diff --git a/.github/ISSUE_TEMPLATE/bug_report.md b/.github/ISSUE_TEMPLATE/bug_report.md
new file mode 100644
index 0000000..188544e
--- /dev/null
+++ b/.github/ISSUE_TEMPLATE/bug_report.md
@@ -0,0 +1,25 @@
+---
+name: Bug report
+about: Report a bug
+title: "[Bug]: "
+labels: bug
+assignees: ''
+
+---
+
+**Describe the bug**
+A clear and concise description of what the bug is.
+
+**To Reproduce**
+Steps to reproduce the behavior:
+
+**Expected behavior**
+A clear and concise description of what you expected to happen.
+
+**Environment (please complete the following information):**
+ - OS: [e.g. Windows10, macOS Monteley]
+ - Python version: [e.g. 3.8.1]
+ - Related module versions if applicable: [e.g. numpy=1.23.5]
+
+**Additional context**
+Add any other context about the problem here.
diff --git a/docs/source/_static/img/ghz_circuit.svg b/docs/source/_static/img/ghz_circuit.svg
index f055d95..b3276f6 100644
--- a/docs/source/_static/img/ghz_circuit.svg
+++ b/docs/source/_static/img/ghz_circuit.svg
@@ -1,6 +1,6 @@
\ No newline at end of file
diff --git a/docs/source/_static/img/ghz_pattern.png b/docs/source/_static/img/ghz_pattern.png
index 4715a96..c272ad3 100644
Binary files a/docs/source/_static/img/ghz_pattern.png and b/docs/source/_static/img/ghz_pattern.png differ
diff --git a/docs/source/_static/img/ghz_pattern_updated.png b/docs/source/_static/img/ghz_pattern_updated.png
new file mode 100644
index 0000000..0c1d78c
Binary files /dev/null and b/docs/source/_static/img/ghz_pattern_updated.png differ
diff --git a/docs/source/tutorial.rst b/docs/source/tutorial.rst
index 7755c45..2b79c46 100644
--- a/docs/source/tutorial.rst
+++ b/docs/source/tutorial.rst
@@ -23,8 +23,8 @@ If you have not installed `graphix` yet, you can install it using `pip` as well:
Generating MBQC Pattern
-----------------------
-We first generate a MBQC pattern using ``graphix`` library.
-First, let us import relevant modules and define function we will use:
+We first generate an MBQC pattern using ``graphix`` library.
+First, let us import relevant modules and define the function we will use:
.. code-block:: python
@@ -40,12 +40,13 @@ First, let us import relevant modules and define function we will use:
circuit.h(2)
circuit.cnot(0, 1)
circuit.cnot(0, 2)
+ circuit.ry(1, np.pi/3)
Then we define a circuit:
.. code-block:: python
- # generate the GHZ state generation pattern
+ # generate a slightly modified GHZ state generation pattern
circuit = Circuit(3)
simple_circ(circuit)
pattern = circuit.transpile()
@@ -62,7 +63,34 @@ Then we define a circuit:
.. figure:: ./_static/img/ghz_pattern.png
:scale: 85 %
- :alt: 2-qubit pattern visualization
+ :alt: 3-qubit pattern visualization
+
+This circuit should generate the following state:
+
+.. math::
+
+ \frac{\sqrt{6}}{4} |000\rangle+\frac{\sqrt{2}}{4} |010\rangle- \frac{\sqrt{2}}{4} |101\rangle+\frac{\sqrt{6}}{4} |111\rangle
+
+Next, we update the pattern with Pauli measurements:
+
+.. code-block:: python
+
+ pattern.standardize()
+ pattern.shift_signals()
+ pattern.perform_pauli_measurements()
+
+ # plot the pattern
+ nodes, edges = pattern.get_graph()
+ g = nx.Graph()
+ g.add_nodes_from(nodes)
+ g.add_edges_from(edges)
+ np.random.seed(100)
+ nx.draw(g)
+ plt.show()
+
+.. figure:: ./_static/img/ghz_pattern_updated.png
+ :scale: 85 %
+ :alt: 3-qubit updated pattern visualization
Pattern-to-circuit conversion
-----------------------------
@@ -79,12 +107,12 @@ Now let us convert the pattern into a circuit using the `graphix-perceval` libra
.. figure:: ./_static/img/ghz_circuit.svg
:scale: 85 %
- :alt: 2-qubit pattern visualization
+ :alt: 3-qubit pattern visualization
Running pattern on Perceval simulator
-------------------------------------
-By running the Perceval's computing backends, We can obtain the probability distribution of the measurement outcomes
+By running Perceval's computing backends, we can obtain the probability distribution of the measurement outcomes
.. code-block:: python
@@ -99,8 +127,10 @@ By running the Perceval's computing backends, We can obtain the probability dist
state
probability
-
|000>
0.5
-
|111>
0.5
+
|000>
0.375
+
|011>
0.125
+
|100>
0.125
+
|111>
0.375
@@ -120,13 +150,16 @@ or sampling distribution with a given number of samples:
state
counts
-
|000>
499
-
|111>
501
+
|000>
354
+
|011>
127
+
|100>
128
+
|111>
391
.. note::
Note that the current implementation only supports ``SLOS`` and ``Naive`` as local Perceval processors.
+ ``SLOS`` has a better time complexity, while ``Naive`` has a better space complexity.
See `Perceval documentation `_ for more details.