Incorporate Pauli group functions into existing grouping module. #1181

glassnotes · 2021-03-31T13:47:19Z

Context: Iterating over the Pauli group, and manipulation of Pauli operations at the level of words are common tasks. Pauli operators as observables are available in PennyLane, however more advanced functionality is not fully implemented.

Description of the Change: Adds the function pauli_group to construct the Pauli group, and pauli_mult/pauli_mult_with_phase to compute products of Pauli words. Adds other miscellaneous utility functions.

Benefits: Users can now quickly iterate over the full Pauli group, convert back and forth between Pauli observables and their string representation, and multiply Paulis together at the level of their words without full matrix multiplication.

Possible Drawbacks: None

Related GitHub Issues: None

codecov · 2021-03-31T13:57:26Z

Codecov Report

Merging #1181 (e72c76e) into master (8fe31ad) will increase coverage by 0.02%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master    #1181      +/-   ##
==========================================
+ Coverage   98.12%   98.14%   +0.02%     
==========================================
  Files         146      147       +1     
  Lines       11071    11197     +126     
==========================================
+ Hits        10863    10989     +126     
  Misses        208      208

Impacted Files	Coverage Δ
pennylane/grouping/__init__.py	`100.00% <100.00%> (ø)`
pennylane/grouping/pauli.py	`100.00% <100.00%> (ø)`
pennylane/grouping/utils.py	`100.00% <100.00%> (ø)`

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josh146

Thanks @glassnotes! Did a first pass, and left some documentation suggestions and implementation questions

josh146 · 2021-04-15T12:23:36Z

pennylane/grouping/pauli.py

+    This function is called by ``pauli_group`` in order to actually generate the
+    group elements. They are split so that the outer function can handle input
+    validation, while this generator is responsible for performing the actual
+    operations.


josh146 · 2021-04-15T12:23:53Z

doc/code/qml_grouping.rst

+:class:`~pennylane.PauliZ`) or identity (:class:`~pennylane.Identity`) acting on
+the :math:`i^{th}` qubit. The full :math:`n`-qubit Pauli group has size
+:math:`4^n` (neglecting the four possible global phases that may arise from
+multiplication of its elements).


This is a great introduction!

doc/code/qml_grouping.rst

pennylane/grouping/utils.py

josh146 · 2021-04-15T12:43:44Z

pennylane/grouping/utils.py

+def pauli_word_to_matrix(pauli_word, wire_map=None):
+    """Convert a Pauli word from a tensor to its matrix representation.


This is great to have. Perhaps we can have Tensor.__matmul__ call this function at some point?

The only problem with using __matmul__ though is that it doesn't permit you to include wire maps, so there is ambiguity as to the ordering of the wires.

josh146 · 2021-04-15T12:44:58Z

pennylane/grouping/utils.py

+            op_idx = pauli_word.wires.labels.index(wire_label)
+            pauli_mats[wire_idx] = getattr(qml, pauli_names[op_idx]).matrix
+
+    return reduce(np.kron, pauli_mats)


Out of curiosity, how does this logic scale for larger and larger Pauli words?

... exponentially 😞 Since it will compute the full 2^n x 2^n unitary matrix. The key use-case I had in mind was for computing matrix representations of qml.Hamiltonian.

pennylane/grouping/utils.py

Co-authored-by: Josh Izaac <josh146@gmail.com>

…I/pennylane into pauli_group_functions

pennylane/grouping/pauli.py

antalszava

This is looking great @glassnotes! 💯 Mostly minor suggestions. For the tests, worth adding some cases with more exotic wire maps and reiterating on the docstrings.

antalszava · 2021-04-26T18:53:40Z

.github/CHANGELOG.md

+  >>> from pennylane.grouping import pauli_group
+  >>> pauli_group_3_qubits = list(pauli_group(3))


Just a thought: could it be worth having the 1 qubit version to also show the output?

