def _unitary_(self) -> Union[np.ndarray, NotImplementedType]:
qubits = cirq.LineQid.for_gate(self)
op = self.sub_gate.on(*qubits[self.num_controls() :])
c_op = cop.ControlledOperation(qubits[: self.num_controls()], op, self.control_values)
return protocols.unitary(c_op, default=NotImplemented)
def _unitary_(self) -> Union[np.ndarray, NotImplementedType]:
return protocols.unitary(self.sub_operation, NotImplemented)
def _unitary_(self) -> np.ndarray:
mat = np.eye(2)
qubit = named_qubit.NamedQubit('arbitrary')
for op in protocols.decompose_once_with_qubits(self, (qubit, )):
mat = protocols.unitary(op).dot(mat)
return mat
def _translate_one_qubit_cirq_operation_to_braket_instruction(
op: Union[np.ndarray, "cirq.Operation"], target: Optional[int] = None,
) -> List[Instruction]:
"""Translates a one-qubit Cirq operation to a (sequence of) Braket
instruction(s) according to the following rules:
1. Attempts to find a "standard translation" from Cirq to Braket.
- e.g., checks if `op` is Pauli-X and, if so, returns the Braket X.
2. If (1) is not successful, decomposes the unitary of `op` to
Rz(theta) Ry(phi) Rz(lambda) and returns the series of rotations as Braket
instructions.
Args:
op: One-qubit Cirq operation to translate.
target: Qubit index for the op to act on. Must be specified and if only
if `op` is given as a numpy array.
"""
# Translate qubit index.
if not isinstance(op, np.ndarray):
target = op.qubits[0].x
if target is None:
raise ValueError(
"Arg `target` must be specified when `op` is a matrix."
)
# Check common single-qubit gates.
if isinstance(op, cirq_ops.Operation):
if isinstance(op.gate, cirq_ops.XPowGate):
exponent = op.gate.exponent
if np.isclose(exponent, 1.0) or np.isclose(exponent, -1.0):
return [Instruction(braket_gates.X(), target)]
elif np.isclose(exponent, 0.5):
return [Instruction(braket_gates.V(), target)]
elif np.isclose(exponent, -0.5):
return [Instruction(braket_gates.Vi(), target)]
return [Instruction(braket_gates.Rx(exponent * np.pi), target)]
elif isinstance(op.gate, cirq_ops.YPowGate):
exponent = op.gate.exponent
if np.isclose(exponent, 1.0) or np.isclose(exponent, -1.0):
return [Instruction(braket_gates.Y(), target)]
return [Instruction(braket_gates.Ry(exponent * np.pi), target)]
elif isinstance(op.gate, cirq_ops.ZPowGate):
exponent = op.gate.exponent
if np.isclose(exponent, 1.0) or np.isclose(exponent, -1.0):
return [Instruction(braket_gates.Z(), target)]
elif np.isclose(exponent, 0.5):
return [Instruction(braket_gates.S(), target)]
elif np.isclose(exponent, -0.5):
return [Instruction(braket_gates.Si(), target)]
elif np.isclose(exponent, 0.25):
return [Instruction(braket_gates.T(), target)]
elif np.isclose(exponent, -0.25):
return [Instruction(braket_gates.Ti(), target)]
return [Instruction(braket_gates.Rz(exponent * np.pi), target)]
elif isinstance(op.gate, cirq_ops.HPowGate) and np.isclose(
abs(op.gate.exponent), 1.0
):
return [Instruction(braket_gates.H(), target)]
# Arbitrary single-qubit unitary decomposition.
# TODO: This does not account for global phase.
if isinstance(op, cirq_ops.Operation):
unitary_matrix = protocols.unitary(op)
else:
unitary_matrix = op
a, b, c = deconstruct_single_qubit_matrix_into_angles(unitary_matrix)
return [
Instruction(braket_gates.Rz(a), target),
Instruction(braket_gates.Ry(b), target),
Instruction(braket_gates.Rz(c), target),
]
def _unitary_(self) -> np.ndarray:
mat = np.eye(2)
qubit = raw_types.QubitId()
for op in op_tree.flatten_op_tree(self.default_decompose((qubit, ))):
mat = protocols.unitary(op).dot(mat)
return mat
def _unitary_(self) -> Union[np.ndarray, NotImplementedType]:
sub_matrix = protocols.unitary(self.sub_operation, None)
if sub_matrix is None:
return NotImplemented
return self._extend_matrix(sub_matrix)
def scatter_plot_normalized_kak_interaction_coefficients(
interactions: Iterable[Union[np.ndarray, 'cirq.SupportsUnitary',
'KakDecomposition']],
*,
include_frame: bool = True,
ax: Optional[plt.Axes] = None,
**kwargs,
):
r"""Plots the interaction coefficients of many two-qubit operations.
