mqpa

MQPA: A (Potentially) New Paradigm in Quantum Computing

The Real-World Inspiration

In practical terms, particle dynamics exhibit free movement, akin to the natural flow of water and wind. Extreme weather events like tsunamis, tornadoes, and hurricanes showcase diverse and unpredictable movement patterns, significantly impacting society. Similar to the butterfly effect, wherein one physical force influences another, particles intrinsically react in a non-linear fashion. It’s reasonable to hypothesize that particles can move both forwards and backwards, with arbitrary gates marking Eigenvalues at each “step” or movement, despite the lack of formal mathematical proof. Current theories and algorithms do not fully elucidate the juxtaposition of particle effects while maintaining entanglement and continuous superposition. In scenarios involving quantum tunneling, particles may traverse different benchmarks simultaneously from distinct Eigensmarks, with one particle moving backwards and another moving laterally. Specifically, the resulting interactions are quantified by the particle’s spin, examining how the spin influences the entanglement and what alterations occur with each movement—whether additional particles attach or the overall state evolves from the initial Eigenstate to the present configuration.

Layman’s Terms

In the real world, particles move around freely, much like water flowing back and forth or the wind blowing. Extreme weather events such as tsunamis, tornadoes, and hurricanes move unpredictably and cause significant disruptions. Just like in the butterfly effect, where a small change can influence larger events, particles interact in a complex way, not just in straight lines. we can assume that particles can move in different directions, and the checkpoints we use to measure their movement are just markers for their energy levels, even though this isn’t fully proven by math yet.

I haven’t found any theories or algorithms that explain how particles stay connected and influence each other while being in a state of constant uncertainty. However, even with quantum tunneling, particles can cross different checkpoints at the same time from different starting points—one might move backwards while another moves sideways. The effects of this movement are measured by the particle’s spin, showing how the connection between particles changes with each movement, whether other particles join in, and how the situation changes from the start to the current state. This scientific supposition is the basis for building my theory.

In Nature

Particles move in complex, non-linear ways. Water ebbs and flows, winds swirl, and storms surge. These dynamic movements, often unpredictable and interconnected, are reminiscent of the behavior of quantum particles. Current quantum algorithms, however, tend to be linear and don’t fully capture this inherent dynamism.

Enter:

MQPA: A Quantum Leap in Thinking

MQPA (McPhaul Quantum Pathway Algorithm) proposes a radical shift in quantum computing. It embraces the non-linearity and interconnectedness of quantum particles, allowing quantum gates (operations that change the state of qubits, the quantum equivalent of bits) to be applied dynamically and adaptively.

Instead of following a predetermined sequence, MQPA determines which gate to apply based on the qubit’s current state and movement. This means qubits can interact with gates multiple times, move backward, or even change direction, mirroring the fluidity of natural phenomena.

How MQPA Works

Initialization: Qubits are prepared in their initial states, and quantum gates are placed at arbitrary points.
Dynamic Gate Application: At each step, the algorithm analyzes the qubit’s state and movement to determine which gate to apply next. This allows for a highly flexible and adaptive computational process.
State Update and Measurement: The qubit’s state is updated after each gate application, and measurements are taken to track its evolution.
Distance and Relationship Analysis: MQPA calculates the distances and relationships between qubit states after each set of gate operations. This reveals patterns, correlations, and anomalies that can provide insights into the underlying quantum system.
Multi-Qubit Interactions: The algorithm can be extended to handle interactions between multiple qubits, further enriching the analysis.
Probabilistic and Exponential Insights: MQPA leverages statistical methods to calculate probabilities and explore exponential growth or decay in qubit states and interactions.

Why MQPA Matters

MQPA offers several potential advantages over traditional quantum algorithms:

Flexibility: Its dynamic gate application allows for more adaptability and versatility in solving complex problems.
Efficiency: By optimizing gate sequences based on the qubit’s behavior, MQPA could potentially reduce computational overhead.
Deeper Insights: MQPA’s focus on measuring distances and relationships between qubit states could uncover new patterns and behaviors in quantum systems.
Applications: MQPA could have applications in fields such as quantum chemistry, materials science, optimization, and machine learning.

The Road Ahead

MQPA is still a theoretical proposal, but it represents a promising new direction in quantum computing. Further research and development will be needed to validate its potential and explore its full range of applications.

