From 520f01e249758fdfde90c364b68cbf77d84a3bc3 Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Mon, 22 Jul 2024 18:05:26 +0200
Subject: [PATCH 01/17] fix lie closure to work with sums of paulis

---
 pennylane/pauli/dla/lie_closure.py  | 20 ++++++++++++++++++--
 tests/pauli/dla/test_lie_closure.py |  4 +++-
 2 files changed, 21 insertions(+), 3 deletions(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index aadfad83210..d5d204d8cdd 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -14,6 +14,7 @@
 """A function to compute the Lie closure of a set of operators"""
 # pylint: disable=too-many-arguments
 import itertools
+import warnings
 from copy import copy
 from functools import reduce
 from typing import Iterable, Union
@@ -32,6 +33,7 @@ def lie_closure(
     verbose: bool = False,
     pauli: bool = False,
     tol: float = None,
+    dtype = None
 ) -> Iterable[Union[PauliWord, PauliSentence, Operator]]:
     r"""Compute the dynamical Lie algebra from a set of generators.
 
@@ -49,6 +51,10 @@ def lie_closure(
             This can help with performance to avoid unnecessary conversions to :class:`~pennylane.operation.Operator`
             and vice versa. Default is ``False``.
         tol (float): Numerical tolerance for the linear independence check used in :class:`~.PauliVSpace`.
+        dtype: Dtype for the underlyding matrix representation in :class:`~.PauliVSpace`.
+            For generators that are pure Pauli words (:class:`~PauliWord`), it can be set
+            to ``float``. For sums of Paulis (i.e. :class:`~PauliSentence`) it should be
+            set to ``complex`` (default).
 
     Returns:
         Union[list[:class:`~.PauliSentence`], list[:class:`~.Operator`]]: a basis of either :class:`~.PauliSentence` or :class:`~.Operator` instances that is closed under
@@ -78,7 +84,7 @@ def lie_closure(
     This can be done in short via ``lie_closure`` as follows.
 
     >>> ops = [X(0) @ X(1), Z(0), Z(1)]
-    >>> dla = qml.lie_closure(ops)
+    >>> dla = qml.lie_closure(ops, dtype=float)
     >>> print(dla)
     [X(1) @ X(0),
      Z(0),
@@ -125,7 +131,10 @@ def lie_closure(
             for op in generators
         ]
 
-    vspace = PauliVSpace(generators, tol=tol)
+    if dtype is None:
+        dtype = complex
+
+    vspace = PauliVSpace(generators, tol=tol, dtype=dtype)
 
     epoch = 0
     old_length = 0  # dummy value
@@ -134,8 +143,11 @@ def lie_closure(
     while (new_length > old_length) and (epoch < max_iterations):
         if verbose:
             print(f"epoch {epoch+1} of lie_closure, DLA size is {new_length}")
+            print(f"Basis: {vspace}")
         for ps1, ps2 in itertools.combinations(vspace.basis, 2):
             com = ps1.commutator(ps2)
+            com.simplify()
+
             if len(com) == 0:  # skip because operators commute
                 continue
 
@@ -143,6 +155,7 @@ def lie_closure(
             # remove common factor 2 with Pauli commutators
             for pw, val in com.items():
                 com[pw] = val.imag / 2
+
             vspace.add(com, tol=tol)
 
         # Updated number of linearly independent PauliSentences from previous and current step
@@ -150,6 +163,9 @@ def lie_closure(
         new_length = len(vspace)
         epoch += 1
 
+        if epoch == max_iterations:
+            warnings.warn(f"reached the maximum number of iterations {max_iterations}", UserWarning)
+
     if verbose > 0:
         print(f"After {epoch} epochs, reached a DLA size of {new_length}")
 
diff --git a/tests/pauli/dla/test_lie_closure.py b/tests/pauli/dla/test_lie_closure.py
index fc2f4361e90..7927b5f252a 100644
--- a/tests/pauli/dla/test_lie_closure.py
+++ b/tests/pauli/dla/test_lie_closure.py
@@ -344,7 +344,9 @@ def test_max_iterations(self, capsys):
             PauliSentence({PauliWord({i: "X", (i + 1) % n: "Z"}): 1.0}) for i in range(n - 1)
         ]
 
