacing (list[float]): a list of spacings between the DD gates.
The available slack will be divided according to this.
The list length must be one more than the length of dd_sequence,
and the elements must sum to 1. If None, a balanced spacing
will be used [d/2, d, d, ..., d, d, d/2].
skip_reset_qubits (bool): if True, does not insert DD on idle
periods that immediately follow initialized/reset qubits (as
qubits in the ground state are less susceptile to decoherence).
"""
super().__init__()
self._durations = durations
self._dd_sequence = dd_sequence
self._qubits = qubits
self._spacing = spacing
self._skip_reset_qubits = skip_reset_qubits
[docs] def run(self, dag):
"""Run the DynamicalDecoupling pass on dag.
Args:
dag (DAGCircuit): a scheduled DAG.
Returns:
DAGCircuit: equivalent circuit with delays interrupted by DD,
where possible.
Raises:
TranspilerError: if the circuit is not mapped on physical qubits.
"""
if len(dag.qregs) != 1 or dag.qregs.get("q", None) is None:
raise TranspilerError("DD runs on physical circuits only.")
if dag.duration is None:
raise TranspilerError("DD runs after circuit is scheduled.")
num_pulses = len(self._dd_sequence)
sequence_gphase = 0
if num_pulses != 1:
if num_pulses % 2 != 0:
raise TranspilerError("DD sequence must contain an even number of gates (or 1).")
noop = np.eye(2)
for gate in self._dd_sequence:
noop = noop.dot(gate.to_matrix())
if not matrix_equal(noop, IGate().to_matrix(), ignore_phase=True):
raise TranspilerError("The DD sequence does not make an identity operation.")
sequence_gphase = np.angle(noop[0][0])
if self._qubits is None:
self._qubits = set(range(dag.num_qubits()))
else:
self._qubits = set(self._qubits)
if self._spacing:
if sum(self._spacing) != 1 or any(a < 0 for a in self._spacing):
raise TranspilerError(
"The spacings must be given in terms of fractions "
"of the slack period and sum to 1."
)
else: # default to balanced spacing
mid = 1 / num_pulses
end = mid / 2
self._spacing = [end] + [mid] * (num_pulses - 1) + [end]
new_dag = dag._copy_circuit_metadata()
qubit_index_map = {qubit: index for index, qubit in enumerate(new_dag.qubits)}
index_sequence_duration_map = {}
for qubit in new_dag.qubits:
physical_qubit = qubit_index_map[qubit]
dd_sequence_duration = 0
for gate in self._dd_sequence:
gate.duration = self._durations.get(gate, physical_qubit)
dd_sequence_duration += gate.duration
index_sequence_duration_map[physical_qubit] = dd_sequence_duration
for nd in dag.topological_op_nodes():
if not isinstance(nd.op, Delay):
new_dag.apply_operation_back(nd.op, nd.qargs, nd.cargs)
continue
dag_qubit = nd.qargs[0]
physical_qubit = qubit_index_map[dag_qubit]
if physical_qubit not in self._qubits: # skip unwanted qubits
new_dag.apply_operation_back(nd.op, nd.qargs, nd.cargs)
continue
pred = next(dag.predecessors(nd))
succ = next(dag.successors(nd))
if self._skip_reset_qubits: # discount initial delays
if pred.type == "in" or isinstance(pred.op, Reset):
new_dag.apply_operation_back(nd.op, nd.qargs, nd.cargs)
continue
dd_sequence_duration = index_sequence_duration_map[physical_qubit]
slack = nd.op.duration - dd_sequence_duration
if slack <= 0: # dd doesn't fit
new_dag.apply_operation_back(nd.op, nd.qargs, nd.cargs)
continue
if num_pulses == 1: # special case of using a single gate for DD
u_inv = self._dd_sequence[0].inverse().to_matrix()
theta, phi, lam, phase = OneQubitEulerDecomposer().angles_and_phase(u_inv)
# absorb the inverse into the successor (from left in circuit)
if succ.type == "op" and isinstance(succ.op, (UGate, U3Gate)):
theta_r, phi_r, lam_r = succ.op.params
succ.op.params = Optimize1qGates.compose_u3(
theta_r, phi_r, lam_r, theta, phi, lam
)
sequence_gphase += phase
# absorb the inverse into the predecessor (from right in circuit)
elif pred.type == "op" and isinstance(pred.op, (UGate, U3Gate)):
theta_l, phi_l, lam_l = pred.op.params
pred.op.params = Optimize1qGates.compose_u3(
theta, phi, lam, theta_l, phi_l, lam_l
)
sequence_gphase += phase
# don't do anything if there's no single-qubit gate to absorb the inverse
else:
new_dag.apply_operation_back(nd.op, nd.qargs, nd.cargs)
continue
# insert the actual DD sequence
taus = [int(slack * a) for a in self._spacing]
unused_slack = slack - sum(taus) # unused, due to rounding to int multiples of dt
middle_index = int((len(taus) - 1) / 2) # arbitrary: redistribute to middle
taus[middle_index] += unused_slack # now we add up to original delay duration
for tau, gate in itertools.zip_longest(taus, self._dd_sequence):
if tau > 0:
new_dag.apply_operation_back(Delay(tau), [dag_qubit])
if gate is not None:
new_dag.apply_operation_back(gate, [dag_qubit])
new_dag.global_phase = _mod_2pi(new_dag.global_phase + sequence_gphase)
return new_dag
def _mod_2pi(angle: float, atol: float = 0):
"""Wrap angle into interval [-π,π). If within atol of the endpoint, clamp to -π"""
wrapped = (angle + np.pi) % (2 * np.pi) - np.pi
if abs(wrapped - np.pi) < atol:
wrapped = -np.pi
return wrapped