def __call__(self, target, basis_fidelity=None):
"""Decompose a two-qubit unitary over fixed basis + SU(2) using the best approximation given
that each basis application has a finite fidelity.
"""
basis_fidelity = basis_fidelity or self.basis_fidelity
if hasattr(target, '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`.
target = target.to_operator().data
if hasattr(target, 'to_matrix'):
# If input is Gate subclass or some other class object that has
# a to_matrix method this will call that method.
target = target.to_matrix()
# Convert to numpy array incase not already an array
target = np.asarray(target, dtype=complex)
# Check input is a 2-qubit unitary
if target.shape != (4, 4):
raise QiskitError(
"TwoQubitBasisDecomposer: expected 4x4 matrix for target")
if not is_unitary_matrix(target):
raise QiskitError(
"TwoQubitBasisDecomposer: target matrix is not unitary.")
target_decomposed = TwoQubitWeylDecomposition(target)
traces = self.traces(target_decomposed)
expected_fidelities = [
trace_to_fid(traces[i]) * basis_fidelity**i for i in range(4)
]
best_nbasis = np.argmax(expected_fidelities)
decomposition = self.decomposition_fns[best_nbasis](target_decomposed)
decomposition_angles = [_DECOMPOSER1Q.angles(x) for x in decomposition]
q = QuantumRegister(2)
return_circuit = QuantumCircuit(q)
for i in range(best_nbasis):
return_circuit.append(U3Gate(*decomposition_angles[2 * i]), [q[0]])
return_circuit.append(U3Gate(*decomposition_angles[2 * i + 1]),
[q[1]])
return_circuit.append(self.gate, [q[0], q[1]])
return_circuit.append(U3Gate(*decomposition_angles[2 * best_nbasis]),
[q[0]])
return_circuit.append(
U3Gate(*decomposition_angles[2 * best_nbasis + 1]), [q[1]])
return return_circuit
def _define(self):
"""
gate ms2(theta, phi) a,b
{
rz(phi) a;
rz(phi+pi/2) b;
CX b,a;
rz(-pi/2) a;
ry(theta+pi/2) b;
CX a,b;
ry(-pi/2) b;
CX b,a;
rz(-phi-pi/2) a;
rz(-phi) b;
}
"""
definition = []
q = QuantumRegister(2, "q")
theta, phi = tuple(self.params)
# rule = [
# (U3Gate(0, 0, phi), [q[0]], []),
# (U3Gate(0, 0, phi+pi/2), [q[1]], []),
# (CnotGate(), [q[1], q[0]], []),
# (U3Gate(0, 0, -pi/2), [q[0]], []),
# (U3Gate(theta+pi/2,0,0), [q[1]], []),
# (CnotGate(), [q[0], q[1]], []),
# (U3Gate(-pi/2,0,0), [q[1]], []),
# (CnotGate(), [q[1], q[0]], []),
# (U3Gate(0, 0, -phi-pi/2), [q[0]], []),
# (U3Gate(0, 0, -phi), [q[1]], []),
# ]
rule = [
(U3Gate(0, 0, phi), [q[0]], []),
(U3Gate(0, 0, phi), [q[1]], []),
(RXXGate(theta), [q[0], q[1]], []),
(U3Gate(0, 0, -phi), [q[0]], []),
(U3Gate(0, 0, -phi), [q[1]], []),
]
for inst in rule:
definition.append(inst)
self.definition = definition
def _process_node(self, node):
"""Carry out the action associated with a node."""
if node.type == "program":
self._process_children(node)
elif node.type == "qreg":
qreg = QuantumRegister(node.index, node.name)
self.dag.add_qreg(qreg)
elif node.type == "creg":
creg = ClassicalRegister(node.index, node.name)
self.dag.add_creg(creg)
elif node.type == "id":
raise QiskitError("internal error: _process_node on id")
elif node.type == "int":
raise QiskitError("internal error: _process_node on int")
elif node.type == "real":
raise QiskitError("internal error: _process_node on real")
elif node.type == "indexed_id":
raise QiskitError("internal error: _process_node on indexed_id")
elif node.type == "id_list":
# We process id_list nodes when they are leaves of barriers.
return [self._process_bit_id(node_children)
for node_children in node.children]
elif node.type == "primary_list":
# We should only be called for a barrier.
return [self._process_bit_id(m) for m in node.children]
elif node.type == "gate":
self._process_gate(node)
elif node.type == "custom_unitary":
self._process_custom_unitary(node)
elif node.type == "universal_unitary":
args = self._process_node(node.children[0])
qid = self._process_bit_id(node.children[1])
for element in qid:
u3_gate = U3Gate(*args, element)
u3_gate.condition = self.condition
self.dag.apply_operation_back(u3_gate)
elif node.type == "cnot":
self._process_cnot(node)
elif node.type == "expression_list":
return node.children
elif node.type == "binop":
raise QiskitError("internal error: _process_node on binop")
elif node.type == "prefix":
raise QiskitError("internal error: _process_node on prefix")
elif node.type == "measure":
self._process_measure(node)
elif node.type == "format":
self.version = node.version()
elif node.type == "barrier":
ids = self._process_node(node.children[0])
qubits = []
for qubit in ids:
for j, _ in enumerate(qubit):
qubits.append(qubit[j])
self.dag.apply_operation_back(Barrier(len(qubits)), qubits, [])
elif node.type == "reset":
id0 = self._process_bit_id(node.children[0])
for i, _ in enumerate(id0):
reset = Reset()
reset.condition = self.condition
self.dag.apply_operation_back(reset, [id0[i]], [])
elif node.type == "if":
self._process_if(node)
elif node.type == "opaque":
self._process_gate(node, opaque=True)
elif node.type == "external":
raise QiskitError("internal error: _process_node on external")
else:
raise QiskitError("internal error: undefined node type",
node.type, "line=%s" % node.line,
"file=%s" % node.file)
return None
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:
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 (current_node.condition 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.
left_parameters = tuple([float(x) for x in left_parameters])
# 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 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 == "u3" or 'u':
# 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 right_name in ("u1", "p") and abs(
np.mod(right_parameters[2], 2 * np.pi)) < self.eps:
right_name = "nop"
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
