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---------

Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Gregoire Cattan <gregoire.cattan@ibm.com>

README.md

@@ -1,32 +1,38 @@
+[<img src=https://github.com/Qiskit/ecosystem/blob/main/badges/pyRiemann-qiskit.svg>](https://qiskit.org/ecosystem)
+
 # pyRiemann-qiskit
 
-Litterature on quantum computing suggests it may offer an advantage as compared with
-classical computing in terms of computational time and outcomes, such as for pattern
-recognition or when using limited training sets [1, 2].
+Literature on quantum computing suggests it may offer an advantage compared with classical
+computing in terms of computational time and outcomes, such as for pattern recognition or
+when using limited training sets [1, 2].
 
 A ubiquitous library on quantum computing is Qiskit [3]. Qiskit is an IBM library
 distributed under Apache 2.0 which provides both quantum algorithms and backends. A
-backend can be either your local machine or a remote machine, which one can emulates or be
-a quantum machine. Qiskit abstraction over the type of machine you want to use, make
-designing quantum algorithm seamless.
-
-Qiskit implements a quantum version of support vector -like classifiers, known as
-quantum-enhanced support vector classifier (QSVC) and varitional quantum classifier (VQC)
-[4]. These classifiers likely offer an advantage over classical SVM in situations where
-the classification task is complex. Task complexity is raised by the encoding of the data
-into a quantum state, the number of available data and the quality of the data. An initial
-study is available in [5], and it can be downloaded from
+backend can be either your local machine or a remote machine, which one can emulate or be
+a quantum machine. Qiskit abstraction over the type of machine you want to use, makes
+designing quantum algorithms seamless.
+
+Qiskit implements a quantum version of support vector-like classifiers, known as
+quantum-enhanced support vector classifiers (QSVCs) and variational quantum classifiers
+(VQCs) [4]. These classifiers likely offer an advantage over classical SVM in situations
+where the classification task is complex. Task complexity is raised by the encoding of the
+data into a quantum state, the number of available data, and the quality of the data. An
+initial study is available in [5], and it can be downloaded from
 [here](doc/Presentations/QuantumERPClassification.pdf). Although there is no study on this
-topic at the time of writting, this could be an interesting research direction to
+topic at the time of writing, this could be an interesting research direction to
 investigate BCI illiteracy.
 
-pyRiemann-qiskit implements a wrapper around QSVC and VQC, to use quantum classification
+`pyRiemann-qiskit` implements a wrapper around QSVC and VQC, to use quantum classification
 with Riemannian geometry. A use case would be to use vectorized covariance matrices in the
 tangent space as an input for these classifiers, enabling a possible sandbox for
 researchers and engineers in the field.
 
-The remaining details some of the quantum drawbacks and will guide you through
-installation. Full documentation, including API description, is available at
+`pyRiemann-qiskit` also introduces a quantum version of the famous MDM algorithm. There is
+a dedicated example on quantum-MDM
+[here](https://github.com/pyRiemann/pyRiemann-qiskit/blob/main/examples/ERP/classify_P300_bi_quantum_mdm.py).
+
+The remaining of this readme details some of the quantum drawbacks and will guide you
+through installation. Full documentation, including API description, is available at
 <https://pyriemann-qiskit.readthedocs.io/>. The repository also includes a
 [wiki](https://github.com/pyRiemann/pyRiemann-qiskit/wiki) where you can find additional
 information.
@@ -37,23 +43,23 @@ information.
 
   The number of qubits (and therefore the feature dimension) is limited to:
 
-  - 24 on a local quantum simulator, and up to:
+  - ~36 (depends on system memory size) on a local quantum simulator, and up to:
   - 5000 on a remote quantum simulator;
-  - 5 on free real quantum computers, and up to:
-  - 65 on exploratory quantum computers (not available for public use).
+  - 7 on free real quantum computers, and up to:
+  - 127 on exploratory quantum computers (not available for public use).
 
 - Time complexity
 
-  A higher number of trials or dimension increases time to completion of the quantum
+  A higher number of trials or dimensions increases the time to completion of the quantum
   algorithm, especially when running on a local machine. This is why the number of trials
   is limited in the examples we provided. However, you should avoid such practices in your
   own analysis.
 
   Although these aspects are less important in a remote backend, it may happen that the
   quantum algorithm is queued depending on the number of concurrent users.
 
-  For all these aspects, the use of pyRiemann-qiskit should be limited to offline analysis
-  only.
+  For all these aspects, the use of `pyRiemann-qiskit` should be limited to offline
+  analysis only.
 
 ## References
 
@@ -83,6 +89,8 @@ Anton Andreev, Grégoire Cattan, Sylvain Chevallier, and Quentin Barthélemy.
 Geometry’. Research Ideas and Outcomes 9 (20 March 2023).
 https://doi.org/10.3897/rio.9.e101006.
 
