.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/memory.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_auto_examples_memory.py>`
        to download the full example code.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_memory.py:

Logical Memory
==============

This example demonstrates the simplest (trivial) form of computation:
logical memory. More specifically, a logical qubit with distance ``d``
remains idle for ``d`` error correction cycles
[<cite data-footcite-t="Acharya_2024"></cite>].

Construction
------------

A memory experiment can be represented with a single cube. The color of
the cube determines the spatial/temporal boundary types.

``tqec`` provides builtin functions in ``tqec.gallery.memory`` to
construct it.

.. GENERATED FROM PYTHON SOURCE LINES 18-25

.. code-block:: Python


    # ruff: noqa: E402

    from tqec import Basis
    from tqec.gallery import memory

    graph = memory(Basis.Z)







.. GENERATED FROM PYTHON SOURCE LINES 26-29

.. code-block:: Python


    graph.view_as_html()






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            return Math.abs(p.x) &lt; 1 &amp;&amp; Math.abs(p.y) &lt; 1 &amp;&amp; p.z &gt;= 0 &amp;&amp; p.z &lt; 1;
          };
          let unit = new THREE.Vector3(0.3, 0.4, 1.8);
          unit.normalize();
          let setCameraDistance = (d) =&gt; {
            controls.target.copy(mid);
            camera.position.copy(mid);
            camera.position.addScaledVector(unit, d);
            controls.update();
            return boxPoints.every(isInView);
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          renderer.setPixelRatio(window.devicePixelRatio);
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      &lt;/script&gt;
    &lt;/body&gt;

    &lt;/html&gt;
    "></iframe>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 30-31

The memory experiment preserves its logical observable through time.

.. GENERATED FROM PYTHON SOURCE LINES 31-33

.. code-block:: Python


    correlation_surfaces = graph.find_correlation_surfaces()







.. GENERATED FROM PYTHON SOURCE LINES 34-40

.. code-block:: Python


    graph.view_as_html(
        pop_faces_at_directions=("-Y",),
        show_correlation_surface=correlation_surfaces[0],
    )






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&quot;&gt;
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        JavaScript Blocked?
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        const downloadLink = document.getElementById(&quot;model-download-link&quot;);

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            scene.background = new THREE.Color(&quot;#CBDFC6&quot;);

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            // Prepare and add the model to the scene
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            scene.add(collada.scene);

            // Set up the camera and controls
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              35,
              container.clientWidth / container.clientHeight,
              0.1,
              100000,
            );
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            scene.add(axesHelper);

            // Set up renderer
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            setupRenderer(renderer, container, camera, scene);

            // Start rendering
            renderScene(renderer, scene, camera, controls, container);
          } catch (ex) {
            container.textContent = &quot;Failed to show model. &quot; + ex;
            console.error(ex);
          }
        }

        function setupLights(scene) {
          const ambientLight = new THREE.AmbientLight(0xffffff, 1.4);
          scene.add(ambientLight);

          const directionalLight = new THREE.DirectionalLight(0xffffff, 1.0);
          directionalLight.position.set(10, 10, 10);
          directionalLight.castShadow = true;
          scene.add(directionalLight);
        }

        function processModel(modelScene) {
          modelScene.traverse((node) =&gt; {
            if (node.isMesh) {
              node.material.side = THREE.DoubleSide;

              if (node.name.endsWith(&quot;correlation_surface&quot;)) {
                return;
              }
              // Add edges for better visibility
              const edgesGeometry = new THREE.EdgesGeometry(node.geometry);
              const edgesMaterial = new THREE.LineBasicMaterial({
                color: 0x000000,
              });
              const edgeMesh = new THREE.LineSegments(
                edgesGeometry,
                edgesMaterial,
              );
              node.add(edgeMesh);
            }
          });
        }

        function fitCameraToObject(camera, controls, scene) {
          let bounds = new THREE.Box3().setFromObject(scene);
          let mid = new THREE.Vector3(
            (bounds.min.x + bounds.max.x) * 0.5,
            (bounds.min.y + bounds.max.y) * 0.5,
            (bounds.min.z + bounds.max.z) * 0.5,
          );
          let boxPoints = [];
          for (let dx of [0, 0.5, 1]) {
            for (let dy of [0, 0.5, 1]) {
              for (let dz of [0, 0.5, 1]) {
                boxPoints.push(
                  new THREE.Vector3(
                    bounds.min.x + (bounds.max.x - bounds.min.x) * dx,
                    bounds.min.y + (bounds.max.y - bounds.min.y) * dy,
                    bounds.min.z + (bounds.max.z - bounds.min.z) * dz,
                  ),
                );
              }
            }
          }
          let isInView = (p) =&gt; {
            p = new THREE.Vector3(p.x, p.y, p.z);
            p.project(camera);
            return Math.abs(p.x) &lt; 1 &amp;&amp; Math.abs(p.y) &lt; 1 &amp;&amp; p.z &gt;= 0 &amp;&amp; p.z &lt; 1;
          };
          let unit = new THREE.Vector3(0.3, 0.4, 1.8);
          unit.normalize();
          let setCameraDistance = (d) =&gt; {
            controls.target.copy(mid);
            camera.position.copy(mid);
            camera.position.addScaledVector(unit, d);
            controls.update();
            return boxPoints.every(isInView);
          };

          let maxDistance = 1;
          for (let k = 0; k &lt; 20; k++) {
            if (setCameraDistance(maxDistance)) {
              break;
            }
            maxDistance *= 2;
          }
          let minDistance = maxDistance;
          for (let k = 0; k &lt; 20; k++) {
            minDistance /= 2;
            if (!setCameraDistance(minDistance)) {
              break;
            }
          }
          for (let k = 0; k &lt; 20; k++) {
            let mid = (minDistance + maxDistance) / 2;
            if (setCameraDistance(mid)) {
              maxDistance = mid;
            } else {
              minDistance = mid;
            }
          }
          setCameraDistance(maxDistance);
        }