Plots:
A point for the (x, y, z) normalized interaction coefficients of
each interaction from the given interactions. The (x, y, z) coordinates
are normalized so that the maximum value is at 1 instead of at pi/4.
If `include_frame` is set to True, then a black wireframe outline of the
canonicalized normalized KAK coefficient space. The space is defined by
the following two constraints:
0 <= abs(z) <= y <= x <= 1
if x = 1 then z >= 0
The wireframe includes lines along the surface of the space at z=0.
The space is a prism with the identity at the origin, a crease along
y=z=0 leading to the CZ/CNOT at x=1 and a vertical triangular face that
contains the iswap at x=y=1,z=0 and the swap at x=y=z=1:
(x=1,y=1,z=0)
swap___iswap___swap (x=1,y=1,z=+-1)
_/\ | /
_/ \ | /
_/ \ | /
_/ \ | /
_/ \|/
(x=0,y=0,z=0) I---------------CZ (x=1,y=0,z=0)
Args:
interactions: An iterable of two qubit unitary interactions. Each
interaction can be specified as a raw 4x4 unitary matrix, or an
object with a 4x4 unitary matrix according to `cirq.unitary` (
(e.g. `cirq.CZ` or a `cirq.KakDecomposition` or a `cirq.Circuit`
over two qubits).
include_frame: Determines whether or not to draw the kak space
wireframe. Defaults to `True`.
ax: A matplotlib 3d axes object to plot into. If not specified, a new
figure is created, plotted, and shown.
**kwargs: Arguments forwarded into the call to `scatter` that plots the
points. Working arguments include color `c='blue'`, scale `s=2`,
labelling `label="theta=pi/4"`, etc. For reference see the
`matplotlib.pyplot.scatter` documentation:
https://matplotlib.org/3.1.1/api/_as_gen/matplotlib.pyplot.scatter.html
Returns:
The matplotlib 3d axes object that was plotted into.
Examples:
>>> ax = None
>>> for y in np.linspace(0, 0.5, 4):
... a, b = cirq.LineQubit.range(2)
... circuits = [
... cirq.Circuit(
... cirq.CZ(a, b)**0.5,
... cirq.X(a)**y, cirq.X(b)**x,
... cirq.CZ(a, b)**0.5,
... cirq.X(a)**x, cirq.X(b)**y,
... cirq.CZ(a, b) ** 0.5,
... )
... for x in np.linspace(0, 1, 25)
... ]
... ax = cirq.scatter_plot_normalized_kak_interaction_coefficients(
... circuits,
... include_frame=ax is None,
... ax=ax,
... s=1,
... label=f'y={y:0.2f}')
>>> _ = ax.legend()
>>> import matplotlib.pyplot as plt
>>> plt.show()
"""
show_plot = not ax
if not ax:
fig = plt.figure()
ax = fig.add_subplot(1, 1, 1, projection='3d')
def coord_transform(
pts: Sequence[Tuple[float, float, float]]
) -> Tuple[Iterable[float], Iterable[float], Iterable[float]]:
if len(pts) == 0:
return [], [], []
xs, ys, zs = zip(*pts)
return xs, zs, ys
if include_frame:
envelope = [
(0, 0, 0),
(1, 1, 1),
(1, 1, -1),
(0, 0, 0),
(1, 1, 1),
(1, 0, 0),
(0, 0, 0),
(1, 1, -1),
(1, 0, 0),
(0, 0, 0),
(1, 0, 0),
(1, 1, 0),
(0, 0, 0),
]
ax.plot(*coord_transform(envelope), c='black', linewidth=1)
# parse input and extract KAK vector
if not isinstance(interactions, np.ndarray):
interactions_extracted: List[np.ndarray] = [
a if isinstance(a, np.ndarray) else protocols.unitary(a)
for a in interactions
]
else:
interactions_extracted = [interactions]
points = kak_vector(interactions_extracted) * 4 / np.pi
ax.scatter(*coord_transform(points), **kwargs)
ax.set_xlim(0, +1)
ax.set_ylim(-1, +1)
ax.set_zlim(0, +1)
if show_plot:
fig.show()
return ax
def _decompose_single_qubit(self,
operation: 'cirq.Operation') -> ops.OP_TREE:
qubit = operation.qubits[0]
mat = protocols.unitary(operation)
for gate in optimizers.single_qubit_matrix_to_gates(mat, self.atol):
yield gate(qubit)
def _unitary_(self) -> Union[np.ndarray, type(NotImplemented)]:
return protocols.unitary(self._gate, NotImplemented)
def _unitary_(self) -> Union[np.ndarray, NotImplementedType]:
sub_matrix = protocols.unitary(self.sub_operation, None)
if sub_matrix is None:
return NotImplemented
return linalg.block_diag(
np.eye(pow(2, len(self.qubits)) - sub_matrix.shape[0]), sub_matrix)
def _circuit_as_layers(circuit: circuits.Circuit,
grouping: _QubitGrouping) -> List[_TransformsThenCzs]:
"""Transforms a circuit into a series of GroupMatrix+CZ layers.
