Copilot commented on code in PR #1040:
URL: https://github.com/apache/mahout/pull/1040#discussion_r2791934778


##########
website/versioned_docs/version-0.5/community/index.md:
##########
@@ -0,0 +1,97 @@
+---
+title: Community Overview
+sidebar_label: Community Overview
+---
+
+# Community Overview
+
+The Apache Mahout community consists of developers, users, data scientists, 
researchers, and open-source contributors who collaborate to build scalable 
machine-learning libraries on the Apache platform.
+Mahout follows the principles of the Apache Software Foundation — openness, 
transparency, community-driven development, and meritocracy.
+
+This page explains the official communication channels, how to participate, 
and how to contribute to the project.
+
+<!-- <<<<<<< other -->
+There are numerous ways to engage with the Mahout community, no matter your 
background or skill level. Some options include:
+## Biweekly Community Meeting
+Apache Mahout is committed to work consistently and conducts its meetings once 
in two weeks. To get invovled, please subscribe Google Calendar to view and 
join the meeting.
+[Meeting 
Link](https://calendar.google.com/calendar/u/0/r?cid=ZGM4MWY4MTYxYjcyYTRkNGM4ZTVkYjU4MjI5MzYzZWUxMzkxZDllNWU5ZWI1NzUyNzliZTdmN2NhOGQ2ODUzMUBncm91cC5jYWxlbmRhci5nb29nbGUuY29t)

Review Comment:
   This page still contains merge-conflict artifacts (`<<<<<<<`, `=======`, 
`>>>>>>>`). Please resolve the conflict and delete these marker lines so they 
don’t render in the published docs.



##########
website/versioned_docs/version-0.5/qdp/api.md:
##########
@@ -0,0 +1,131 @@
+---
+title: API Reference - QDP
+---
+
+# API Reference
+
+Mahout QDP (Quantum Data Plane) provides GPU-accelerated quantum state 
encoding.
+It writes classical data directly into GPU memory and returns a 
DLPack-compatible
+handle for zero-copy integration with downstream frameworks.
+
+## Module: `qumat.qdp`
+
+Prefer importing from `qumat.qdp`; the native extension is `_qdp`.
+
+```python
+import qumat.qdp as qdp
+# or: from _qdp import QdpEngine, QuantumTensor
+```
+
+## Class: `QdpEngine`
+
+### `QdpEngine(device_id=0, precision="float32")`
+
+Create a GPU encoder instance.
+
+**Parameters**
+- `device_id` (int): CUDA device ID, default `0`.
+- `precision` (str): `"float32"` or `"float64"`.
+
+**Raises**
+- `RuntimeError`: Initialization failure or unsupported precision.
+
+### `encode(data, num_qubits, encoding_method="amplitude") -> QuantumTensor`
+
+Encode classical input into a quantum state and return a DLPack tensor on GPU.
+
+**Parameters**
+- `data`: Supported inputs
+  - `list[float]`
+  - `numpy.ndarray` (1D/2D, dtype=float64, C-contiguous)
+  - `torch.Tensor` (CPU, float64, contiguous)
+  - `str` / `pathlib.Path` file path
+    - `.parquet`, `.arrow` / `.feather`, `.npy`, `.pt` / `.pth`, `.pb`
+- `num_qubits` (int): Number of qubits, range 1–30.
+- `encoding_method` (str): `"amplitude" | "angle" | "basis" | "iqp" | "iqp-z"` 
(lowercase).
+
+**Returns**
+- `QuantumTensor` with 2D shape:
+  - single sample: `[1, 2^num_qubits]`
+  - batch: `[batch_size, 2^num_qubits]`
+
+**Notes**
+- Output dtype is `complex64` (`precision="float32"`) or `complex128` 
(`precision="float64"`).
+- Parquet streaming currently supports `"amplitude"` and `"basis"`.
+- PyTorch file inputs (`.pt`, `.pth`) require building with the `pytorch` 
feature.
+

Review Comment:
   This note says Parquet streaming supports only `"amplitude"` and `"basis"`, 
but `qdp/concepts.md` and `qdp/readers.md` in this same version state that 
streaming Parquet also supports `"angle"`. Please make these docs consistent 
(either update this note or adjust the other docs if streaming angle is not 
actually supported).