Yes, that's a better idea 😄

pennylane/grouping/pauli.py

antalszava · 2021-04-26T18:59:41Z

pennylane/grouping/pauli.py

+    PauliZ(wires=[0])
+    PauliZ(wires=[0]) @ PauliZ(wires=[2])
+    PauliZ(wires=[0]) @ PauliZ(wires=[1])
+    ...


Using the three dots might be confused with the multi-line statement block, perhaps there could be a note about having only part of the output prior to the example?

This is recurring for other examples too.

Suggested change

...

pennylane/grouping/pauli.py

tests/grouping/test_grouping_utils.py

antalszava · 2021-04-26T20:06:34Z

tests/grouping/test_grouping_utils.py

+        ],
+    )
+    def test_pauli_word_to_matrix(self, pauli_word, wire_map, expected_matrix):
+        """Test that Pauli words are correctly converted into strings."""


Docstring needs an update. (seems to apply in other cases to in going forward)

antalszava · 2021-04-26T20:11:14Z

tests/grouping/test_pauli_group.py

+    """Testing for Pauli group construction and manipulation functions."""
+
+    def test_pauli_group_size(self):
+        """Test that the Pauli group is constructed correctly given the wire map."""


Docstring seems to be unrelated to the test case.

antalszava · 2021-04-26T20:11:58Z

tests/grouping/test_pauli_group.py

+        # With no wire map; ordering is based on construction from binary representation
+        expected_pg_1 = [Identity(0), PauliZ(0), PauliX(0), PauliY(0)]
+        pg_1 = list(pauli_group(1))
+        assert all([expected.compare(obtained) for expected, obtained in zip(expected_pg_1, pg_1)])
+
+        # With an arbitrary wire map


Worth separating these into two separate tests.

Co-authored-by: antalszava <antalszava@gmail.com>

…test cases."

glassnotes · 2021-04-27T17:25:57Z

pennylane/grouping/pauli.py

+
+    phase = 1
+
+    for qubit_1_char, qubit_2_char in zip(pauli_1_string, pauli_2_string):


This function has been streamlined from the first iteration by converting the Pauli words into strings, and using the strings as a means to compare. This automatically handles any issues that might otherwise occur with qubits in the tensor product that are ordered differently than they are in the wire map; the pauli_word_to_string function takes care of that internally by virtue of ordering them and then inserting "I" on the unused wires.

glassnotes · 2021-05-03T20:41:57Z

tests/grouping/test_grouping_utils.py

+                np.array([[0, -1j, 0, 0], [1j, 0, 0, 0], [0, 0, 0, 1j], [0, 0, -1j, 0]]),
+            ),
+            (
+                PauliY(1) @ PauliZ(0),


Two of these three tests involving PauliY/PauliZ on two qubits are new, and are intended to test that the matrix is computed correctly even when the mapping and wires are scrambled.

glassnotes · 2021-05-03T20:42:27Z

tests/grouping/test_pauli_group.py

+        pg_1 = list(pauli_group(1))
+        assert all([expected.compare(obtained) for expected, obtained in zip(expected_pg_1, pg_1)])
+
+    def test_one_qubit_pauli_group_valid_float_input(self):


glassnotes · 2021-05-03T20:46:58Z

tests/grouping/test_pauli_group.py

+            ),
+            (PauliZ(0) @ PauliY(1), PauliX(1) @ PauliY(0), {0: 0, 1: 1}, -1),
+            (PauliZ(0) @ PauliY(1), PauliX(1) @ PauliY(0), {1: 0, 0: 1}, -1),
+            (PauliZ(0) @ PauliY(3) @ PauliZ(1), PauliX(1) @ PauliX(2) @ PauliY(0), None, 1),


New cases with mixed up order.

glassnotes · 2021-05-03T20:47:34Z

tests/grouping/test_pauli_group.py

+                PauliZ(0) @ PauliY(3) @ PauliZ(1),
+                PauliX(1) @ PauliX(2) @ PauliY(0),
+                None,
+                PauliX(0) @ PauliY(3) @ PauliY(1) @ PauliX(2)


New case that ensures that mixed up qubit orderings when no wire map is specified get constructed using combined set of wires in the order presented.