-        res = qml.pauli.lie_closure(generators, verbose=True, max_iterations=1)
+        with pytest.warns(UserWarning, match="reached the maximum number of iterations"):
+            res = qml.pauli.lie_closure(generators, verbose=True, max_iterations=1)
+
         captured = capsys.readouterr()
         assert (
             captured.out

From 1f23bb733760144a4f61f71561368cea2eab6194 Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Mon, 22 Jul 2024 18:05:52 +0200
Subject: [PATCH 02/17] black

---
 pennylane/pauli/dla/lie_closure.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index d5d204d8cdd..04113f3961b 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -33,7 +33,7 @@ def lie_closure(
     verbose: bool = False,
     pauli: bool = False,
     tol: float = None,
-    dtype = None
+    dtype=None,
 ) -> Iterable[Union[PauliWord, PauliSentence, Operator]]:
     r"""Compute the dynamical Lie algebra from a set of generators.
 

From f2882b9c215fffa4ecf245510ec8d5c4a8cfbc25 Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Mon, 22 Jul 2024 18:07:52 +0200
Subject: [PATCH 03/17] [ci skip]


From 2e92770fc1f83eca3c2adb85fa16a42f1358e0dd Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 00:14:27 +0200
Subject: [PATCH 04/17] updates

---
 pennylane/pauli/dla/lie_closure.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index 04113f3961b..6a9b261b585 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -143,7 +143,7 @@ def lie_closure(
     while (new_length > old_length) and (epoch < max_iterations):
         if verbose:
             print(f"epoch {epoch+1} of lie_closure, DLA size is {new_length}")
-            print(f"Basis: {vspace}")
+
         for ps1, ps2 in itertools.combinations(vspace.basis, 2):
             com = ps1.commutator(ps2)
             com.simplify()
@@ -156,6 +156,7 @@ def lie_closure(
             for pw, val in com.items():
                 com[pw] = val.imag / 2
 
+            print(com)
             vspace.add(com, tol=tol)
 
         # Updated number of linearly independent PauliSentences from previous and current step

From 604ab3d392641e4cb041ae3712df46cd3110f4d6 Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 13:47:58 +0200
Subject: [PATCH 05/17] remove print

---
 pennylane/pauli/dla/lie_closure.py | 1 -
 1 file changed, 1 deletion(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index 6a9b261b585..26b6d679cd5 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -156,7 +156,6 @@ def lie_closure(
             for pw, val in com.items():
                 com[pw] = val.imag / 2
 
-            print(com)
             vspace.add(com, tol=tol)
 
         # Updated number of linearly independent PauliSentences from previous and current step

From 9ff10af7c272c4a62272e8a090788cb203ba34aa Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 14:35:19 +0200
Subject: [PATCH 06/17] test for summed heisenberg model

---
 tests/pauli/dla/test_lie_closure.py | 11 +++++++++++
 1 file changed, 11 insertions(+)

diff --git a/tests/pauli/dla/test_lie_closure.py b/tests/pauli/dla/test_lie_closure.py
index 7927b5f252a..f035f24370c 100644
--- a/tests/pauli/dla/test_lie_closure.py
+++ b/tests/pauli/dla/test_lie_closure.py
@@ -502,6 +502,17 @@ def test_lie_closure_heisenberg_generators_even(self):
 
         res = qml.pauli.lie_closure(generators)
         assert len(res) == 4 * ((2 ** (n - 2)) ** 2 - 1)
+    
+    @pytest.mark.parametrize("n, res", [(3, 4), (4, 12), (5, 40)])
+    def test_lie_closure_heisenberg(self, n, res):
+        """Test the resulting DLA from Heisenberg model with summed generators"""
+        genXX = [X(i) @ X(i+1) for i in range(n-1)]
+        genYY = [Y(i) @ Y(i+1) for i in range(n-1)]
+        genZZ = [Z(i) @ Z(i+1) for i in range(n-1)]
+
+        generators = [qml.sum(XX + YY + ZZ) for XX, YY, ZZ in zip(genXX, genYY, genZZ)]
+        g = qml.lie_closure(generators, dtype=complex)
+        assert len(g) == res
 
     def test_universal_gate_set(self):
         """Test universal gate set"""

