Update README.md

README.md

@@ -1,23 +1,25 @@
+[<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
+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.
+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 classifier (QSVC) and varitional quantum classifier (VQC)
+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
+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
@@ -37,14 +39,14 @@ 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.
@@ -83,6 +85,8 @@ 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
@@ -229,38 +233,4 @@ 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.