Args:
circuit: The circuit to transform.
grouping: How the circuit's qubits are combined into groups.
Returns:
A list of layers. Each layer has a matrix to apply to each group of
qubits, and a list of CZs to apply to pairs of qubits crossing
between groups.
"""
frontier = {q: 0 for q in circuit.all_qubits()}
layers = []
while True:
# Pull within-group operations into per-group matrices.
any_group_matrices = False
group_matrices = []
for g in grouping.groups:
# Scan for reachable operations contained within the group qubits.
start_frontier = {q: frontier[q] for q in g}
end_frontier = circuit.reachable_frontier_from(start_frontier)
mergeable_ops = circuit.findall_operations_between(start_frontier,
end_frontier)
# Advance frontier.
for q, v in end_frontier.items():
frontier[q] = v
# Fold reachable operations into a single group matrix.
group_matrix = np.eye(1 << len(g)).reshape((2, 2) * len(g))
if mergeable_ops:
any_group_matrices = True
for _, op in mergeable_ops:
group_matrix = linalg.targeted_left_multiply(
left_matrix=protocols.unitary(op).reshape(
(2, 2) * len(op.qubits)),
right_target=group_matrix,
target_axes=[grouping.loc(q)[1] for q in op.qubits])
group_matrices.append(np.transpose(group_matrix.reshape(
1 << len(g), 1 << len(g))))
# Scan for reachable CZ operations between groups.
end_frontier = circuit.reachable_frontier_from(
frontier,
is_blocker=lambda op: grouping.all_in_same_group(*op.qubits))
cz_ops = circuit.findall_operations_between(frontier, end_frontier)
# Advance frontier.
frontier = end_frontier
# List out qubit index pairs for each CZ.
cz_indices = []
for _, cz in cz_ops:
a, b = cz.qubits
assert cz == ops.CZ(a, b)
cz_indices.append((grouping.ind(a), grouping.ind(b)))
# Combine group and CZ operations into a simulation layer.
if not any_group_matrices and not cz_indices:
break
layer = _TransformsThenCzs(group_matrices=group_matrices,
cz_indices=cz_indices)
layers.append(layer)
# We should have processed the whole circuit.
assert frontier == {q: len(circuit) for q in circuit.all_qubits()}
return layers
def _decompose_two_qubit_operation(self, op: 'cirq.Operation', _) -> DecomposeResult:
if protocols.has_unitary(op):
return transformers.two_qubit_matrix_to_ion_operations(
op.qubits[0], op.qubits[1], protocols.unitary(op)
)
return NotImplemented
def _mixture_(self) -> Sequence[Tuple[float, np.ndarray]]:
return ((self._p_ii, protocols.unitary(cirq.IdentityGate(2))),
(self._p_xi, protocols.unitary(XIGate())),
(self._p_xx,
protocols.unitary(XXGate())), (self._p_xy,
protocols.unitary(XYGate())),
(self._p_xz,
protocols.unitary(XZGate())), (self._p_yi,
protocols.unitary(YIGate())),
(self._p_yx,
protocols.unitary(YXGate())), (self._p_yy,
protocols.unitary(YYGate())),
(self._p_yz,
protocols.unitary(YZGate())), (self._p_zi,
protocols.unitary(ZIGate())),
(self._p_zx,
protocols.unitary(ZXGate())), (self._p_zy,
protocols.unitary(ZYGate())),
(self._p_zz,
protocols.unitary(ZZGate())), (self._p_ix,
protocols.unitary(IXGate())),
(self._p_iy,
protocols.unitary(IYGate())), (self._p_iz,
protocols.unitary(IZGate())))
def assert_qasm_is_consistent_with_unitary(val: Any):
"""Uses `val._unitary_` to check `val._qasm_`'s behavior."""