…I/pennylane into pauli_group_functions

antalszava · 2021-05-03T22:17:20Z

@glassnotes nice! 🥇 overall looks good, it seems that codecov found a line that is not covered pennylane/grouping/utils.py#L450. Was that something newly added or was just missed before and rearranged now?

glassnotes · 2021-05-04T11:57:21Z

@glassnotes nice! 1st_place_medal overall looks good, it seems that codecov found a line that is not covered pennylane/grouping/utils.py#L450. Was that something newly added or was just missed before and rearranged now?

I'm not sure, but I've updated the tests to get it incorporated now. Thanks for the heads up!

antalszava

Looks good to me! 💯

josh146

Thanks Olivia, this is a great addition!

Olivia Di Matteo added 2 commits March 31, 2021 09:43

Incorporate new functions into existing grouping module.

3160683

Reformat init.

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Update module name in changelog.

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glassnotes requested review from josh146 and antalszava March 31, 2021 14:27

Olivia Di Matteo and others added 2 commits March 31, 2021 10:38

Tweak phase mult.

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Merge branch 'master' into pauli_group_functions

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Co-authored-by: Josh Izaac <josh146@gmail.com>

Update doc strings.

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Add missing examples.

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Add examples; fix some issues in docs.

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Merge branch 'master' into pauli_group_functions

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Update CHANGELOG.

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Merge branch 'master' into pauli_group_functions

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Merge branch 'pauli_group_functions' of https://github.com/PennyLaneA…

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…I/pennylane into pauli_group_functions

Update wire handling to use Wires.all_wires.

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Fix missing closing backticks in CHANGELOG

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glassnotes requested a review from josh146 April 20, 2021 21:01

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pennylane/grouping/pauli.py Outdated Show resolved Hide resolved

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Apply suggestions from code review

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Co-authored-by: antalszava <antalszava@gmail.com>

Update example in CHANGELOG.

9889b19

Update docstrings and pauli_mult.

8a7e512

Utility function for wire map from two Paulis.

dcb8ace

Add missing docstrings and fix copy/paste errors.

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Fix docstrings in Pauli group tests. Split test.

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Olivia Di Matteo added 3 commits April 27, 2021 12:40

Fix issues caught by Codefactor.

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Fix comment.

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Greatly streamline the phase multiplication function. Add disordered …

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…test cases."

glassnotes commented Apr 27, 2021

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josh146 added this to the v0.16.0 milestone Apr 29, 2021

Olivia Di Matteo added 2 commits May 3, 2021 16:32

Add more scrambled test cases.

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Add handling of valid floats.

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More test cases.

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Merge branch 'master' into pauli_group_functions

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Merge branch 'pauli_group_functions' of https://github.com/PennyLaneA…

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…I/pennylane into pauli_group_functions

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Merge branch 'master' into pauli_group_functions

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glassnotes merged commit d400c15 into master May 5, 2021

glassnotes deleted the pauli_group_functions branch May 5, 2021 11:50

josh146 mentioned this pull request May 6, 2021

Prevent Hamiltonians that share wires from being multiplied together #1273

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		def pauli_word_to_matrix(pauli_word, wire_map=None):
		"""Convert a Pauli word from a tensor to its matrix representation.

		>>> from pennylane.grouping import pauli_group
		>>> pauli_group_3_qubits = list(pauli_group(3))


		phase = 1

		for qubit_1_char, qubit_2_char in zip(pauli_1_string, pauli_2_string):

Incorporate Pauli group functions into existing grouping module. #1181

Incorporate Pauli group functions into existing grouping module. #1181

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