From 6bb1ee6e65497780af6fe6ebb38a14c9381fac7f Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 14:36:08 +0200
Subject: [PATCH 07/17] test for summed heisenberg model

---
 tests/pauli/dla/test_lie_closure.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/tests/pauli/dla/test_lie_closure.py b/tests/pauli/dla/test_lie_closure.py
index f035f24370c..cf254755664 100644
--- a/tests/pauli/dla/test_lie_closure.py
+++ b/tests/pauli/dla/test_lie_closure.py
@@ -503,7 +503,7 @@ def test_lie_closure_heisenberg_generators_even(self):
         res = qml.pauli.lie_closure(generators)
         assert len(res) == 4 * ((2 ** (n - 2)) ** 2 - 1)
     
-    @pytest.mark.parametrize("n, res", [(3, 4), (4, 12), (5, 40)])
+    @pytest.mark.parametrize("n, res", [(3, 4), (4, 12)])
     def test_lie_closure_heisenberg(self, n, res):
         """Test the resulting DLA from Heisenberg model with summed generators"""
         genXX = [X(i) @ X(i+1) for i in range(n-1)]

From d1d0df08fbea031d127ed2f06e19f148c5471ed4 Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 14:36:12 +0200
Subject: [PATCH 08/17] black formatting

---
 tests/pauli/dla/test_lie_closure.py | 8 ++++----
 1 file changed, 4 insertions(+), 4 deletions(-)

diff --git a/tests/pauli/dla/test_lie_closure.py b/tests/pauli/dla/test_lie_closure.py
index cf254755664..e61eae472b9 100644
--- a/tests/pauli/dla/test_lie_closure.py
+++ b/tests/pauli/dla/test_lie_closure.py
@@ -502,13 +502,13 @@ def test_lie_closure_heisenberg_generators_even(self):
 
         res = qml.pauli.lie_closure(generators)
         assert len(res) == 4 * ((2 ** (n - 2)) ** 2 - 1)
-    
+
     @pytest.mark.parametrize("n, res", [(3, 4), (4, 12)])
     def test_lie_closure_heisenberg(self, n, res):
         """Test the resulting DLA from Heisenberg model with summed generators"""
-        genXX = [X(i) @ X(i+1) for i in range(n-1)]
-        genYY = [Y(i) @ Y(i+1) for i in range(n-1)]
-        genZZ = [Z(i) @ Z(i+1) for i in range(n-1)]
+        genXX = [X(i) @ X(i + 1) for i in range(n - 1)]
+        genYY = [Y(i) @ Y(i + 1) for i in range(n - 1)]
+        genZZ = [Z(i) @ Z(i + 1) for i in range(n - 1)]
 
         generators = [qml.sum(XX + YY + ZZ) for XX, YY, ZZ in zip(genXX, genYY, genZZ)]
         g = qml.lie_closure(generators, dtype=complex)

From e21c978543cb8e461a02dbbeb48b6542a331771f Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 14:48:54 +0200
Subject: [PATCH 09/17] changelog

---
 doc/releases/changelog-dev.md | 4 ++++
 1 file changed, 4 insertions(+)

diff --git a/doc/releases/changelog-dev.md b/doc/releases/changelog-dev.md
index cf17ad442a4..68aaac3d804 100644
--- a/doc/releases/changelog-dev.md
+++ b/doc/releases/changelog-dev.md
@@ -138,6 +138,9 @@
 * `qml.AmplitudeEmbedding` has better support for features using low precision integer data types.
 [(#5969)](https://github.com/PennyLaneAI/pennylane/pull/5969)
 
