# Source code for mitiq.zne.scaling.folding

```
# Copyright (C) 2020 Unitary Fund
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
"""Functions for local and global unitary folding on supported circuits."""
from copy import deepcopy
from typing import Any, Dict, FrozenSet, List, Optional, cast
import numpy as np
from cirq import Circuit, InsertStrategy, inverse, ops, has_unitary, Moment
from mitiq.interface import noise_scaling_converter
from mitiq.utils import (
_append_measurements,
_is_measurement,
_pop_measurements,
)
_cirq_gates_to_string_keys = {
ops.H: "H",
ops.X: "X",
ops.Y: "Y",
ops.Z: "Z",
ops.T: "T",
ops.I: "I",
ops.CNOT: "CNOT",
ops.CZ: "CZ",
ops.TOFFOLI: "TOFFOLI",
}
_string_keys_to_cirq_gates = dict(
zip(_cirq_gates_to_string_keys.values(), _cirq_gates_to_string_keys.keys())
)
# Helper functions
def _check_foldable(circuit: Circuit) -> None:
"""Raises an error if the input circuit cannot be folded.
Args:
circuit: Checks whether this circuit is able to be folded.
Raises:
UnfoldableCircuitError:
* If the circuit has intermediate measurements.
* If the circuit has non-unitary channels which are not terminal
measurements.
"""
if not circuit.are_all_measurements_terminal():
raise UnfoldableCircuitError(
"Circuit contains intermediate measurements and cannot be folded."
)
if not has_unitary(circuit):
circ_measurements = _pop_measurements(circuit)
if inverse(circuit, default=None) is None:
raise UnfoldableCircuitError(
"Circuit contains non-invertible channels which are not"
"terminal measurements and cannot be folded."
)
else:
_append_measurements(circuit, circ_measurements)
def _squash_moments(circuit: Circuit) -> Circuit:
"""Returns a copy of the input circuit with all gates squashed into as few
moments as possible.
Args:
circuit: Circuit to squash moments of.
"""
output_circuit = circuit.copy()
output_circuit = output_circuit[0:0] # Remove moments
output_circuit.append(
circuit.all_operations(), strategy=InsertStrategy.EARLIEST
)
return output_circuit
def _fold_all(
circuit: Circuit,
num_folds: int = 1,
exclude: FrozenSet[Any] = frozenset(),
skip_moments: FrozenSet[int] = frozenset(),
) -> Circuit:
"""Returns a circuit with all gates folded locally.
Args:
circuit: Circuit to fold.
num_folds: Number of times to add G G^dag for each gate G. If not an
integer, this gets rounded to the nearest integer.
exclude: Do not fold these gates.
skip_moments: Do not fold these moments.
"""
num_folds = round(num_folds)
if num_folds < 0:
raise ValueError(
f"Arg `num_folds` must be positive but was {num_folds}."
)
# Parse the exclude argument.
all_gates = set(cast(ops.Gate, op.gate) for op in circuit.all_operations())
to_exclude = set()
for item in exclude:
if isinstance(item, str):
try:
to_exclude.add(_string_keys_to_cirq_gates[item])
except KeyError:
if item == "single":
to_exclude.update(
gate for gate in all_gates if gate.num_qubits() == 1
)
elif item == "double":
to_exclude.update(
gate for gate in all_gates if gate.num_qubits() == 2
)
elif item == "triple":
to_exclude.update(
gate for gate in all_gates if gate.num_qubits() == 3
)
else:
raise ValueError(
f"Do not know how to parse item '{item}' in exclude. "
f"Valid items are Cirq gates, string keys specifying"
f"gates, and 'single', 'double', or 'triple'."
)
elif isinstance(item, ops.Gate):
to_exclude.add(item)
else:
raise ValueError(
f"Do not know how to exclude {item} of type {type(item)}."
)
folded = deepcopy(circuit)[:0]
for (i, moment) in enumerate(circuit):
if i in skip_moments:
folded.append(moment, strategy=InsertStrategy.EARLIEST)
continue
for op in moment:
folded.append(op, strategy=InsertStrategy.EARLIEST)
if op.gate not in to_exclude:
folded.append(
[inverse(op), op] * num_folds,
strategy=InsertStrategy.EARLIEST,
)
return folded
# Helper functions for folding by fidelity
def _default_weight(op: ops.Operation) -> float:
"""Returns a default weight for an operation."""
return 0.99 ** len(op.qubits)
def _get_weight_for_gate(
weights: Optional[Dict[str, float]], op: ops.Operation
) -> float:
"""Returns the weight for a given gate, using a default value of 1.0 if
weights is None or if the weight is not specified.