+This library is part of the [Qiskit Ecosystem](https://qiskit.org/ecosystem)
+
 ## Installation
 
 _We recommend the use of [Anaconda](https://www.anaconda.com/) to manage python
@@ -157,14 +165,14 @@ everything went smoothly by typing:
 import pyriemann_qiskit
 ```
 
-Alternatively you can from the console (Windows or Linux) build the docker image from our
-Dockerfile. Go to the root folder of pyRiemann-qiskit and type:
+Alternatively, you can from the console (Windows or Linux) build the docker image from our
+Dockerfile. Go to the root folder of `pyRiemann-qiskit` and type:
 
 ```
 docker build -t pyrq .
 ```
 
-Next use `docker run --detach pyrq` to enter the pyRiemann-qiskit image.
+Next use `docker run --detach pyrq` to enter the `pyRiemann-qiskit` image.
 
 If you wish, you can also download docker images directly from github docker registry:
 https://github.com/pyRiemann/pyRiemann-qiskit/pkgs/container/pyriemann-qiskit
@@ -229,38 +237,5 @@ automation.
 
 # Troubleshooting
 
-## Version of pyRiemann not updated
-
-There is a known issue when you install `pyRiemann-qiskit` in an environement where there
-is already `pyRiemann` installed. In such case, the `pyRiemann` version is not updated.
-Therefore before installing or updating `pyRiemann-qiskit`, we recommend to install
-`pyRiemann` as it follows:
-
-```
-pip uninstall pyriemann
-pip install pyriemann@git+https://github.com/pyRiemann/pyRiemann#egg=pyriemann
-```
-
-## Firebase admin not loading
-
-In some environment, the firebase admin module is not loaded. There is two reasons:
-
-1. The protobuf package is missing an `__init__.py` file. You can fix this issue by adding
-   it manually as it is done in the DockerFile:
-
-```
-touch /usr/local/lib/python3.9/site-packages/protobuf-4.24.4-py3.9.egg/google/__init__.py
-```
-
-2. The Firestore service contains unused dependency to `google.cloud.location`. You can
-   fix this issue by removing the dependencies manually, as it is done in the DockerFile
-   too:
-
-```
-sed -i 's/from google.cloud.location import locations_pb2//g' '/usr/local/lib/python3.9/site-packages/google_cloud_firestore-2.12.0-py3.9.egg/google/cloud/firestore_v1/services/firestore/client.py'
-sed -i 's/from google.cloud.location import locations_pb2//g' '/usr/local/lib/python3.9/site-packages/google_cloud_firestore-2.12.0-py3.9.egg/google/cloud/firestore_v1/services/firestore/transports/base.py'
-sed -i 's/from google.cloud.location import locations_pb2//g' '/usr/local/lib/python3.9/site-packages/google_cloud_firestore-2.12.0-py3.9.egg/google/cloud/firestore_v1/services/firestore/transports/grpc.py'
-sed -i 's/from google.cloud.location import locations_pb2//g' '/usr/local/lib/python3.9/site-packages/google_cloud_firestore-2.12.0-py3.9.egg/google/cloud/firestore_v1/services/firestore/transports/grpc_asyncio.py'
-sed -i 's/from google.cloud.location import locations_pb2//g' '/usr/local/lib/python3.9/site-packages/google_cloud_firestore-2.12.0-py3.9.egg/google/cloud/firestore_v1/services/firestore/transports/rest.py'
-sed -i 's/from google.cloud.location import locations_pb2//g' '/usr/local/lib/python3.9/site-packages/google_cloud_firestore-2.12.0-py3.9.egg/google/cloud/firestore_v1/services/firestore/async_client.py'
-```
+See our [dedicated](https://github.com/pyRiemann/pyRiemann-qiskit/wiki/Troubleshooting)
+wiki page.

doc/index.rst

@@ -68,6 +68,7 @@ pyRiemann-qiskit provides through Qiskit:
 
 A typical use case would be to use vectorized covariance matrices in
 tangent space as an input for quantum classifiers.
+You could also try the quantum version of the MDM algorithm.
 
 For a brief introduction to the ideas behind the package, you can read the
 :ref:`introductory notes <introduction>`. More practical information is on the

doc/introduction.rst

@@ -29,6 +29,7 @@ pyRiemann-qiskit implements a wrapper around QSVC and VQC, to use quantum
 classification with Riemannian geometry. A use case would be to use vectorized
 covariance matrices in the TangentSpace as an input for these classifiers,
 enabling a possible sandbox for researchers and engineers in the field.
+`pyRiemann-qiskit` also introduces a quantum version of the famous MDM algorithm.
 
 Quantum drawbacks
 ================================
@@ -37,10 +38,10 @@ Quantum drawbacks
 
     The number of qubits (and therefore the feature dimension) is limited to:
 
-    - 24 on a local quantum simulator, and up to:
+    - ~36 (depends on system memory size) on a local quantum simulator, and up to:
     - 5000 on a remote quantum simulator;
-    - 5 on free real quantum computers, and up to:
-    - 65 on exploratory quantum computers (not available for public use).
+    - 7 on free real quantum computers, and up to:
+    - 127 on exploratory quantum computers (not available for public use).
 
 - Time complexity