# Only test if qiskit is installed.
try:
import qiskit
except ImportError:
# coverage: ignore
warnings.warn("Skipped assert_qasm_is_consistent_with_unitary because "
"qiskit isn't installed to verify against.")
return
unitary = protocols.unitary(val, None)
if unitary is None:
# Vacuous consistency.
return
if isinstance(val, ops.Operation):
qubits: Sequence[ops.Qid] = val.qubits
op = val
elif isinstance(val, ops.Gate):
qid_shape = protocols.qid_shape(val)
remaining_shape = list(qid_shape)
controls = getattr(val, 'control_qubits', None)
if controls is not None:
for i, q in zip(reversed(range(len(controls))),
reversed(controls)):
if q is not None:
remaining_shape.pop(i)
qubits = devices.LineQid.for_qid_shape(remaining_shape)
op = val.on(*qubits)
else:
raise NotImplementedError(f"Don't know how to test {val!r}")
args = protocols.QasmArgs(
qubit_id_map={q: f'q[{i}]'
for i, q in enumerate(qubits)})
qasm = protocols.qasm(op, args=args, default=None)
if qasm is None:
return
num_qubits = len(qubits)
header = f"""
OPENQASM 2.0;
include "qelib1.inc";
qreg q[{num_qubits}];
"""
qasm = header + qasm
qasm_unitary = None
try:
result = qiskit.execute(
qiskit.QuantumCircuit.from_qasm_str(qasm),
backend=qiskit.Aer.get_backend('unitary_simulator'),
)
qasm_unitary = result.result().get_unitary()
qasm_unitary = _reorder_indices_of_matrix(
qasm_unitary, list(reversed(range(num_qubits))))
lin_alg_utils.assert_allclose_up_to_global_phase(qasm_unitary,
unitary,
rtol=1e-8,
atol=1e-8)
except Exception as ex:
p_unitary: Optional[np.ndarray]
p_qasm_unitary: Optional[np.ndarray]
if qasm_unitary is not None:
p_unitary, p_qasm_unitary = linalg.match_global_phase(
unitary, qasm_unitary)
else:
p_unitary = None
p_qasm_unitary = None
raise AssertionError(
'QASM not consistent with cirq.unitary(op) up to global phase.\n\n'
'op:\n{}\n\n'
'cirq.unitary(op):\n{}\n\n'
'Generated QASM:\n\n{}\n\n'
'Unitary of generated QASM:\n{}\n\n'
'Phased matched cirq.unitary(op):\n{}\n\n'
'Phased matched unitary of generated QASM:\n{}\n\n'
'Underlying error:\n{}'.format(
_indent(repr(op)),
_indent(repr(unitary)),
_indent(qasm),
_indent(repr(qasm_unitary)),
_indent(repr(p_unitary)),
_indent(repr(p_qasm_unitary)),
_indent(str(ex)),
))
def assert_qasm_is_consistent_with_unitary(val: Any):
"""Uses `val._unitary_` to check `val._qasm_`'s behavior."""
# Only test if qiskit is installed.
try:
import qiskit
except ImportError:
# coverage: ignore
warnings.warn("Skipped assert_qasm_is_consistent_with_unitary because "
"qiskit isn't installed to verify against.")
return
unitary = protocols.unitary(val, None)
if unitary is None:
# Vacuous consistency.
return
controls = getattr(val, 'control_qubits', None)
if controls is None:
qubit_count = len(unitary).bit_length() - 1
else:
qubit_count = len(unitary).bit_length() - 1 - (len(controls) -
controls.count(None))
if isinstance(val, ops.Operation):
qubits = val.qubits
op = val
elif isinstance(val, ops.Gate):
qubits = tuple(line.LineQubit.range(qubit_count))
op = val.on(*qubits)
else:
raise NotImplementedError("Don't know how to test {!r}".format(val))
args = protocols.QasmArgs(
qubit_id_map={q: 'q[{}]'.format(i)
for i, q in enumerate(qubits)})
qasm = protocols.qasm(op, args=args, default=None)
if qasm is None:
return
else:
header = """
OPENQASM 2.0;
include "qelib1.inc";
qreg q[{}];
""".format(len(qubits))
qasm = header + qasm
qasm_unitary = None
try:
result = qiskit.execute(
qiskit.load_qasm_string(qasm),
backend=qiskit.Aer.get_backend('unitary_simulator'))
qasm_unitary = result.result().get_unitary()
qasm_unitary = _reorder_indices_of_matrix(
qasm_unitary, list(reversed(range(len(qubits)))))
lin_alg_utils.assert_allclose_up_to_global_phase(qasm_unitary,
unitary,
rtol=1e-8,
atol=1e-8)
except Exception as ex:
if qasm_unitary is not None:
p_unitary, p_qasm_unitary = linalg.match_global_phase(
unitary, qasm_unitary)
else:
p_unitary = None
p_qasm_unitary = None
raise AssertionError(
'QASM be consistent with cirq.unitary(op) up to global phase.\n\n'
'op:\n{}\n\n'
'cirq.unitary(op):\n{}\n\n'
'Generated QASM:\n\n{}\n\n'
'Unitary of generated QASM:\n{}\n\n'
'Phased matched cirq.unitary(op):\n{}\n\n'
'Phased matched unitary of generated QASM:\n{}\n\n'
'Underlying error:\n{}'.format(_indent(repr(op)),
_indent(repr(unitary)),
_indent(qasm),
_indent(repr(qasm_unitary)),
_indent(repr(p_unitary)),
_indent(repr(p_qasm_unitary)),
_indent(str(ex))))
def _unitary_(self) -> Union[np.ndarray, NotImplementedType]:
sub_matrix = protocols.unitary(self.sub_gate, None)
if sub_matrix is None:
return NotImplemented
return linalg.block_diag(np.eye(sub_matrix.shape[0]), sub_matrix)
def _unitary_(self) -> Union[np.ndarray, type(NotImplemented)]:
if isinstance(self.half_turns, value.Symbol):
return NotImplemented
return protocols.unitary(ops.Rot11Gate(half_turns=self.half_turns))
def apply_unitary(self, op: 'cirq.Operation'):
"""Applies a unitary operation, mutating the object to represent the new state.