Args:
weights: Dictionary of string keys mapping gates to weights.
op: Operation to get the weight of.
"""
weight = _default_weight(op)
if not weights:
return weight
if "single" in weights.keys() and len(op.qubits) == 1:
weight = weights["single"]
elif "double" in weights.keys() and len(op.qubits) == 2:
weight = weights["double"]
elif "triple" in weights.keys() and len(op.qubits) == 3:
weight = weights["triple"]
if op.gate and op.gate in _cirq_gates_to_string_keys.keys():
# Get the string key for this gate
key = _cirq_gates_to_string_keys[op.gate]
if key in weights.keys():
weight = weights[_cirq_gates_to_string_keys[op.gate]]
return weight
# Local folding functions
[docs]@noise_scaling_converter
def fold_all(
circuit: Circuit,
scale_factor: float,
exclude: FrozenSet[Any] = frozenset(),
) -> Circuit:
"""Returns a circuit with all gates folded locally.
Args:
circuit: Circuit to fold.
scale_factor: Approximate factor by which noise is scaled in the
circuit. Each gate is folded round((scale_factor - 1.0) / 2.0)
times. For example::
scale_factor | num_folds
------------------------
1.0 | 0
3.0 | 1
5.0 | 2
exclude: Do not fold these gates. Supported gate keys are listed in
the following table.::
Gate key | Gate
-------------------------
"H" | Hadamard
"X" | Pauli X
"Y" | Pauli Y
"Z" | Pauli Z
"I" | Identity
"CNOT" | CNOT
"CZ" | CZ gate
"TOFFOLI" | Toffoli gate
"single" | All single qubit gates
"double" | All two-qubit gates
"triple" | All three-qubit gates
"""
if not 1.0 <= scale_factor:
raise ValueError(
f"Requires scale_factor >= 1 but scale_factor = {scale_factor}."
)
_check_foldable(circuit)
folded = deepcopy(circuit)
measurements = _pop_measurements(folded)
folded = _fold_all(folded, round((scale_factor - 1.0) / 2.0), exclude)
_append_measurements(folded, measurements)
return folded
# Global folding function
[docs]@noise_scaling_converter
def fold_global(
circuit: Circuit, scale_factor: float, **kwargs: Any
) -> Circuit:
"""Returns a new circuit obtained by folding the global unitary of the
input circuit.
The returned folded circuit has a number of gates approximately equal to
scale_factor * len(circuit).
Args:
circuit: Circuit to fold.
scale_factor: Factor to scale the circuit by.
Keyword Args:
return_mitiq (bool): If True, returns a Mitiq circuit instead of
the input circuit type (if different). Default is False.
Returns:
folded: the folded quantum circuit as a QPROGRAM.
"""
_check_foldable(circuit)
if not (scale_factor >= 1):
raise ValueError("The scale factor must be a real number >= 1.")
folded = deepcopy(circuit)
measurements = _pop_measurements(folded)
base_circuit = deepcopy(folded)
# Determine the number of global folds and the final fractional scale
num_global_folds, fraction_scale = divmod(scale_factor - 1, 2)
# Do the global folds
for _ in range(int(num_global_folds)):
folded += Circuit(inverse(base_circuit), base_circuit)
# Fold remaining gates until the scale is reached
operations = list(base_circuit.all_operations())
num_to_fold = int(round(fraction_scale * len(operations) / 2))
if num_to_fold > 0:
# Create the inverse of the final partial circuit
inverse_partial = Circuit()
num_partial = 0
for moment in base_circuit[::-1]:
new_moment = Moment()
for op in moment.operations[::-1]:
new_moment = new_moment.with_operation(inverse(op))
num_partial += 1
if num_partial == num_to_fold:
break
inverse_partial.append(new_moment)
if num_partial == num_to_fold:
break
# Append partially folded circuit
folded += inverse_partial + inverse(inverse_partial)
_append_measurements(folded, measurements)
return folded
def _create_weight_mask(
circuit: Circuit,
fidelities: Optional[Dict[str, float]],
) -> List[float]:
"""Returns a list of weights associated to each gate if the input
circuit. Measurement gates are ignored.
The gate ordering is equal to the one used in the `all_operations()`
method of the :class:`cirq.Circuit` class: gates from earlier moments
come first and gates within the same moment follow the order in which
they were given to the moment's constructor.
Args:
circuit: The circuit from which a weight mask is created.
fidelities: The dictionary of gate fidelities.
If None, default fidelities will be used. See the
docstring of local folding function for mode details.