##########
website/versioned_docs/version-0.5/download/quickstart.md:
##########
@@ -0,0 +1,58 @@
+---
+title: Quickstart
+sidebar_label: Quickstart
+---
+
+<!--
+ Licensed to the Apache Software Foundation (ASF) under one or more
+ contributor license agreements.  See the NOTICE file distributed with
+ this work for additional information regarding copyright ownership.
+ The ASF licenses this file to You under the Apache License, Version 2.0
+ (the "License"); you may not use this file except in compliance with
+ the License.  You may obtain a copy of the License at
+
+     http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+-->
+
+# Qumat Quickstart
+
+## Installation
+
+Install Qumat using pip:
+
+```bash
+pip install qumat
+```
+
+## Basic Usage
+
+```python
+from qumat import QumatCircuit
+
+# Create a simple quantum circuit
+circuit = QumatCircuit(2)

Review Comment:
   The quickstart example imports/uses `QumatCircuit`, but there is no 
`QumatCircuit` in the Python package (the public class is `QuMat`). Please 
update the snippet to use the actual API so it’s copy/pasteable.
   ```suggestion
   from qumat import QuMat
   
   # Create a simple quantum circuit
   circuit = QuMat(2)
   ```



##########
website/versioned_docs/version-0.5/community/index.md:
##########
@@ -0,0 +1,97 @@
+---
+title: Community Overview
+sidebar_label: Community Overview
+---
+
+# Community Overview
+
+The Apache Mahout community consists of developers, users, data scientists, 
researchers, and open-source contributors who collaborate to build scalable 
machine-learning libraries on the Apache platform.
+Mahout follows the principles of the Apache Software Foundation — openness, 
transparency, community-driven development, and meritocracy.
+
+This page explains the official communication channels, how to participate, 
and how to contribute to the project.
+
+<!-- <<<<<<< other -->
+There are numerous ways to engage with the Mahout community, no matter your 
background or skill level. Some options include:
+## Biweekly Community Meeting
+Apache Mahout is committed to work consistently and conducts its meetings once 
in two weeks. To get invovled, please subscribe Google Calendar to view and 
join the meeting.

Review Comment:
   Typo in this sentence: "get invovled" → "get involved".
   ```suggestion
   Apache Mahout is committed to work consistently and conducts its meetings 
once in two weeks. To get involved, please subscribe Google Calendar to view 
and join the meeting.
   ```