+* `qml.lie_closure` works with sums of Paulis.
+  [(#6023)](https://github.com/PennyLaneAI/pennylane/pull/6023)
+
 
 <h3>Contributors ✍️</h3>
 
@@ -152,6 +155,7 @@ Lillian M. A. Frederiksen,
 Pietropaolo Frisoni,
 Emiliano Godinez,
 Renke Huang,
+Korbinian Kottmann,
 Christina Lee,
 Austin Huang,
 Christina Lee,

From 9c8bbfefaa557eb5787bd23987fd64bb791be11a Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 14:49:06 +0200
Subject: [PATCH 10/17] formatting

---
 pennylane/pauli/dla/lie_closure.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index 26b6d679cd5..833105415e5 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -33,7 +33,7 @@ def lie_closure(
     verbose: bool = False,
     pauli: bool = False,
     tol: float = None,
-    dtype=None,
+    dtype = None,
 ) -> Iterable[Union[PauliWord, PauliSentence, Operator]]:
     r"""Compute the dynamical Lie algebra from a set of generators.
 

From 7d76dc93cf096617136b66ddc7e036dd825fe898 Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 14:49:09 +0200
Subject: [PATCH 11/17] black formatting

---
 pennylane/pauli/dla/lie_closure.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index 833105415e5..26b6d679cd5 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -33,7 +33,7 @@ def lie_closure(
     verbose: bool = False,
     pauli: bool = False,
     tol: float = None,
-    dtype = None,
+    dtype=None,
 ) -> Iterable[Union[PauliWord, PauliSentence, Operator]]:
     r"""Compute the dynamical Lie algebra from a set of generators.
 

From 3efb200e4fee686f8e14a64f882cf377f0050f04 Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 16:18:58 +0200
Subject: [PATCH 12/17] update

---
 pennylane/pauli/dla/lie_closure.py  | 8 ++------
 tests/pauli/dla/test_lie_closure.py | 2 +-
 2 files changed, 3 insertions(+), 7 deletions(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index 26b6d679cd5..3163b7dd979 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -32,8 +32,7 @@ def lie_closure(
     max_iterations: int = 10000,
     verbose: bool = False,
     pauli: bool = False,
-    tol: float = None,
-    dtype=None,
+    tol: float = None
 ) -> Iterable[Union[PauliWord, PauliSentence, Operator]]:
     r"""Compute the dynamical Lie algebra from a set of generators.
 
@@ -131,10 +130,7 @@ def lie_closure(
             for op in generators
         ]
 
-    if dtype is None:
-        dtype = complex
-
-    vspace = PauliVSpace(generators, tol=tol, dtype=dtype)
+    vspace = PauliVSpace(generators, tol=tol, dtype=float)
 
     epoch = 0
     old_length = 0  # dummy value
diff --git a/tests/pauli/dla/test_lie_closure.py b/tests/pauli/dla/test_lie_closure.py
index e61eae472b9..50babf8e000 100644
--- a/tests/pauli/dla/test_lie_closure.py
+++ b/tests/pauli/dla/test_lie_closure.py
@@ -511,7 +511,7 @@ def test_lie_closure_heisenberg(self, n, res):
         genZZ = [Z(i) @ Z(i + 1) for i in range(n - 1)]
 
         generators = [qml.sum(XX + YY + ZZ) for XX, YY, ZZ in zip(genXX, genYY, genZZ)]
-        g = qml.lie_closure(generators, dtype=complex)
+        g = qml.lie_closure(generators)
         assert len(g) == res
 
     def test_universal_gate_set(self):

From 417d531b99c47d28cedcafd6166281aa08c06d4d Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 16:19:01 +0200
Subject: [PATCH 13/17] black formatting

---
 pennylane/pauli/dla/lie_closure.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index 3163b7dd979..77b66fb5b6f 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -32,7 +32,7 @@ def lie_closure(
     max_iterations: int = 10000,
     verbose: bool = False,
     pauli: bool = False,
-    tol: float = None
+    tol: float = None,
 ) -> Iterable[Union[PauliWord, PauliSentence, Operator]]:
     r"""Compute the dynamical Lie algebra from a set of generators.
 

