def _generate_gate_set_for_arc_prob(target, params, cond_probs):
# Here we deviate slightly from the original paper, by using Gray coding as described in:
# [arXiv:1306.3991](https://arxiv.org/abs/1306.3991){:.external}
#
# The goal is to reduce the total number of gates, but the math is unchanged.
graycode = GrayCode(len(params))
previous_binary = '1' * (2**len(params))
for notted_binary in graycode.generate_gray():
# We get the NOT of the code because we want to start with 111...1 so that we don't need
# to have X gates on all qubits from the begining. This does not change the output and is
# simply an optimization.
binary = ''.join('1' if bit == '0' else '0' for bit in notted_binary)
# TODO(tonybruguier): Further reduce the number of gates in case the prob is 0.0. This
# would mean skipping a Gray code, so the accounting of the X gates must be done
# carefully.
for bit, previous_bit, param in zip(binary, previous_binary, params):
if bit != previous_bit:
yield pauli_gates.X(param)
yield common_gates.ry(_prob_to_angle(cond_probs[int(
binary, 2)])).on(target).controlled_by(*params)
previous_binary = binary
for previous_bit, param in zip(previous_binary, params):
if previous_bit == '0':
yield pauli_gates.X(param)
def _decompose_outside_control(
self, control: 'cirq.Qid', near_target: 'cirq.Qid', far_target: 'cirq.Qid'
) -> 'cirq.OP_TREE':
"""A decomposition assuming one of the targets is in the middle.
control: ───T──────@────────@───@────────────@────────────────
│ │ │ │
near: ─X─T──────X─@─T^-1─X─@─X────@─X^0.5─X─@─X^0.5────────
│ │ │ │ │
far: ─@─Y^-0.5─T─X─T──────X─T^-1─X─T^-1────X─S─────X^-0.5─
"""
a, b, c = control, near_target, far_target
t = common_gates.T
sweep_abc = [common_gates.CNOT(a, b), common_gates.CNOT(b, c)]
yield common_gates.CNOT(c, b)
yield pauli_gates.Y(c) ** -0.5
yield t(a), t(b), t(c)
yield sweep_abc
yield t(b) ** -1, t(c)
yield sweep_abc
yield t(c) ** -1
yield sweep_abc
yield t(c) ** -1
yield pauli_gates.X(b) ** 0.5
yield sweep_abc
yield common_gates.S(c)
yield pauli_gates.X(b) ** 0.5
yield pauli_gates.X(c) ** -0.5
def _decompose_(self, qubits: Sequence['cirq.Qid']) -> 'cirq.OP_TREE':
if len(self.dense_pauli_string) <= 0:
return
any_qubit = qubits[0]
to_z_ops = op_tree.freeze_op_tree(self._to_z_basis_ops(qubits))
xor_decomp = tuple(xor_nonlocal_decompose(qubits, any_qubit))
yield to_z_ops
yield xor_decomp
if self.exponent_neg:
yield pauli_gates.Z(any_qubit)**self.exponent_neg
if self.exponent_pos:
yield pauli_gates.X(any_qubit)
yield pauli_gates.Z(any_qubit)**self.exponent_pos
yield pauli_gates.X(any_qubit)
yield protocols.inverse(xor_decomp)
yield protocols.inverse(to_z_ops)
def _decompose_(self) -> op_tree.OP_TREE:
if len(self.pauli_string) <= 0:
return
qubits = self.qubits
any_qubit = qubits[0]
to_z_ops = op_tree.freeze_op_tree(self.pauli_string.to_z_basis_ops())
xor_decomp = tuple(xor_nonlocal_decompose(qubits, any_qubit))
yield to_z_ops
yield xor_decomp
if self.exponent_neg:
yield pauli_gates.Z(any_qubit)**self.exponent_neg
if self.exponent_pos:
yield pauli_gates.X(any_qubit)
yield pauli_gates.Z(any_qubit)**self.exponent_pos
yield pauli_gates.X(any_qubit)
yield protocols.inverse(xor_decomp)
yield protocols.inverse(to_z_ops)
def _decompose_inside_control(self,
target1: raw_types.QubitId,
control: raw_types.QubitId,
target2: raw_types.QubitId
) -> op_tree.OP_TREE:
"""A decomposition assuming the control separates the targets.