op:
The operation that mutates the object. Note that currently, only 1-
and 2- qubit operations are currently supported.
"""
old_inds = tuple(
[self.i_str(self.qubit_map[qubit]) for qubit in op.qubits])
new_inds = tuple(['new_' + old_ind for old_ind in old_inds])
U = protocols.unitary(op).reshape(
[qubit.dimension for qubit in op.qubits] * 2)
U = qtn.Tensor(U, inds=(new_inds + old_inds))
# TODO(tonybruguier): Explore using the Quimb's tensor network natively.
if len(op.qubits) == 1:
n = self.grouping[op.qubits[0]]
self.M[n] = (U @ self.M[n]).reindex({new_inds[0]: old_inds[0]})
elif len(op.qubits) == 2:
n, p = [self.grouping[qubit] for qubit in op.qubits]
if n == p:
self.M[n] = (U @ self.M[n]).reindex({
new_inds[0]: old_inds[0],
new_inds[1]: old_inds[1]
})
else:
self.num_svd_splits += 1
# This is the index on which we do the contraction. We need to add it iff it's
# the first time that we do the joining for that specific pair.
mu_ind = self.mu_str(n, p)
if mu_ind not in self.M[n].inds:
self.M[n].new_ind(mu_ind)
if mu_ind not in self.M[p].inds:
self.M[p].new_ind(mu_ind)
T = U @ self.M[n] @ self.M[p]
left_inds = tuple(set(T.inds)
& set(self.M[n].inds)) + (new_inds[0], )
X, Y = T.split(
left_inds,
cutoff=self.rsum2_cutoff,
cutoff_mode='rsum2',
get='tensors',
absorb='both',
bond_ind=mu_ind,
)
self.M[n] = X.reindex({new_inds[0]: old_inds[0]})
self.M[p] = Y.reindex({new_inds[1]: old_inds[1]})
else:
# NOTE(tonybruguier): There could be a way to handle higher orders. I think this could
# involve HOSVDs:
# https://en.wikipedia.org/wiki/Higher-order_singular_value_decomposition
#
# TODO(tonybruguier): Evaluate whether it's even useful to implement and learn more
# about HOSVDs.
raise ValueError('Can only handle 1 and 2 qubit operations')
def _unitary_(self):
return protocols.unitary(self.kak)
def _mixture_(self) -> Sequence[Tuple[float, np.ndarray]]:
return ((self._p_i, protocols.unitary(common_gates.I)),
(self._p_x, protocols.unitary(pauli_gates.X)),
(self._p_y, protocols.unitary(pauli_gates.Y)),
(self._p_z, protocols.unitary(pauli_gates.Z)))
def kak_decomposition(
unitary_object: Union[np.ndarray, 'cirq.SupportsUnitary', 'cirq.Gate',
'cirq.Operation', KakDecomposition],
*,
rtol: float = 1e-5,
atol: float = 1e-8,
check_preconditions: bool = True,
) -> KakDecomposition:
"""Decomposes a 2-qubit unitary into 1-qubit ops and XX/YY/ZZ interactions.
Args:
unitary_object: The value to decompose. Can either be a 4x4 unitary
matrix, or an object that has a 4x4 unitary matrix (via the
`cirq.SupportsUnitary` protocol).
rtol: Per-matrix-entry relative tolerance on equality.
atol: Per-matrix-entry absolute tolerance on equality.
check_preconditions: If set, verifies that the input corresponds to a
4x4 unitary before decomposing.