Implementing an MQPA-inspired approach on the QM9 dataset, followed by training an autoencoder for anomaly detection. This will be done using Python, TensorFlow, and other relevant libraries. The following steps will take me through the process:

Step 1: Setup and Import Libraries

First, let’s set up the environment and import the necessary libraries.

# Install the necessary libraries
!pip install tensorflow pandas scikit-learn matplotlib

# Import libraries
import tensorflow as tf
from tensorflow.keras.layers import Input, Dense, Lambda
from tensorflow.keras.models import Model
from tensorflow.keras import backend as K
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split
from sklearn.metrics import mean_squared_error

Step 2: Load and Preprocess the QM9 Dataset

we will load the QM9 dataset and preprocess it. The QM9 dataset is a collection of molecular structures and their properties.

# Load the QM9 dataset
# Note: Replace the path with the actual path to my QM9 dataset file
data = pd.read_csv('qm9.csv')

# Drop non-numeric columns if any
data = data.select_dtypes(include=[np.number])

# Standardize the data
scaler = StandardScaler()
data_scaled = scaler.fit_transform(data)

# Split the data into training and testing sets
X_train, X_test = train_test_split(data_scaled, test_size=0.2, random_state=42)

Step 3: Define the Autoencoder Model

we will define an autoencoder model for anomaly detection.

# Define the autoencoder model
input_dim = X_train.shape[1]
encoding_dim = 32  # This can be adjusted

input_layer = Input(shape=(input_dim,))
encoded = Dense(encoding_dim, activation='relu')(input_layer)
decoded = Dense(input_dim, activation='sigmoid')(encoded)

autoencoder = Model(input_layer, decoded)

autoencoder.compile(optimizer='adam', loss='mse')

Step 4: Train the Autoencoder

we will train the autoencoder on the training data.

# Train the autoencoder
history = autoencoder.fit(X_train, X_train,
                          epochs=50,
                          batch_size=256,
                          shuffle=True,
                          validation_data=(X_test, X_test),
                          verbose=1)

Step 5: Evaluate the Autoencoder and Detect Anomalies

we will evaluate the autoencoder and detect anomalies in the test set.

# Get the reconstruction loss
X_train_pred = autoencoder.predict(X_train)
train_loss = np.mean(np.square(X_train - X_train_pred), axis=1)

X_test_pred = autoencoder.predict(X_test)
test_loss = np.mean(np.square(X_test - X_test_pred), axis=1)

# Set the threshold for anomaly detection
threshold = np.percentile(train_loss, 95)  # 95th percentile

# Identify anomalies
anomalies = test_loss > threshold

# Print the results
print(f'Number of anomalies detected: {np.sum(anomalies)}')

# Plot the reconstruction loss
plt.figure(figsize=(10, 6))
plt.hist(test_loss, bins=50)
plt.axvline(threshold, color='r', linestyle='dashed', linewidth=2)
plt.xlabel('Reconstruction loss')
plt.ylabel('Number of samples')
plt.title('Reconstruction Loss for Test Data')
plt.show()

Step 6: Integrating MQPA-inspired Dynamic Gate Application

Here is a simplified example that simulates MQPA-inspired dynamic gate application within the autoencoder framework. This example focuses on dynamically adjusting the encoding dimension based on the data.

# Define a function to dynamically adjust the encoding dimension
def dynamic_encoding_dim(data_point):
    # Example: Adjust the encoding dimension based on the mean of the data point
    mean_val = np.mean(data_point)
    if mean_val < -1:
        return 16
    elif mean_val < 0:
        return 32
    else:
        return 64

# Define the autoencoder model with dynamic encoding dimension
def create_autoencoder(input_dim, encoding_dim):
    input_layer = Input(shape=(input_dim,))
    encoded = Dense(encoding_dim, activation='relu')(input_layer)
    decoded = Dense(input_dim, activation='sigmoid')(encoded)
    autoencoder = Model(input_layer, decoded)
    autoencoder.compile(optimizer='adam', loss='mse')
    return autoencoder

# Train the autoencoder with dynamic encoding dimension
for epoch in range(50):  # Number of epochs
    for batch_start in range(0, X_train.shape[0], 256):  # Batch size
        batch_end = min(batch_start + 256, X_train.shape[0])
        X_batch = X_train[batch_start:batch_end]
        encoding_dim = dynamic_encoding_dim(np.mean(X_batch, axis=0))
        autoencoder = create_autoencoder(input_dim, encoding_dim)
        autoencoder.fit(X_batch, X_batch, epochs=1, verbose=0)

This example provides a high-level overview of how I might approach implementing MQPA and autoencoder-based anomaly detection. I can further refine and expand this approach to suit my specific needs and data characteristics.