Returns: The list of weights associated to all the gates.
"""
if fidelities and not all(0.0 < f <= 1.0 for f in fidelities.values()):
raise ValueError("Fidelities should be in the interval (0, 1].")
weights = None
if fidelities:
# Round to avoid ugly numbers like 0.09999999999999998 instead of 0.1
weights = {k: round(1.0 - f, 12) for k, f in fidelities.items()}
# Build mask with weights of each gate
return [
_get_weight_for_gate(weights, op)
for op in circuit.all_operations()
if not _is_measurement(op)
]
def _create_fold_mask(
weight_mask: List[float],
scale_factor: float,
folding_method: str,
seed: Optional[int] = None,
) -> List[int]:
r"""Returns a list of integers determining how many times each gate a
circuit should be folded to realize the desired input scale_factor.
More precicely, the j_th element of the returned list is associated
to the j_th gate G_j of a circuit that we want to scale and determines
how many times G_j^\dag G_j should be applied after G_j.
The gate ordering is equal to the one used in the `all_operations()`
method of the :class:`cirq.Circuit` class: gates from earlier moments
come first and gates within the same moment follow the order in which
they were given to the moment's constructor.
The returned list is built such that the total weight of the
folded circuit is approximately equal to scale_factor times the
total weight of the input circuit.
For equal weights, this function reproduces the local unitary folding
method defined in equation (5) of :cite:`Giurgica_Tiron_2020_arXiv`.
Args:
weight_mask: The weights of all the gates of the circuit to fold.
Highly noisy gates should have a corresponding high weight.
Gates with zero weight are assumed to be ideal and are not folded.
scale_factor: The effective noise scale factor.
folding_method: A string equal to "at_random", or "from_left", or
"from_right". Determines the partial folding method described in
:cite:`Giurgica_Tiron_2020_arXiv`. If scale_factor is an odd
integer, all methods are equivalent and this option is irrelevant.
seed: A seed for the random number generator. This is used only when
folding_method is "at_random".
Returns: The list of integers determining to how many times one should
fold the j_th gate of the circuit to be scaled.
Example:
>>>_create_fold_mask(
weight_mask=[1.0, 0.5, 2.0, 0.0],
scale_factor=4,
folding_method="from_left",
)
[2, 2, 1, 0]
"""
if not 1.0 <= scale_factor:
raise ValueError(
f"Requires scale_factor >= 1 but scale_factor = {scale_factor}."
)
# Find the maximum odd integer smaller or equal to scale_factor
num_uniform_folds = int((scale_factor - 1.0) / 2.0)
odd_integer_scale_factor = 2 * num_uniform_folds + 1
# Uniformly folding all gates to reach odd_integer_scale_factor
num_folds_mask = []
for w in weight_mask:
if np.isclose(w, 0.0):
num_folds_mask.append(0)
else:
num_folds_mask.append(num_uniform_folds)
# If the scale_factor is an odd integer, we are done.
if np.isclose(odd_integer_scale_factor, scale_factor):
return num_folds_mask
# Express folding order through a list of indices
folding_order = list(range(len(weight_mask)))
if folding_method == "from_left":
pass
elif folding_method == "from_right":
folding_order.reverse()
elif folding_method == "at_random":
rnd_state = np.random.RandomState(seed)
rnd_state.shuffle(folding_order)
else:
raise ValueError(
"The option 'folding_method' is not valid."
"It must be 'at_random', or 'from_left', or 'from_right'."
)
# Fold gates until the input scale_factor is better approximated
input_circuit_weight = sum(weight_mask)
output_circuit_weight = odd_integer_scale_factor * input_circuit_weight
approx_error = np.abs(
output_circuit_weight - scale_factor * input_circuit_weight
)
for j in folding_order:
# Skip gates with 0 weight
if np.isclose(weight_mask[j], 0.0):
continue
# Compute the approx error if a new fold would be applied
new_output_circuit_weight = output_circuit_weight + 2 * weight_mask[j]
new_approx_error = np.abs(
new_output_circuit_weight - scale_factor * input_circuit_weight
)
# Fold the candidate gate only if it helps improving the approximation
if new_approx_error >= approx_error:
break
approx_error = new_approx_error
output_circuit_weight = new_output_circuit_weight
num_folds_mask[j] += 1
return num_folds_mask
def _apply_fold_mask(
circuit: Circuit,
num_folds_mask: List[int],
squash_moments: Optional[bool] = True,
) -> Circuit:
r"""Applies local unitary folding to the gates of the input circuit
according to the input num_folds_mask.