Returns:
A `cirq.KakDecomposition` canonicalized such that the interaction
coefficients x, y, z satisfy:
0 ≤ abs(z2) ≤ y2 ≤ x2 ≤ π/4
if x2 = π/4, z2 >= 0
Raises:
ValueError: Bad matrix.
ArithmeticError: Failed to perform the decomposition.
References:
'An Introduction to Cartan's KAK Decomposition for QC Programmers'
https://arxiv.org/abs/quant-ph/0507171
"""
if isinstance(unitary_object, KakDecomposition):
return unitary_object
if isinstance(unitary_object, np.ndarray):
mat = unitary_object
else:
mat = protocols.unitary(unitary_object)
if check_preconditions and (
mat.shape !=
(4, 4) or not predicates.is_unitary(mat, rtol=rtol, atol=atol)):
raise ValueError(
f'Input must correspond to a 4x4 unitary matrix. Received matrix:\n{mat}'
)
# Diagonalize in magic basis.
left, d, right = diagonalize.bidiagonalize_unitary_with_special_orthogonals(
KAK_MAGIC_DAG @ mat @ KAK_MAGIC,
atol=atol,
rtol=rtol,
check_preconditions=False)
# Recover pieces.
a1, a0 = so4_to_magic_su2s(left.T,
atol=atol,
rtol=rtol,
check_preconditions=False)
b1, b0 = so4_to_magic_su2s(right.T,
atol=atol,
rtol=rtol,
check_preconditions=False)
w, x, y, z = (KAK_GAMMA @ np.vstack(np.angle(d))).flatten()
g = np.exp(1j * w)
# Canonicalize.
inner_cannon = kak_canonicalize_vector(x, y, z)
b1 = np.dot(inner_cannon.single_qubit_operations_before[0], b1)
b0 = np.dot(inner_cannon.single_qubit_operations_before[1], b0)
a1 = np.dot(a1, inner_cannon.single_qubit_operations_after[0])
a0 = np.dot(a0, inner_cannon.single_qubit_operations_after[1])
return KakDecomposition(
interaction_coefficients=inner_cannon.interaction_coefficients,
global_phase=g * inner_cannon.global_phase,
single_qubit_operations_before=(b1, b0),
single_qubit_operations_after=(a1, a0),
)
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Iterator, List, Optional, TYPE_CHECKING
import math
import numpy as np
import scipy.linalg
from cirq import circuits, google, linalg, ops, optimizers, protocols
from cirq.google.ops import SycamoreGate
from cirq.google.optimizers.two_qubit_gates.gate_compilation import GateTabulation
if TYPE_CHECKING:
import cirq
UNITARY_ZZ = np.kron(protocols.unitary(ops.Z), protocols.unitary(ops.Z))
PAULI_OPS = [
np.eye(2),
protocols.unitary(ops.X),
protocols.unitary(ops.Y),
protocols.unitary(ops.Z),
]
class ConvertToSycamoreGates(circuits.PointOptimizer):
"""Attempts to convert non-native gates into SycamoreGates.
First, checks if the given operation is already a native sycamore operation.
Second, checks if the operation has a known unitary. If so, and the gate
is a 1-qubit or 2-qubit gate, then performs circuit synthesis of the
def _translate_two_qubit_cirq_operation_to_braket_instruction(
op: "cirq.Operation",
) -> List[Instruction]:
"""Translates a two-qubit Cirq operation to a (sequence of) Braket
instruction(s) according to the following rules:
1. Attempts to find a "standard translation" from Cirq to Braket.
- e.g., checks if `op` is a CNOT and, if so, returns the Braket CNOT.
2. If (1) is not successful, performs a KAK decomposition of the unitary of
`op` to obtain a circuit
──A1──X^0.5───@───X^a───X──────────────────@───B1───
│ │ │
──A2──────────X───Y^b───@───X^-0.5───Z^c───X───B2────
where A1, A2, B1, and B2 are arbitrary single-qubit unitaries and a, b, c
are floats.
Args:
op: Two-qubit Cirq operation to translate.