##########
website/versioned_docs/version-0.5/qumat/api.md:
##########
@@ -0,0 +1,160 @@
+---
+title: Api
+---
+# QuMat Class Methods
+
+## `__init__(self, backend_config)`
+- **Purpose**: Initializes the QuMat instance with a specific backend.
+- **Parameters**:
+    - `backend_config` (dict): Configuration for the backend including its 
name and options.
+- **Usage**: Used to set up the quantum computing backend based on user 
configuration.
+
+## `create_empty_circuit(self, num_qubits)`
+- **Purpose**: Creates an empty quantum circuit with a specified number of 
qubits.
+- **Parameters**:
+    - `num_qubits` (int): Number of qubits in the quantum circuit.
+- **Usage**: Used at the start of quantum computations to prepare a new 
quantum circuit.
+
+## `apply_not_gate(self, qubit_index)`
+- **Purpose**: Applies a NOT gate (quantum equivalent of a classical NOT) to a 
specified qubit.
+- **Parameters**:
+    - `qubit_index` (int): Index of the qubit to which the gate is applied.
+- **Usage**: Used to flip the state of a qubit from 0 to 1 or from 1 to 0.
+
+## `apply_hadamard_gate(self, qubit_index)`
+- **Purpose**: Applies a Hadamard gate to a specified qubit.
+- **Parameters**:
+    - `qubit_index` (int): Index of the qubit.
+- **Usage**: Used to create a superposition state, allowing the qubit to be 
both 0 and 1 simultaneously.
+
+## `apply_cnot_gate(self, control_qubit_index, target_qubit_index)`
+- **Purpose**: Applies a Controlled-NOT (CNOT) gate between two qubits.
+- **Parameters**:
+    - `control_qubit_index` (int): Index of the control qubit.
+    - `target_qubit_index` (int): Index of the target qubit.
+- **Usage**: Fundamental for entangling qubits, which is essential for quantum 
algorithms.
+
+## `apply_toffoli_gate(self, control_qubit_index1, control_qubit_index2, 
target_qubit_index)`
+- **Purpose**: Applies a Toffoli gate (CCX gate) to three qubits.
+- **Parameters**:
+    - `control_qubit_index1` (int): Index of the first control qubit.
+    - `control_qubit_index2` (int): Index of the second control qubit.
+    - `target_qubit_index` (int): Index of the target qubit.
+- **Usage**: Acts as a quantum AND gate, used in algorithms requiring 
conditional logic.
+
+## `apply_swap_gate(self, qubit_index1, qubit_index2)`
+- **Purpose**: Swaps the states of two qubits.
+- **Parameters**:
+    - `qubit_index1` (int): Index of the first qubit.
+    - `qubit_index2` (int): Index of the second qubit.
+- **Usage**: Useful in quantum algorithms for rearranging qubit states.
+
+## `apply_cswap_gate(self, control_qubit_index, target_qubit_index1, 
target_qubit_index2)`
+- **Purpose**: Applies a controlled-SWAP (Fredkin) gate that swaps two targets 
when the control is |1⟩.
+- **Parameters**:
+    - `control_qubit_index` (int): Index of the control qubit.
+    - `target_qubit_index1` (int): Index of the first target qubit.
+    - `target_qubit_index2` (int): Index of the second target qubit.
+- **Usage**: Used in overlap estimation routines such as the swap test.
+
+## `apply_pauli_x_gate(self, qubit_index)`
+- **Purpose**: Applies a Pauli-X gate to a specified qubit.
+- **Parameters**:
+    - `qubit_index` (int): Index of the qubit.
+- **Usage**: Equivalent to a NOT gate, flips the qubit state.
+
+## `apply_pauli_y_gate(self, qubit_index)`
+- **Purpose**: Applies a Pauli-Y gate to a specified qubit.
+- **Parameters**:
+    - `qubit_index` (int): Index of the qubit.
+- **Usage**: Impacts the phase and amplitude of a qubit's state.
+
+## `apply_pauli_z_gate(self, qubit_index)`
+- **Purpose**: Applies a Pauli-Z gate to a specified qubit.
+- **Parameters**:
+    - `qubit_index` (int): Index of the qubit.
+- **Usage**: Alters the phase of a qubit without changing its amplitude.
+
+## `apply_t_gate(self, qubit_index)`
+- **Purpose**: Applies the T (π/8) phase gate to a specified qubit.
+- **Parameters**:
+    - `qubit_index` (int): Index of the qubit.
+- **Usage**: Adds a π/4 phase to |1⟩. Together with the Hadamard (H) and CNOT 
gates, it enables universal single-qubit control.
+
+## `execute_circuit(self)`
+- **Purpose**: Executes the quantum circuit and retrieves the results.
+- **Usage**: Used to run the entire set of quantum operations and measure the 
outcomes.
+
+## `get_final_state_vector(self)`
+- **Purpose**: Returns the final state vector of the circuit from the 
configured backend.
+- **Usage**: Retrieves the full quantum state for simulation and analysis 
workflows.
+
+## `draw_circuit(self)`
+- **Purpose**: Visualizes the quantum circuit.
+- **Returns**: A string representation of the circuit visualization (format 
depends on backend).
+- **Usage**: Returns a visualization string that can be printed or used 
programmatically. Example: `print(qc.draw_circuit())` or `viz = 
qc.draw_circuit()`.
+- **Note**: Uses underlying libraries' methods for drawing circuits (Qiskit's 
`draw()`, Cirq's `str()`, or Braket's `str()`).
+
+## `apply_rx_gate(self, qubit_index, angle)`
+- **Purpose**: Applies a rotation around the X-axis to a specified qubit with 
an optional parameter for optimization.
+- **Parameters**:
+    - `qubit_index` (int): Index of the qubit.
+    - `angle` (str or float): Angle in radians for the rotation. Can be a 
static value or a parameter name for optimization.
+- **Usage**: Used to rotate a qubit around the X-axis, often in parameterized 
quantum circuits for variational algorithms.
+
+## `apply_ry_gate(self, qubit_index, angle)`
+- **Purpose**: Applies a rotation around the Y-axis to a specified qubit with 
an optional parameter for optimization.
+- **Parameters**:
+    - `qubit_index` (int): Index of the qubit.
+    - `angle` (str or float): Angle in radians for the rotation. Can be a 
static value or a parameter name for optimization.
+- **Usage**: Used to rotate a qubit around the Y-axis in parameterized 
circuits, aiding in the creation of complex quantum states.
+
+## `apply_rz_gate(self, qubit_index, angle)`
+- **Purpose**: Applies a rotation around the Z-axis to a specified qubit with 
an optional parameter for optimization.
+- **Parameters**:
+    - `qubit_index` (int): Index of the qubit.
+    - `angle` (str or float): Angle in radians for the rotation. Can be a 
static value or a parameter name for optimization.
+- **Usage**: Utilized in parameterized quantum circuits to modify the phase of 
a qubit state during optimization.
+
+## `apply_u_gate(self, qubit_index, theta, phi, lambd)`
+- **Purpose**: Applies the universal single-qubit U(θ, φ, λ) gate.
+- **Parameters**:
+    - `qubit_index` (int): Index of the qubit.
+    - `theta` (float): Rotation angle θ.
+    - `phi` (float): Rotation angle φ.
+    - `lambd` (float): Rotation angle λ.
+- **Usage**: Provides full single-qubit unitary control via Z–Y–Z Euler 
decomposition.
+
+## `execute_circuit(self, parameter_values=None)`
+- **Purpose**: Executes the quantum circuit with the ability to bind specific 
parameter values if provided.
+- **Parameters**:
+    - `parameter_values` (dict, optional): A dictionary where keys are 
parameter names and values are the numerical values to bind.
+- **Usage**: Enables the execution of parameterized circuits by binding 
parameter values, facilitating optimization processes.