If the current environment does not support TensorFlow, let’s look at and examine the expected output of each step in the code. I can run the code on my local machine to observe the actual results.

Expected Output Description

Training Output: During training, I should see output similar to this for each epoch, showing the loss and validation loss:

Epoch 1/10
4/4 [==============================] - 0s 30ms/step - loss: 0.2954 - val_loss: 0.2518
Epoch 2/10
4/4 [==============================] - 0s 6ms/step - loss: 0.2408 - val_loss: 0.2047
...

Number of Anomalies Detected: The output should show the number of anomalies detected in the test data:
```
Number of anomalies detected: X
```
Where X is the number of anomalies found based on the reconstruction loss threshold.
Reconstruction Loss Histogram: The plot will display the histogram of the reconstruction loss for the test data, with a vertical line indicating the threshold for anomaly detection. The anomalies are the samples with reconstruction loss above this threshold.

Running the Code Locally

Here is the complete code again to run on my local machine:

import tensorflow as tf
from tensorflow.keras.layers import Input, Dense
from tensorflow.keras.models import Model
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

# Generate synthetic data similar to QM9 dataset for demonstration purposes
np.random.seed(42)
data = np.random.rand(1000, 100)  # 1000 samples, 100 features

# Standardize the data
scaler = StandardScaler()
data_scaled = scaler.fit_transform(data)

# Split the data into training and testing sets
X_train, X_test = train_test_split(data_scaled, test_size=0.2, random_state=42)

# Define the autoencoder model
input_dim = X_train.shape[1]
encoding_dim = 32

input_layer = Input(shape=(input_dim,))
encoded = Dense(encoding_dim, activation='relu')(input_layer)
decoded = Dense(input_dim, activation='sigmoid')(encoded)

autoencoder = Model(input_layer, decoded)
autoencoder.compile(optimizer='adam', loss='mse')

# Train the autoencoder
history = autoencoder.fit(X_train, X_train,
                          epochs=10,  # Reduced epochs for demo
                          batch_size=256,
                          shuffle=True,
                          validation_data=(X_test, X_test),
                          verbose=1)

# Get the reconstruction loss
X_train_pred = autoencoder.predict(X_train)
train_loss = np.mean(np.square(X_train - X_train_pred), axis=1)

X_test_pred = autoencoder.predict(X_test)
test_loss = np.mean(np.square(X_test - X_test_pred), axis=1)

# Set the threshold for anomaly detection
threshold = np.percentile(train_loss, 95)

# Identify anomalies
anomalies = test_loss > threshold

# Print the number of anomalies detected
num_anomalies = np.sum(anomalies)
print(f'Number of anomalies detected: {num_anomalies}')

# Plot the reconstruction loss
plt.figure(figsize=(10, 6))
plt.hist(test_loss, bins=50)
plt.axvline(threshold, color='r', linestyle='dashed', linewidth=2)
plt.xlabel('Reconstruction loss')
plt.ylabel('Number of samples')
plt.title('Reconstruction Loss for Test Data')
plt.show()

This code provides the training process, number of detected anomalies, and the histogram plot for reconstruction loss. Let me know if I need further assistance!

If the current environment does not support TensorFlow, I can run the code on my local machine to observe the actual results.

Expected Output Description

Training Output: During training, I should see output similar to this for each epoch, showing the loss and validation loss:

Epoch 1/10
4/4 [==============================] - 0s 30ms/step - loss: 0.2954 - val_loss: 0.2518
Epoch 2/10
4/4 [==============================] - 0s 6ms/step - loss: 0.2408 - val_loss: 0.2047
...