"""
# Translate qubit indices.
q1, q2 = [qubit.x for qubit in op.qubits]
# Check common two-qubit gates.
if isinstance(op.gate, cirq_ops.CNotPowGate) and np.isclose(
abs(op.gate.exponent), 1.0
):
return [Instruction(braket_gates.CNot(), [q1, q2])]
elif isinstance(op.gate, cirq_ops.CZPowGate) and np.isclose(
abs(op.gate.exponent), 1.0
):
return [Instruction(braket_gates.CZ(), [q1, q2])]
elif isinstance(op.gate, cirq_ops.ISwapPowGate) and np.isclose(
op.gate.exponent, 1.0
):
return [Instruction(braket_gates.ISwap(), [q1, q2])]
elif isinstance(op.gate, cirq_ops.XXPowGate):
return [
Instruction(braket_gates.XX(op.gate.exponent * np.pi), [q1, q2])
]
elif isinstance(op.gate, cirq_ops.YYPowGate):
return [
Instruction(braket_gates.YY(op.gate.exponent * np.pi), [q1, q2])
]
elif isinstance(op.gate, cirq_ops.ZZPowGate):
return [
Instruction(braket_gates.ZZ(op.gate.exponent * np.pi), [q1, q2])
]
# Arbitrary two-qubit unitary decomposition.
kak = kak_decomposition(protocols.unitary(op))
A1, A2 = kak.single_qubit_operations_before
x, y, z = kak.interaction_coefficients
a = x * -2 / np.pi + 0.5
b = y * -2 / np.pi + 0.5
c = z * -2 / np.pi + 0.5
B1, B2 = kak.single_qubit_operations_after
return [
*_translate_one_qubit_cirq_operation_to_braket_instruction(A1, q1),
*_translate_one_qubit_cirq_operation_to_braket_instruction(A2, q2),
Instruction(braket_gates.Rx(0.5 * np.pi), q1),
Instruction(braket_gates.CNot(), [q1, q2]),
Instruction(braket_gates.Rx(a * np.pi), q1),
Instruction(braket_gates.Ry(b * np.pi), q2),
Instruction(braket_gates.CNot(), [q2, q1]),
Instruction(braket_gates.Rx(-0.5 * np.pi), q2),
Instruction(braket_gates.Rz(c * np.pi), q2),
Instruction(braket_gates.CNot(), [q1, q2]),
*_translate_one_qubit_cirq_operation_to_braket_instruction(B1, q1),
*_translate_one_qubit_cirq_operation_to_braket_instruction(B2, q2),
]
def _decomp_2sqrt_iswap_matrices(
kak: 'cirq.KakDecomposition',
atol: float = 1e-8,
) -> Tuple[Sequence[Tuple[np.ndarray, np.ndarray]], complex]:
"""Returns the single-qubit matrices for the 2-SQRT_ISWAP decomposition.
Assumes canonical x, y, z and x >= y + |z| within tolerance. For x, y, z
that violate this inequality, three sqrt-iSWAP gates are required.
References:
Towards ultra-high fidelity quantum operations: SQiSW gate as a native
two-qubit gate
https://arxiv.org/abs/2105.06074
"""
# Follows the if-branch of procedure DECOMP(U) in Algorithm 1 of the paper
x, y, z = kak.interaction_coefficients
b0, b1 = kak.single_qubit_operations_before
a0, a1 = kak.single_qubit_operations_after
# Computed gate parameters: Eq. 4, 6, 7, 8 of the paper
# range limits added for robustness to numerical error
def safe_arccos(v):
return np.arccos(np.clip(v, -1, 1))
def nonzero_sign(v):
return -1 if v < 0 else 1
_c = np.clip(
np.sin(x + y - z) * np.sin(x - y + z) * np.sin(-x - y - z) *
np.sin(-x + y + z), 0, 1)
alpha = safe_arccos(
np.cos(2 * x) - np.cos(2 * y) + np.cos(2 * z) + 2 * np.sqrt(_c))
beta = safe_arccos(
np.cos(2 * x) - np.cos(2 * y) + np.cos(2 * z) - 2 * np.sqrt(_c))
# Don't need to limit this value because it will always be positive and the clip in the
# following `safe_arccos` handles the cases where this could be slightly greater than 1.
_4ccs = 4 * (np.cos(x) * np.cos(z) * np.sin(y))**2 # Intermediate value
gamma = safe_arccos(
nonzero_sign(z) * np.sqrt(_4ccs / (_4ccs + np.clip(
np.cos(2 * x) * np.cos(2 * y) * np.cos(2 * z), 0, 1))))
# Inner single-qubit gates: Fig. 4 of the paper
# Gate angles here are multiplied by -2 to adjust for non-standard gate definitions in the paper
c0 = (protocols.unitary(ops.rz(-gamma)) @ protocols.unitary(ops.rx(-alpha))
@ protocols.unitary(ops.rz(-gamma)))
c1 = protocols.unitary(ops.rx(-beta))
# Compute KAK on the decomposition to determine outer single-qubit gates
# There is no known closed form solution for these gates
u_sqrt_iswap = protocols.unitary(ops.SQRT_ISWAP)
u = u_sqrt_iswap @ np.kron(c0,
c1) @ u_sqrt_iswap # Unitary of decomposition
kak_fix = linalg.kak_decomposition(u,
atol=atol / 10,
rtol=0,
check_preconditions=False)
e0, e1 = kak_fix.single_qubit_operations_before
d0, d1 = kak_fix.single_qubit_operations_after
return [ # Pairs of single-qubit unitaries, SQRT_ISWAP between each is implied
(e0.T.conj() @ b0, e1.T.conj() @ b1),
(c0, c1),
(a0 @ d0.T.conj(), a1 @ d1.T.conj()),
], kak.global_phase / kak_fix.global_phase
def apply_op(self, op: 'cirq.Operation', prng: np.random.RandomState):
"""Applies a unitary operation, mutating the object to represent the new state.