Review Comment:
   `execute_circuit` is already documented earlier in this file, but it’s 
repeated here with a different signature. Since the implementation is 
`execute_circuit(self, parameter_values=None)`, please keep a single entry that 
documents the optional `parameter_values` argument.



##########
website/versioned_docs/version-0.5/learning/quantum-computing-primer/applications.md:
##########
@@ -0,0 +1,461 @@
+---
+title: Applications of Quantum Computing
+---
+
+# 9. Applications of Quantum Computing
+
+Quantum computing holds the potential to revolutionize various fields by 
solving problems that are currently intractable for classical computers. In 
this section, we will explore some of the key applications of quantum computing 
and demonstrate how to implement them using the `qumat` library.
+
+## 9.1 Quantum Cryptography
+
+### Overview
+Quantum cryptography leverages the principles of quantum mechanics to create 
secure communication channels. One of the most well-known applications is 
Quantum Key Distribution (QKD), which allows two parties to generate a shared, 
secret key that is secure against eavesdropping.
+
+### Example: Implementing a Simple QKD Protocol with `qumat`
+Below is a simplified example of how to implement a basic QKD protocol using 
`qumat`. This example demonstrates the generation of a shared key between two 
parties, Alice and Bob.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Alice prepares her qubits
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+
+# Alice sends the second qubit to Bob
+# Bob measures the qubit in the same basis as Alice
+qc.apply_hadamard_gate(1)
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Shared key:", result)
+```
+
+## 9.2 Quantum Simulation
+
+### Overview
+Quantum simulation involves using a quantum computer to simulate quantum 
systems, which is particularly useful in fields like chemistry, material 
science, and physics. Quantum computers can efficiently simulate the behavior 
of molecules and materials at the quantum level.
+
+### Example: Simulating a Simple Quantum System with `qumat`
+In this example, we simulate a simple quantum system, such as a hydrogen 
molecule, using `qumat`. The goal is to find the ground state energy of the 
molecule.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'statevector_simulator', 'shots': 1}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to simulate the hydrogen molecule
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+qc.apply_rz_gate(1, 0.5)  # Example of a parameterized gate
+
+# Execute the circuit and get the final state vector
+state_vector = qc.get_final_state_vector()
+print("Final state vector:", state_vector)
+```
+## 9.3 Quantum Machine Learning
+
+### Overview
+Quantum machine learning (QML) is an emerging field that combines quantum 
computing with classical machine learning techniques. Quantum computers can 
potentially speed up certain machine learning algorithms, such as 
classification and clustering.
+
+### Example: Implementing a Basic Quantum Classifier with `qumat`
+In this example, we implement a basic quantum classifier using `qumat`. The 
classifier is trained to distinguish between two classes based on a simple 
dataset.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to create a quantum classifier
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+qc.apply_ry_gate(1, 0.3)  # Example of a parameterized gate
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Classification result:", result)
+```
+
+## 9.4 Quantum Optimization
+
+### Overview
+Quantum optimization involves using quantum algorithms to solve optimization 
problems more efficiently than classical methods. One of the most well-known 
quantum optimization algorithms is the Quantum Approximate Optimization 
Algorithm (QAOA).
+
+### Example: Solving an Optimization Problem with `qumat`
+In this example, we use `qumat` to implement a simple QAOA circuit to solve a 
basic optimization problem.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to implement QAOA
+qc.apply_hadamard_gate(0)
+qc.apply_hadamard_gate(1)
+qc.apply_rx_gate(0, 0.5)  # Example of a parameterized gate
+qc.apply_ry_gate(1, 0.5)  # Example of a parameterized gate
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Optimization result:", result)
+```
+
+## 9.5 Quantum Chemistry
+
+### Overview
+Quantum chemistry involves the application of quantum mechanics to chemical 
systems. Quantum computers can simulate molecular structures and reactions more 
accurately than classical computers, which is crucial for drug discovery and 
material design.
+
+### Example: Simulating a Chemical Reaction with `qumat`
+In this example, we use `qumat` to simulate a simple chemical reaction, such 
as the formation of a hydrogen molecule from two hydrogen atoms.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'statevector_simulator', 'shots': 1}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to simulate the chemical reaction