From 3df11e838bdf5f222518695bf7dc99a2c27dbf8c Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 16:19:57 +0200
Subject: [PATCH 14/17] update docs

---
 pennylane/pauli/dla/lie_closure.py | 6 +-----
 1 file changed, 1 insertion(+), 5 deletions(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index 77b66fb5b6f..cccf63ddc9e 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -50,10 +50,6 @@ def lie_closure(
             This can help with performance to avoid unnecessary conversions to :class:`~pennylane.operation.Operator`
             and vice versa. Default is ``False``.
         tol (float): Numerical tolerance for the linear independence check used in :class:`~.PauliVSpace`.
-        dtype: Dtype for the underlyding matrix representation in :class:`~.PauliVSpace`.
-            For generators that are pure Pauli words (:class:`~PauliWord`), it can be set
-            to ``float``. For sums of Paulis (i.e. :class:`~PauliSentence`) it should be
-            set to ``complex`` (default).
 
     Returns:
         Union[list[:class:`~.PauliSentence`], list[:class:`~.Operator`]]: a basis of either :class:`~.PauliSentence` or :class:`~.Operator` instances that is closed under
@@ -83,7 +79,7 @@ def lie_closure(
     This can be done in short via ``lie_closure`` as follows.
 
     >>> ops = [X(0) @ X(1), Z(0), Z(1)]
-    >>> dla = qml.lie_closure(ops, dtype=float)
+    >>> dla = qml.lie_closure(ops)
     >>> print(dla)
     [X(1) @ X(0),
      Z(0),

From b4895c3781f89407d25d0fcf1cf863aa45ac05a3 Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Tue, 23 Jul 2024 17:04:34 +0200
Subject: [PATCH 15/17] remove dtype mention

---
 pennylane/pauli/dla/lie_closure.py | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index cccf63ddc9e..a6e18eb53fb 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -126,7 +126,7 @@ def lie_closure(
             for op in generators
         ]
 
-    vspace = PauliVSpace(generators, tol=tol, dtype=float)
+    vspace = PauliVSpace(generators, tol=tol)
 
     epoch = 0
     old_length = 0  # dummy value

From 00cf476351aecf9cfe476753247786630e704d76 Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Thu, 25 Jul 2024 14:04:15 +0200
Subject: [PATCH 16/17] black formatting

---
 pennylane/pauli/dla/lie_closure.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index 7ed9a939314..01ed9c4a11a 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -139,7 +139,9 @@ def lie_closure(
 
         for ps1, ps2 in itertools.combinations(vspace.basis, 2):
             com = ps1.commutator(ps2)
+            print("1", com)
             com.simplify()
+            print("2", com)
 
             if len(com) == 0:  # skip because operators commute
                 continue

From 8dd7c306ac96149ab117a5e8e672e95f3742a5d8 Mon Sep 17 00:00:00 2001
From: qottmann <korbinian.kottmann@gmail.com>
Date: Thu, 25 Jul 2024 16:43:50 +0200
Subject: [PATCH 17/17] remove prints

---
 pennylane/pauli/dla/lie_closure.py | 2 --
 1 file changed, 2 deletions(-)

diff --git a/pennylane/pauli/dla/lie_closure.py b/pennylane/pauli/dla/lie_closure.py
index 01ed9c4a11a..7ed9a939314 100644
--- a/pennylane/pauli/dla/lie_closure.py
+++ b/pennylane/pauli/dla/lie_closure.py
@@ -139,9 +139,7 @@ def lie_closure(
 
         for ps1, ps2 in itertools.combinations(vspace.basis, 2):
             com = ps1.commutator(ps2)
-            print("1", com)
             com.simplify()
-            print("2", com)
 
             if len(com) == 0:  # skip because operators commute
                 continue