        function setupRenderer(renderer, container, camera, scene) {
          container.textContent = &quot;&quot;;
          renderer.setSize(container.clientWidth, container.clientHeight);
          renderer.setPixelRatio(window.devicePixelRatio);
          renderer.physicallyCorrectLights = true;
          renderer.toneMapping = THREE.ACESFilmicToneMapping;
          renderer.toneMappingExposure = 1.2;
          renderer.outputEncoding = THREE.sRGBEncoding;
          renderer.setClearColor(0xdedede);
          container.appendChild(renderer.domElement);
        }

        function renderScene(renderer, scene, camera, controls, container) {
          const render = () =&gt; {
            renderer.render(scene, camera);
          };

          render();

          new ResizeObserver(() =&gt; {
            const width = container.clientWidth;
            const height = container.clientHeight;
            camera.aspect = width / height;
            camera.updateProjectionMatrix();
            renderer.setSize(width, height);
            render();
          }).observe(container);

          controls.addEventListener(&quot;change&quot;, render);
        }

        init();
      &lt;/script&gt;
    &lt;/body&gt;

    &lt;/html&gt;
    "></iframe>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 41-56

Circuit
-------

You can download the circuit for a ``d=3`` logical ``Z`` memory
experiment from
:download:`here <../media/gallery/memory/circuit.stim>`, or generate
it with the code below. You can also open the circuit in
`Crumble <https://algassert.com/crumble>`_.

.. note::

   Note that the syndrome extraction circuits used here are of depth
   7 because we use an extra layer of two-qubit gates to align with
   the potential spatial cubes. The depth can be reduced to 6 with
   some post-processing on the circuit.

.. GENERATED FROM PYTHON SOURCE LINES 56-64

.. code-block:: Python


    from tqec import NoiseModel, compile_block_graph

    compiled_graph = compile_block_graph(graph)
    circuit = compiled_graph.generate_stim_circuit(
        k=1, noise_model=NoiseModel.uniform_depolarizing(p=0.001)
    )








.. GENERATED FROM PYTHON SOURCE LINES 65-72

Simulation
----------

Here we show the simulation results of both ``Z``-basis and ``X``-basis
memory experiments under the **uniform depolarizing** noise model.

The full code used for the simulation is shown below.

.. GENERATED FROM PYTHON SOURCE LINES 72-131

.. code-block:: Python


    from multiprocessing import cpu_count
    from pathlib import Path

    import matplotlib.pyplot as plt
    import numpy
    import sinter

    from tqec.gallery.memory import memory
    from tqec.simulation.plotting.inset import plot_observable_as_inset
    from tqec.simulation.simulation import start_simulation_using_sinter
    from tqec.utils.enums import Basis


    def generate_graphs(support_observable_basis: Basis) -> None:
        """Generate the logical error-rate graphs corresponding to the provided basis."""
        block_graph = memory(support_observable_basis)
        zx_graph = block_graph.to_zx_graph()

        correlation_surfaces = block_graph.find_correlation_surfaces()

        stats = start_simulation_using_sinter(
            block_graph,
            range(1, 4),
            list(numpy.logspace(-4, -1, 10)),
            NoiseModel.uniform_depolarizing,
            manhattan_radius=2,
            observables=correlation_surfaces,
            num_workers=cpu_count(),
            max_shots=1_000_000,
            max_errors=5_000,
            decoders=["pymatching"],
            # note that save_resume_filepath and database_path can help reduce the time taken
            # by the simulation after the database and result statistics have been saved to
            # the chosen path
            save_resume_filepath=Path(
                f"../_examples_database/memory_stats_{support_observable_basis.value}.csv"
            ),
            database_path=Path("../_examples_database/database.pkl"),
        )

        for i, stat in enumerate(stats):
            _, ax = plt.subplots()
            sinter.plot_error_rate(
                ax=ax,
                stats=stat,
                x_func=lambda stat: stat.json_metadata["p"],
                failure_units_per_shot_func=lambda stat: stat.json_metadata["d"],
                group_func=lambda stat: stat.json_metadata["d"],
            )
            plot_observable_as_inset(ax, zx_graph, correlation_surfaces[i])
            ax.grid(axis="both")
            ax.legend()
            ax.loglog()
            ax.set_title("Logical Memory Error Rate")
            ax.set_xlabel("Physical Error Rate")
            ax.set_ylabel("Logical Error Rate(per round)")









.. GENERATED FROM PYTHON SOURCE LINES 132-136

Z Basis
-------

Generate the logical memory error-rate graphs for the ``Z`` basis.

.. GENERATED FROM PYTHON SOURCE LINES 136-139

.. code-block:: Python


    generate_graphs(Basis.Z)




.. image-sg:: /auto_examples/images/sphx_glr_memory_001.png
   :alt: Logical Memory Error Rate
   :srcset: /auto_examples/images/sphx_glr_memory_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 140-144

X Basis
-------

Generate the logical memory error-rate graphs for the ``X`` basis.

.. GENERATED FROM PYTHON SOURCE LINES 144-147

.. code-block:: Python


    generate_graphs(Basis.X)




.. image-sg:: /auto_examples/images/sphx_glr_memory_002.png
   :alt: Logical Memory Error Rate
   :srcset: /auto_examples/images/sphx_glr_memory_002.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 148-152

References
----------

.. footbibliography::


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 24.485 seconds)


.. _sphx_glr_download_auto_examples_memory.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: memory.ipynb <memory.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: memory.py <memory.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: memory.zip <memory.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_