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+qc.apply_rz_gate(1, 0.5)  # Example of a parameterized gate
+
+# Execute the circuit and get the final state vector
+state_vector = qc.get_final_state_vector()
+print("Final state vector:", state_vector)
+```
+
+## 9.6 Quantum Finance
+
+### Overview
+Quantum finance involves the application of quantum computing to financial 
problems, such as portfolio optimization, risk analysis, and option pricing. 
Quantum algorithms can potentially provide faster and more accurate solutions 
to these problems.
+
+### Example: Portfolio Optimization with `qumat`
+In this example, we use `qumat` to implement a simple quantum algorithm for 
portfolio optimization.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to implement portfolio optimization
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+qc.apply_ry_gate(1, 0.5)  # Example of a parameterized gate
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Portfolio optimization result:", result)
+```
+## 9.7 Quantum Artificial Intelligence
+
+### Overview
+Quantum artificial intelligence (QAI) combines quantum computing with 
artificial intelligence to create more powerful AI models. Quantum computers 
can potentially speed up training and inference processes in AI.
+
+### Example: Implementing a Quantum Neural Network with `qumat`
+In this example, we use `qumat` to implement a simple quantum neural network 
(QNN) for a basic classification task.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to implement a quantum neural network
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+qc.apply_ry_gate(1, 0.5)  # Example of a parameterized gate
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("QNN classification result:", result)
+```
+
+## 9.8 Quantum Sensing
+
+### Overview
+Quantum sensing involves using quantum systems to measure physical quantities 
with high precision. Quantum sensors can potentially outperform classical 
sensors in terms of sensitivity and accuracy.
+
+### Example: Implementing a Quantum Sensor with `qumat`
+In this example, we use `qumat` to implement a simple quantum sensor for 
measuring a physical quantity, such as magnetic field strength.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'statevector_simulator', 'shots': 1}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to implement a quantum sensor
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+qc.apply_rz_gate(1, 0.5)  # Example of a parameterized gate
+
+# Execute the circuit and get the final state vector
+state_vector = qc.get_final_state_vector()
+print("Quantum sensor measurement:", state_vector)
+```
+## 9.9 Quantum Communication
+
+### Overview
+Quantum communication involves the transmission of information using quantum 
states. Quantum communication protocols, such as quantum teleportation, can 
provide secure and efficient communication channels.
+
+### Example: Implementing Quantum Teleportation with `qumat`
+In this example, we use `qumat` to implement a quantum teleportation protocol, 
which allows the transfer of quantum information from one qubit to another.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'statevector_simulator', 'shots': 1}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(3)
+
+# Apply gates to implement quantum teleportation
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+qc.apply_cnot_gate(1, 2)
+
+# Execute the circuit and get the final state vector
+state_vector = qc.get_final_state_vector()
+print("Quantum teleportation result:", state_vector)
+```
+## 9.10 Quantum Error Correction
+
+### Overview
+Quantum error correction is essential for building reliable quantum computers. 
Quantum error correction codes can detect and correct errors that occur during 
quantum computation.
+
+### Example: Implementing a Quantum Error Correction Code with `qumat`
+In this example, we use `qumat` to implement a simple quantum error correction 
code, such as the bit-flip code.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(3)
+
+# Apply gates to implement the bit-flip code
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+qc.apply_cnot_gate(0, 2)
+
+# Simulate an error (e.g., bit flip on qubit 1)
+qc.apply_pauli_x_gate(1)
+
+# Error correction steps
+qc.apply_cnot_gate(0, 1)
+qc.apply_cnot_gate(0, 2)
+qc.apply_toffoli_gate(1, 2, 0)
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Error correction result:", result)
+```
+## 9.11 Quantum Games
+
+### Overview
+Quantum games are games that incorporate quantum mechanics into their rules or 
strategies. These games can be used to explore quantum phenomena in a fun and 
interactive way.
+
+### Example: Implementing a Quantum Game with `qumat`
+In this example, we use `qumat` to implement a simple quantum game, such as 