op:
The operation that mutates the object. Note that currently, only 1-
and 2- qubit operations are currently supported.
"""
old_inds = tuple(
[self.i_str(self.qubit_map[qubit]) for qubit in op.qubits])
new_inds = tuple(['new_' + old_ind for old_ind in old_inds])
if protocols.has_unitary(op):
U = protocols.unitary(op)
else:
mixtures = protocols.mixture(op)
mixture_idx = int(
prng.choice(len(mixtures),
p=[mixture[0] for mixture in mixtures]))
U = mixtures[mixture_idx][1]
U = qtn.Tensor(U.reshape([qubit.dimension for qubit in op.qubits] * 2),
inds=(new_inds + old_inds))
# TODO(tonybruguier): Explore using the Quimb's tensor network natively.
if len(op.qubits) == 1:
n = self.grouping[op.qubits[0]]
self.M[n] = (U @ self.M[n]).reindex({new_inds[0]: old_inds[0]})
elif len(op.qubits) == 2:
n, p = [self.grouping[qubit] for qubit in op.qubits]
if n == p:
self.M[n] = (U @ self.M[n]).reindex({
new_inds[0]: old_inds[0],
new_inds[1]: old_inds[1]
})
else:
# This is the index on which we do the contraction. We need to add it iff it's
# the first time that we do the joining for that specific pair.
mu_ind = self.mu_str(n, p)
if mu_ind not in self.M[n].inds:
self.M[n].new_ind(mu_ind)
if mu_ind not in self.M[p].inds:
self.M[p].new_ind(mu_ind)
T = U @ self.M[n] @ self.M[p]
left_inds = tuple(set(T.inds)
& set(self.M[n].inds)) + (new_inds[0], )
X, Y = T.split(
left_inds,
method=self.simulation_options.method,
max_bond=self.simulation_options.max_bond,
cutoff=self.simulation_options.cutoff,
cutoff_mode=self.simulation_options.cutoff_mode,
get='tensors',
absorb='both',
bond_ind=mu_ind,
)
# Equations (13), (14), and (15):
# TODO(tonybruguier): When Quimb 2.0.0 is released, the split()
# function should have a 'renorm' that, when set to None, will
# allow to compute e_n exactly as:
# np.sum(abs((X @ Y).data) ** 2).real / np.sum(abs(T) ** 2).real
#
# The renormalization would then have to be done manually.
#
# However, for now, e_n are just the estimated value.
e_n = self.simulation_options.cutoff
self.estimated_gate_error_list.append(e_n)
self.M[n] = X.reindex({new_inds[0]: old_inds[0]})
self.M[p] = Y.reindex({new_inds[1]: old_inds[1]})
else:
# NOTE(tonybruguier): There could be a way to handle higher orders. I think this could
# involve HOSVDs:
# https://en.wikipedia.org/wiki/Higher-order_singular_value_decomposition
#
# TODO(tonybruguier): Evaluate whether it's even useful to implement and learn more
# about HOSVDs.
raise ValueError('Can only handle 1 and 2 qubit operations')
return True
def _gate_seq_to_mats(gate_seq: Sequence[ops.Gate]) -> np.ndarray:
mat_rep = protocols.unitary(gate_seq[0])
for gate in gate_seq[1:]:
mat_rep = np.dot(protocols.unitary(gate), mat_rep)
return mat_rep
def _unitary_(self) -> Optional[np.ndarray]:
if not self._has_unitary_():
return None
return linalg.kron(self.coefficient,
*[protocols.unitary(self[q]) for q in self.qubits])
def _unitary_(self):
if not self._has_unitary_():
return NotImplemented
return self.coefficient * linalg.kron(
*[protocols.unitary(PAULI_GATES[p]) for p in self.pauli_mask])
def _unitary_(self) -> Union[np.ndarray, NotImplementedType]:
return protocols.unitary(self.gate, default=None)
def _unitary_(self):
return protocols.unitary(self.to_circuit())
