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Amend PCPhase operator to support RZ convention (#3926)
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* ammend PCPhase

* lint

* Fix tests

* Update pennylane/ops/qubit/parametric_ops_multi_qubit.py

Co-authored-by: Utkarsh <utkarshazad98@gmail.com>

* update doc-string

* Ci

* ci

---------

Co-authored-by: Utkarsh <utkarshazad98@gmail.com>
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@Jaybsoni @obliviateandsurrender
Jaybsoni and obliviateandsurrender authored Apr 3, 2023
1 parent 9bf1552 commit 6faec4f
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60 changes: 37 additions & 23 deletions pennylane/ops/qubit/parametric_ops_multi_qubit.py
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Original file line number Diff line number Diff line change
Expand Up @@ -514,18 +514,20 @@ class PCPhase(Operation):
A projector-controlled phase gate.
This gate applies a complex phase :math:`\phi` to first :math:`dim`
basis vectors of the input state. This is equivalent to applying a constant
phase shift to the subspace spanned by those vectors. Consider the 2 qubit
basis vectors of the input state while applying a complex phase :math:`- \phi`
to the remaining basis vectors. This is equivalent to applying a constant
phase shift to the subspace spanned by those :math:`dim` vectors. Consider the 2 qubit
case where :math:`dim = 2`.
.. math:: \Pi_{\phi}(\phi, dim=2, wires=[0,1]) = \begin{bmatrix}
e^{i\phi} & 0 & 0 & 0 \\
0 & e^{i\phi} & 0 & 0 \\
0 & 0 & 1 & 0 \\
0 & 0 & 0 & 1
0 & 0 & e^{-i\phi} & 0 \\
0 & 0 & 0 & e^{-i\phi}
\end{bmatrix}.
This applies a phase shift to the subspace spanned by :math:`\lbrace | 00 \rangle , | 01 \rangle \rbrace`.
This is effectively applying a :math:`2*\phi` phase shift to the subspace spanned by
:math:`\lbrace | 00 \rangle , | 01 \rangle \rbrace` excluding global phase.
**Details:**
Expand All @@ -548,7 +550,7 @@ class PCPhase(Operation):
array([[0.33423773+0.9424888j, 0. +0.j , 0. +0.j , 0. +0.j ],
[0. +0.j , 0.33423773+0.9424888j, 0. +0.j , 0. +0.j ],
[0. +0.j , 0. +0.j , 0.33423773+0.9424888j, 0. +0.j ],
[0. +0.j , 0. +0.j , 0. +0.j , 1. +0.j ]])
[0. +0.j , 0. +0.j , 0. +0.j , 0.33423773-0.9424888j]])
"""
num_wires = AnyWires
num_params = 1
Expand All @@ -558,13 +560,13 @@ class PCPhase(Operation):

basis = "Z"
grad_method = "A"
parameter_frequencies = [(1,)]
parameter_frequencies = [(2,)]

def generator(self):
r"""The hermitian matrix, which when exponentiated and scaled (i :math:`\phi`), produces
r"""The Hermitian matrix, which, when exponentiated and scaled (i :math:`\phi`), produces
the PCPhase unitary."""
dim, shape = self.hyperparameters["dimension"]
mat = np.diag([1 if index < dim else 0 for index in range(shape)])
mat = np.diag([1 if index < dim else -1 for index in range(shape)])
return qml.Hermitian(mat, wires=self.wires)

def __init__(self, phi, dim, wires, do_queue=True, id=None):
Expand All @@ -587,21 +589,21 @@ def compute_matrix(*params, **hyperparams):

if qml.math.get_interface(phi) == "tensorflow":
p = qml.math.exp(1j * qml.math.cast_like(phi, 1j))
ones = qml.math.ones_like(p)
minus_p = qml.math.exp(-1j * qml.math.cast_like(phi, 1j))
zeros = qml.math.zeros_like(p)

columns = []
for i in range(t):
columns.append(
[p if j == i else zeros for j in range(t)]
if i < d
else [ones if j == i else zeros for j in range(t)]
else [minus_p if j == i else zeros for j in range(t)]
)
r = qml.math.stack(columns, like="tensorflow", axis=-2)
return r

arg = 1j * phi
prefactors = qml.math.array([1 if index < d else 0 for index in range(t)], like=phi)
prefactors = qml.math.array([1 if index < d else -1 for index in range(t)], like=phi)

if qml.math.ndim(arg) == 0:
return qml.math.diag(qml.math.exp(arg * prefactors))
Expand All @@ -617,12 +619,11 @@ def compute_eigvals(*params, **hyperparams):

if qml.math.get_interface(phi) == "tensorflow":
phase = qml.math.exp(1j * qml.math.cast_like(phi, 1j))
return stack_last(
[phase if index < d else qml.math.ones_like(phase) for index in range(t)]
)
minus_phase = qml.math.exp(-1j * qml.math.cast_like(phi, 1j))
return stack_last([phase if index < d else minus_phase for index in range(t)])