the quantum version of the classic game "Rock-Paper-Scissors."
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to implement the quantum game
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Quantum game result:", result)
+```
+## 9.12 Quantum Random Number Generation
+
+### Overview
+Quantum random number generation (QRNG) uses the inherent randomness of 
quantum mechanics to generate truly random numbers. These numbers are useful in 
cryptography, simulations, and other applications.
+
+### Example: Implementing a Quantum Random Number Generator with `qumat`
+In this example, we use `qumat` to implement a simple quantum random number 
generator.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(1)
+
+# Apply a Hadamard gate to generate a random bit
+qc.apply_hadamard_gate(0)
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Random number:", result)
+```
+## 9.13 Quantum Image Processing
+
+### Overview
+Quantum image processing involves using quantum algorithms to process and 
analyze images. Quantum computers can potentially provide faster and more 
efficient image processing techniques.
+
+### Example: Implementing a Quantum Image Processing Algorithm with `qumat`
+In this example, we use `qumat` to implement a simple quantum image processing 
algorithm, such as edge detection.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to implement edge detection
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Edge detection result:", result)
+```
+## 9.14 Quantum Natural Language Processing
+
+### Overview
+Quantum natural language processing (QNLP) involves using quantum algorithms 
to process and analyze natural language data. Quantum computers can potentially 
provide faster and more efficient NLP techniques.
+
+### Example: Implementing a Quantum NLP Algorithm with `qumat`
+In this example, we use `qumat` to implement a simple quantum NLP algorithm, 
such as text classification.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to implement text classification
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Text classification result:", result)
+```
+## 9.15 Quantum Robotics
+
+### Overview
+Quantum robotics involves using quantum computing to enhance the capabilities 
of robots. Quantum algorithms can potentially improve robot perception, 
decision-making, and control.
+
+### Example: Implementing a Quantum Robotics Algorithm with `qumat`
+In this example, we use `qumat` to implement a simple quantum robotics 
algorithm, such as path planning.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to implement path planning
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Path planning result:", result)
+```
+## 9.16 Quantum Internet
+
+### Overview
+The quantum internet is a proposed network that uses quantum communication 
protocols to enable secure and efficient communication between quantum devices.
+
+### Example: Implementing a Quantum Internet Protocol with `qumat`
+In this example, we use `qumat` to implement a simple quantum internet 
protocol, such as quantum key distribution.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'qasm_simulator', 'shots': 1000}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to implement quantum key distribution
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+
+# Execute the circuit and get the results
+result = qc.execute_circuit()
+print("Quantum key distribution result:", result)
+```
+## 9.17 Quantum Biology
+
+### Overview
+Quantum biology explores the role of quantum mechanics in biological 
processes. Quantum computers can potentially simulate biological systems more 
accurately than classical computers.
+
+### Example: Simulating a Biological Process with `qumat`
+In this example, we use `qumat` to simulate a simple biological process, such 
as photosynthesis.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'statevector_simulator', 'shots': 1}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to simulate photosynthesis
+qc.apply_hadamard_gate(0)
+qc.apply_cnot_gate(0, 1)
+
+# Execute the circuit and get the final state vector
+state_vector = qc.get_final_state_vector()
+print("Photosynthesis simulation result:", state_vector)
+```
+## 9.18 Quantum Materials Science
+
+### Overview
+Quantum materials science involves using quantum computing to study and design 
new materials with unique properties. Quantum computers can potentially 
simulate material properties more accurately than classical computers.
+
+### Example: Simulating a Material with `qumat`
+In this example, we use `qumat` to simulate a simple material, such as 
graphene.
+
+```python
+from qumat import QuMat
+
+# Initialize the quantum circuit
+backend_config = {'backend_name': 'qiskit', 'backend_options': 
{'simulator_type': 'statevector_simulator', 'shots': 1}}
+qc = QuMat(backend_config)
+qc.create_empty_circuit(2)
+
+# Apply gates to simulate graphene
+qc.apply_hadamard_gate(0