More precicely, G_j^\dag G_j is applied after the j_th gate G_j of
the input circuit an integer number of times given by num_folds_mask[j].
The gate ordering is equal to the one used in the `all_operations()`
method of the :class:`cirq.Circuit` class: gates from earlier moments
come first and gates within the same moment follow the order in which
they were given to the moment's constructor.
Args:
circuit: The quantum circuit to fold.
num_folds_mask: The list of integers indicating how many times
the corresponding gates of 'circuit' should be folded.
squash_moments: If True or None, all gates (including folded gates) are
placed as early as possible in the circuit. If False, new moments
are created for folded gates. This option only applies to QPROGRAM
types which have a "moment" or "time" structure. Default is True.
Returns: The folded quantum circuit.
"""
_check_foldable(circuit)
circ_copy = deepcopy(circuit)
measurements = _pop_measurements(circ_copy)
num_gates = len(list(circ_copy.all_operations()))
if num_gates != len(num_folds_mask):
raise ValueError(
"The circuit and the folding mask have incompatible sizes."
f" The number of gates is {num_gates}"
f" but len(num_folds_mask) is {len(num_folds_mask)}."
)
folded_circuit = circ_copy[:0]
if squash_moments:
for op, num_folds in zip(circ_copy.all_operations(), num_folds_mask):
folded_circuit.append([op] + num_folds * [inverse(op), op])
else:
mask_index = 0
for moment in circ_copy:
folded_moment = Circuit(moment)
for op in moment:
num_folds = num_folds_mask[mask_index]
folded_moment.append(num_folds * [inverse(op), op])
mask_index += 1
# New folded gates are only squashed with respect to folded_moment
# while folded_circuit is not squashed.
folded_circuit.append(folded_moment)
_append_measurements(folded_circuit, measurements)
return folded_circuit
[docs]@noise_scaling_converter
def fold_gates_from_left(
circuit: Circuit, scale_factor: float, **kwargs: Any
) -> Circuit:
"""Returns a new folded circuit by applying the map G -> G G^dag G to a
subset of gates of the input circuit, starting with gates at the
left (beginning) of the circuit.
The folded circuit has a number of gates approximately equal to
scale_factor * n where n is the number of gates in the input circuit.
For equal gate fidelities, this function reproduces the local unitary
folding method defined in equation (5) of
:cite:`Giurgica_Tiron_2020_arXiv`.
Args:
circuit: Circuit to fold.
scale_factor: Factor to scale the circuit by. Any real number >= 1.
Keyword Args:
fidelities (Dict[str, float]): Dictionary of gate fidelities. Each key
is a string which specifies the gate and each value is the
fidelity of that gate. When this argument is provided, folded
gates contribute an amount proportional to their infidelity
(1 - fidelity) to the total noise scaling. Fidelity values must be
in the interval (0, 1]. Gates not specified have a default
fidelity of 0.99**n where n is the number of qubits the gates act
on.
Supported gate keys are listed in the following table.::
Gate key | Gate
-------------------------
"H" | Hadamard
"X" | Pauli X
"Y" | Pauli Y
"Z" | Pauli Z
"I" | Identity
"CNOT" | CNOT
"CZ" | CZ gate
"TOFFOLI" | Toffoli gate
"single" | All single qubit gates
"double" | All two-qubit gates
"triple" | All three-qubit gates
Keys for specific gates override values set by "single", "double",
and "triple".
For example, `fidelities = {"single": 1.0, "H", 0.99}` sets all
single-qubit gates except Hadamard to have fidelity one.
squash_moments (bool): If True, all gates (including folded gates) are
placed as early as possible in the circuit. If False, new moments
are created for folded gates. This option only applies to QPROGRAM
types which have a "moment" or "time" structure. Default is True.
return_mitiq (bool): If True, returns a Mitiq circuit instead of
the input circuit type (if different). Default is False.
Returns:
folded: The folded quantum circuit as a QPROGRAM.
"""
weight_mask = _create_weight_mask(circuit, kwargs.get("fidelities"))
num_folds_mask = _create_fold_mask(
weight_mask, scale_factor, folding_method="from_left"
)
return _apply_fold_mask(
circuit,
num_folds_mask,
squash_moments=kwargs.get("squash_moments", True),
)
[docs]@noise_scaling_converter
def fold_gates_from_right(
circuit: Circuit, scale_factor: float, **kwargs: Any
) -> Circuit:
r"""Returns a new folded circuit by applying the map G -> G G^dag G to a
subset of gates of the input circuit, starting with gates at the
right (end) of the circuit.
The folded circuit has a number of gates approximately equal to
scale_factor * n where n is the number of gates in the input circuit.