arg = 1j * phi
prefactors = qml.math.array([1 if index < d else 0 for index in range(t)], like=phi)
prefactors = qml.math.array([1 if index < d else -1 for index in range(t)], like=phi)

if qml.math.ndim(phi) == 0:
product = arg * prefactors
Expand Down Expand Up @@ -654,23 +655,36 @@ def compute_decomposition(*params, wires=None, **hyperparams):
phi = params[0]
k, n = hyperparams["dimension"]

def _get_base_ops(theta, wire):
return PauliX(wire) @ PhaseShift(theta, wire) @ PauliX(wire), PhaseShift(theta, wire)

def _get_op_from_binary_rep(binary_rep, theta, wires):
if len(binary_rep) == 1:
op = _get_base_ops(theta, wire=wires[0])[int(binary_rep)]
op = (
PhaseShift(theta, wires[0])
if int(binary_rep)
else PauliX(wires[0]) @ PhaseShift(theta, wires[0]) @ PauliX(wires[0])
)
else:
base_op = _get_base_ops(theta, wire=wires[-1])[int(binary_rep[-1])]
base_op = (
PhaseShift(theta, wires[-1])
if int(binary_rep[-1])
else PauliX(wires[-1]) @ PhaseShift(theta, wires[-1]) @ PauliX(wires[-1])
)
op = qml.ctrl(
base_op, control=wires[:-1], control_values=[int(i) for i in binary_rep[:-1]]
)
return op

n_log2 = int(np.log2(n))
binary_reps = [bin(_k)[2:].zfill(n_log2) for _k in range(k)]
positive_binary_reps = [bin(_k)[2:].zfill(n_log2) for _k in range(k)]
negative_binary_reps = [bin(_k)[2:].zfill(n_log2) for _k in range(k, n)]

positive_ops = [
_get_op_from_binary_rep(br, phi, wires=wires) for br in positive_binary_reps
]
negative_ops = [
_get_op_from_binary_rep(br, -1 * phi, wires=wires) for br in negative_binary_reps
]

return [_get_op_from_binary_rep(br, phi, wires=wires) for br in binary_reps]
return positive_ops + negative_ops

def adjoint(self):
"""Computes the adjoint of the operator."""
Expand Down
2 changes: 1 addition & 1 deletion tests/ops/qubit/test_attributes.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -465,7 +465,7 @@ def test_pcphase(self):
mat2 = op.compute_matrix(*op.parameters, **op.hyperparameters)

mats = [
np.diag([np.exp(1j * phi) if i < dim else 1.0 for i in range(size)])
np.diag([np.exp(1j * phi) if i < dim else np.exp(-1j * phi) for i in range(size)])
for phi in broadcasted_phi
]
expected_mat = np.array(mats)
Expand Down
48 changes: 29 additions & 19 deletions tests/ops/qubit/test_parametric_ops.py
View file
Original file line number Diff line number Diff line change
Expand Up @@ -176,7 +176,13 @@ def circuit(phase, dim):
return qml.state()

def _get_expected_state(phase, dim, size):
return np.array([np.exp(1j * phase) if i < dim else 1.0 for i in range(size)]) * 1 / 2
return (
np.array(
[np.exp(1j * phase) if i < dim else np.exp(-1j * phase) for i in range(size)]
)
* 1
/ 2
)

assert np.allclose(circuit(theta, d), _get_expected_state(theta, d, 4))

Expand Down Expand Up @@ -1001,7 +1007,7 @@ def test_pcphase(self, phi, dim, wires):
mat2 = op.compute_matrix(*op.parameters, **op.hyperparameters)

expected_mat = np.diag(
[np.exp(1j * phi) if i < dim else 1.0 for i in range(2**num_wires)]
[np.exp(1j * phi) if i < dim else np.exp(-1j * phi) for i in range(2**num_wires)]
)
assert np.allclose(mat1, expected_mat)
assert np.allclose(mat2, expected_mat)
Expand All @@ -1022,7 +1028,9 @@ def test_pcphase_tf(self, phi, dim, wires):
mat2 = op.compute_matrix(*op.parameters, **op.hyperparameters)

expected_mat = tf.Variable(
np.diag([np.exp(1j * phi) if i < dim else 1.0 for i in range(2**num_wires)])
np.diag(
[np.exp(1j * phi) if i < dim else np.exp(-1j * phi) for i in range(2**num_wires)]
)
)

assert np.allclose(mat1, expected_mat)
Expand All @@ -1043,7 +1051,9 @@ def test_pcphase_torch(self, phi, dim, wires):
mat2 = op.compute_matrix(*op.parameters, **op.hyperparameters)

expected_mat = torch.tensor(
np.diag([np.exp(1j * phi) if i < dim else 1.0 for i in range(2**num_wires)])
np.diag(
[np.exp(1j * phi) if i < dim else np.exp(-1j * phi) for i in range(2**num_wires)]
)
)