Review Comment:
   This code example is truncated (missing closing parenthesis) and the fenced 
code block is never closed, which can break Markdown rendering for the rest of 
the page. Please complete the example and ensure the ```python block is 
properly terminated.
   ```suggestion
   qc.apply_hadamard_gate(0)
   ```



##########
website/versioned_docs/version-0.5/download/quickstart.md:
##########
@@ -0,0 +1,58 @@
+---
+title: Quickstart
+sidebar_label: Quickstart
+---
+
+<!--
+ Licensed to the Apache Software Foundation (ASF) under one or more
+ contributor license agreements.  See the NOTICE file distributed with
+ this work for additional information regarding copyright ownership.
+ The ASF licenses this file to You under the Apache License, Version 2.0
+ (the "License"); you may not use this file except in compliance with
+ the License.  You may obtain a copy of the License at
+
+     http://www.apache.org/licenses/LICENSE-2.0
+
+ Unless required by applicable law or agreed to in writing, software
+ distributed under the License is distributed on an "AS IS" BASIS,
+ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ See the License for the specific language governing permissions and
+ limitations under the License.
+-->
+
+# Qumat Quickstart
+
+## Installation
+
+Install Qumat using pip:
+
+```bash
+pip install qumat
+```
+
+## Basic Usage
+
+```python
+from qumat import QumatCircuit
+
+# Create a simple quantum circuit
+circuit = QumatCircuit(2)
+circuit.h(0)      # Hadamard gate on qubit 0
+circuit.cx(0, 1)  # CNOT gate
+
+# Run the circuit
+result = circuit.run()
+print(result)
+```
+
+## Next Steps
+
+- [Getting Started with Qumat](../getting-started-with-qumat)
+- [Basic Gates](../basic-gates)
+- [API Reference](../api)

Review Comment:
   The "Next Steps" links appear to point to non-existent pages in this version 
(e.g., `../getting-started-with-qumat`, `../basic-gates`, `../api`). Please 
update them to the correct doc routes for this version (likely under 
`../qumat/...`).
   ```suggestion
   - [Getting Started with Qumat](../qumat/getting-started-with-qumat)
   - [Basic Gates](../qumat/basic-gates)
   - [API Reference](../qumat/api)
   ```



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