For equal gate fidelities, this function reproduces the local unitary
folding method defined in equation (5) of
:cite:`Giurgica_Tiron_2020_arXiv`.
Args:
circuit: Circuit to fold.
scale_factor: Factor to scale the circuit by. Any real number >= 1.
Keyword Args:
fidelities (Dict[str, float]): Dictionary of gate fidelities. Each key
is a string which specifies the gate and each value is the
fidelity of that gate. When this argument is provided, folded
gates contribute an amount proportional to their infidelity
(1 - fidelity) to the total noise scaling. Fidelity values must be
in the interval (0, 1]. Gates not specified have a default
fidelity of 0.99**n where n is the number of qubits the gates act
on.
Supported gate keys are listed in the following table.::
Gate key | Gate
-------------------------
"H" | Hadamard
"X" | Pauli X
"Y" | Pauli Y
"Z" | Pauli Z
"I" | Identity
"CNOT" | CNOT
"CZ" | CZ gate
"TOFFOLI" | Toffoli gate
"single" | All single qubit gates
"double" | All two-qubit gates
"triple" | All three-qubit gates
Keys for specific gates override values set by "single", "double",
and "triple".
For example, `fidelities = {"single": 1.0, "H", 0.99}` sets all
single-qubit gates except Hadamard to have fidelity one.
squash_moments (bool): If True, all gates (including folded gates) are
placed as early as possible in the circuit. If False, new moments
are created for folded gates. This option only applies to QPROGRAM
types which have a "moment" or "time" structure. Default is True.
return_mitiq (bool): If True, returns a Mitiq circuit instead of
the input circuit type (if different). Default is False.
Returns:
folded: The folded quantum circuit as a QPROGRAM.
"""
weight_mask = _create_weight_mask(circuit, kwargs.get("fidelities"))
num_folds_mask = _create_fold_mask(
weight_mask, scale_factor, folding_method="from_right"
)
return _apply_fold_mask(
circuit,
num_folds_mask,
squash_moments=kwargs.get("squash_moments", True),
)
[docs]@noise_scaling_converter
def fold_gates_at_random(
circuit: Circuit,
scale_factor: float,
seed: Optional[int] = None,
**kwargs: Any,
) -> Circuit:
r"""Returns a new folded circuit by applying the map G -> G G^dag G to a
subset of gates of the input circuit, starting with gates at the
right (end) of the circuit.
The folded circuit has a number of gates approximately equal to
scale_factor * n where n is the number of gates in the input circuit.
For equal gate fidelities, this function reproduces the local unitary
folding method defined in equation (5) of
:cite:`Giurgica_Tiron_2020_arXiv`.
Args:
circuit: Circuit to fold.
scale_factor: Factor to scale the circuit by. Any real number >= 1.
seed: Seed for random number generator.
Keyword Args:
fidelities (Dict[str, float]): Dictionary of gate fidelities. Each key
is a string which specifies the gate and each value is the
fidelity of that gate. When this argument is provided, folded
gates contribute an amount proportional to their infidelity
(1 - fidelity) to the total noise scaling. Fidelity values must be
in the interval (0, 1]. Gates not specified have a default
fidelity of 0.99**n where n is the number of qubits the gates act
on.
Supported gate keys are listed in the following table.::
Gate key | Gate
-------------------------
"H" | Hadamard
"X" | Pauli X
"Y" | Pauli Y
"Z" | Pauli Z
"I" | Identity
"CNOT" | CNOT
"CZ" | CZ gate
"TOFFOLI" | Toffoli gate
"single" | All single qubit gates
"double" | All two-qubit gates
"triple" | All three-qubit gates
Keys for specific gates override values set by "single", "double",
and "triple".
For example, `fidelities = {"single": 1.0, "H", 0.99}` sets all
single-qubit gates except Hadamard to have fidelity one.
squash_moments (bool): If True, all gates (including folded gates) are
placed as early as possible in the circuit. If False, new moments
are created for folded gates. This option only applies to QPROGRAM
types which have a "moment" or "time" structure. Default is True.
return_mitiq (bool): If True, returns a Mitiq circuit instead of
the input circuit type (if different). Default is False.
Returns:
folded: The folded quantum circuit as a QPROGRAM.
"""
weight_mask = _create_weight_mask(circuit, kwargs.get("fidelities"))
num_folds_mask = _create_fold_mask(
weight_mask,
scale_factor,
folding_method="at_random",
seed=seed,
)
return _apply_fold_mask(
circuit,
num_folds_mask,
squash_moments=kwargs.get("squash_moments", True),
)
```