assert np.allclose(mat1, expected_mat)
Expand All @@ -1066,7 +1076,9 @@ def test_pcphase_jax(self, phi, dim, wires):
mat2 = op.compute_matrix(*op.parameters, **op.hyperparameters)

expected_mat = jnp.diag(
jnp.array([jnp.exp(1j * phi) if i < dim else 1.0 for i in range(2**num_wires)])
jnp.array(
[jnp.exp(1j * phi) if i < dim else np.exp(-1j * phi) for i in range(2**num_wires)]
)
)

assert np.allclose(mat1, expected_mat)
Expand All @@ -1085,7 +1097,7 @@ def test_pcphase_broadcasted(self):
mat2 = op.compute_matrix(*op.parameters, **op.hyperparameters)

mats = [
np.diag([np.exp(1j * phi) if i < dim else 1.0 for i in range(size)])
np.diag([np.exp(1j * phi) if i < dim else np.exp(-1j * phi) for i in range(size)])
for phi in broadcasted_phi
]
expected_mat = np.array(mats)
Expand Down Expand Up @@ -2110,13 +2122,17 @@ def test_pcphase_eigvals(self):
# test arbitrary phase shift
phi = 0.5432
op = qml.PCPhase(phi, dim=2, wires=[0, 1])
expected = np.array([np.exp(1j * phi), np.exp(1j * phi), 1.0, 1.0])
expected = np.array(
[np.exp(1j * phi), np.exp(1j * phi), np.exp(-1j * phi), np.exp(-1j * phi)]
)
assert np.allclose(op.eigvals(), expected)

# test arbitrary broadcasted phase shift
phi = np.array([0.5, 0.4, 0.3])
op = qml.PCPhase(phi, dim=2, wires=[0, 1])
expected = np.array([[np.exp(1j * p), np.exp(1j * p), 1.0, 1.0] for p in phi])
expected = np.array(
[[np.exp(1j * p), np.exp(1j * p), np.exp(-1j * p), np.exp(-1j * p)] for p in phi]
)
assert np.allclose(op.eigvals(), expected)

def test_crz_eigvals(self, tol):
Expand Down Expand Up @@ -2810,7 +2826,7 @@ def test_pcphase_grad(self, dev_name, diff_method, phi):
pytest.skip("PCPhase does not support adjoint diff")

dev = qml.device(dev_name, wires=[0, 1])
expected_grad = (1j / 2) * (npp.exp(1j * phi) - npp.exp(-1j * phi)) # computed by hand
expected_grad = -4 * npp.cos(phi) * npp.sin(phi) # computed by hand

@qml.qnode(dev, diff_method=diff_method)
def circ(phi):
Expand All @@ -2837,9 +2853,7 @@ def test_pcphase_grad_tf(self, dev_name, diff_method, phi):
import tensorflow as tf

dev = qml.device(dev_name, wires=[0, 1])
expected_grad = tf.Variable(
(1j / 2) * (npp.exp(1j * phi) - npp.exp(-1j * phi))
) # computed by hand
expected_grad = tf.Variable(-4 * npp.cos(phi) * npp.sin(phi)) # computed by hand
phi = tf.Variable(phi)

@qml.qnode(dev, diff_method=diff_method)
Expand Down Expand Up @@ -2869,9 +2883,7 @@ def test_pcphase_grad_torch(self, dev_name, diff_method, phi):
import torch

dev = qml.device(dev_name, wires=[0, 1])
expected_grad = torch.tensor(
(1j / 2) * (npp.exp(1j * phi) - npp.exp(-1j * phi))
) # computed by hand
expected_grad = torch.tensor(-4 * npp.cos(phi) * npp.sin(phi)) # computed by hand
phi = torch.tensor(phi, requires_grad=True)

@qml.qnode(dev, diff_method=diff_method)
Expand Down Expand Up @@ -2900,9 +2912,7 @@ def test_pcphase_grad_jax(self, dev_name, diff_method, phi):
import jax.numpy as jnp

dev = qml.device(dev_name, wires=[0, 1])
expected_grad = jnp.array(
(1j / 2) * (npp.exp(1j * phi) - npp.exp(-1j * phi))
) # computed by hand
expected_grad = jnp.array(-4 * npp.cos(phi) * npp.sin(phi)) # computed by hand
phi = jnp.array(phi)

@qml.qnode(dev, diff_method=diff_method)
Expand Down Expand Up @@ -2944,7 +2954,7 @@ def test_pcphase_generator(self):
phi = 1.23
op = qml.PCPhase(phi, dim=2, wires=[0, 1])

expected_mat = np.diag([1.0, 1.0, 0.0, 0.0])
expected_mat = np.diag([1.0, 1.0, -1.0, -1.0])

gen, coeff = qml.generator(op)
assert np.allclose(qml.matrix(gen), expected_mat)
Expand Down

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