target1: ─@─X───────T──────@────────@─────────X───@─────X^-0.5─
│ │ │ │ │ │
control: ─X─@─X─────@─T^-1─X─@─T────X─@─X^0.5─@─@─X─@──────────
│ │ │ │ │ │
target2: ─────@─H─T─X─T──────X─T^-1───X─T^-1────X───X─H─S^-1───
"""
a, b, c = target1, control, target2
yield common_gates.CNOT(a, b)
yield common_gates.CNOT(b, a)
yield common_gates.CNOT(c, b)
yield common_gates.H(c)
yield common_gates.T(c)
yield common_gates.CNOT(b, c)
yield common_gates.T(a)
yield common_gates.T(b)**-1
yield common_gates.T(c)
yield common_gates.CNOT(a, b)
yield common_gates.CNOT(b, c)
yield common_gates.T(b)
yield common_gates.T(c)**-1
yield common_gates.CNOT(a, b)
yield common_gates.CNOT(b, c)
yield pauli_gates.X(b)**0.5
yield common_gates.T(c)**-1
yield common_gates.CNOT(b, a)
yield common_gates.CNOT(b, c)
yield common_gates.CNOT(a, b)
yield common_gates.CNOT(b, c)
yield common_gates.H(c)
yield common_gates.S(c)**-1
yield pauli_gates.X(a)**-0.5
def _decompose_inside_control(
self, target1: 'cirq.Qid', control: 'cirq.Qid', target2: 'cirq.Qid'
) -> 'cirq.OP_TREE':
"""A decomposition assuming the control separates the targets.
target1: ─@─X───────T──────@────────@─────────X───@─────X^-0.5─
│ │ │ │ │ │
control: ─X─@─X─────@─T^-1─X─@─T────X─@─X^0.5─@─@─X─@──────────
│ │ │ │ │ │
target2: ─────@─H─T─X─T──────X─T^-1───X─T^-1────X───X─H─S^-1───
"""
a, b, c = target1, control, target2
yield common_gates.CNOT(a, b)
yield common_gates.CNOT(b, a)
yield common_gates.CNOT(c, b)
yield common_gates.H(c)
yield common_gates.T(c)
yield common_gates.CNOT(b, c)
yield common_gates.T(a)
yield common_gates.T(b) ** -1
yield common_gates.T(c)
yield common_gates.CNOT(a, b)
yield common_gates.CNOT(b, c)
yield common_gates.T(b)
yield common_gates.T(c) ** -1
yield common_gates.CNOT(a, b)
yield common_gates.CNOT(b, c)
yield pauli_gates.X(b) ** 0.5
yield common_gates.T(c) ** -1
yield common_gates.CNOT(b, a)
yield common_gates.CNOT(b, c)
yield common_gates.CNOT(a, b)
yield common_gates.CNOT(b, c)
yield common_gates.H(c)
yield common_gates.S(c) ** -1
yield pauli_gates.X(a) ** -0.5
def __pow__(self, exponent: int) -> 'LinearCombinationOfOperations':
if not isinstance(exponent, int):
return NotImplemented
if exponent < 0:
return NotImplemented
if len(self.qubits) != 1:
return NotImplemented
qubit = self.qubits[0]
i = identity.I(qubit)
x = pauli_gates.X(qubit)
y = pauli_gates.Y(qubit)
z = pauli_gates.Z(qubit)
pauli_basis = {i, x, y, z}
if not set(self.keys()).issubset(pauli_basis):
return NotImplemented
ai, ax, ay, az = self[i], self[x], self[y], self[z]
bi, bx, by, bz = operator_spaces.pow_pauli_combination(ai, ax, ay, az, exponent)
return LinearCombinationOfOperations({i: bi, x: bx, y: by, z: bz})