Number of Anomalies Detected: The output should show the number of anomalies detected in the test data:
```
Number of anomalies detected: X
```
Where X is the number of anomalies found based on the reconstruction loss threshold.
Reconstruction Loss Histogram: The plot will display the histogram of the reconstruction loss for the test data, with a vertical line indicating the threshold for anomaly detection. The anomalies are the samples with reconstruction loss above this threshold.

Running the Code Locally

code for local machgine

import tensorflow as tf
from tensorflow.keras.layers import Input, Dense
from tensorflow.keras.models import Model
from sklearn.preprocessing import StandardScaler
from sklearn.model_selection import train_test_split
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd

# Generate synthetic data similar to QM9 dataset for demonstration purposes
np.random.seed(42)
data = np.random.rand(1000, 100)  # 1000 samples, 100 features

# Standardize the data
scaler = StandardScaler()
data_scaled = scaler.fit_transform(data)

# Split the data into training and testing sets
X_train, X_test = train_test_split(data_scaled, test_size=0.2, random_state=42)

# Define the autoencoder model
input_dim = X_train.shape[1]
encoding_dim = 32

input_layer = Input(shape=(input_dim,))
encoded = Dense(encoding_dim, activation='relu')(input_layer)
decoded = Dense(input_dim, activation='sigmoid')(encoded)

autoencoder = Model(input_layer, decoded)
autoencoder.compile(optimizer='adam', loss='mse')

# Train the autoencoder
history = autoencoder.fit(X_train, X_train,
                          epochs=10,  # Reduced epochs for demo
                          batch_size=256,
                          shuffle=True,
                          validation_data=(X_test, X_test),
                          verbose=1)

# Get the reconstruction loss
X_train_pred = autoencoder.predict(X_train)
train_loss = np.mean(np.square(X_train - X_train_pred), axis=1)

X_test_pred = autoencoder.predict(X_test)
test_loss = np.mean(np.square(X_test - X_test_pred), axis=1)

# Set the threshold for anomaly detection
threshold = np.percentile(train_loss, 95)

# Identify anomalies
anomalies = test_loss > threshold

# Print the number of anomalies detected
num_anomalies = np.sum(anomalies)
print(f'Number of anomalies detected: {num_anomalies}')

# Plot the reconstruction loss
plt.figure(figsize=(10, 6))
plt.hist(test_loss, bins=50)
plt.axvline(threshold, color='r', linestyle='dashed', linewidth=2)
plt.xlabel('Reconstruction loss')
plt.ylabel('Number of samples')
plt.title('Reconstruction Loss for Test Data')
plt.show()

This code provides the training process, number of detected anomalies, and the histogram plot for reconstruction loss.

Running an autoencoder for anomaly detection on a quantum computer involves different steps compared to classical computing.

Here’s a simplified example using the qiskit library to demonstrate a basic quantum autoencoder. Please note that current quantum hardware is not yet capable of handling large-scale machine learning tasks, so this example is for educational purposes and may not directly correlate with the performance of classical models.

Step 1: Setup and Import Libraries

set up the environment and import the necessary libraries.

# Install the necessary libraries
!pip install qiskit

# Import libraries
from qiskit import QuantumCircuit, transpile, Aer, execute
from qiskit.visualization import plot_histogram
import numpy as np
import matplotlib.pyplot as plt

# Set up a quantum simulator
backend = Aer.get_backend('qasm_simulator')

Step 2: Define the Quantum Autoencoder Circuit

we will define a simple quantum autoencoder circuit. For simplicity, we’ll use a small number of qubits.

# Define a simple quantum autoencoder circuit
def quantum_autoencoder():
    qc = QuantumCircuit(3, 3)
    
    # Encoder
    qc.h(0)
    qc.cx(0, 1)
    qc.cx(1, 2)
    
    # Decoder
    qc.cx(1, 2)
    qc.cx(0, 1)
    qc.h(0)
    
    # Measurement
    qc.measure([0, 1, 2], [0, 1, 2])
    
    return qc

# Create the circuit
qc = quantum_autoencoder()

# Transpile the circuit for the simulator
qc = transpile(qc, backend)

# Execute the circuit
job = execute(qc, backend, shots=1024)
result = job.result()

# Get the counts
counts = result.get_counts(qc)
print(counts)

# Plot the results
plot_histogram(counts)
plt.show()

Step 3: Simulating Anomaly Detection

For the purpose of anomaly detection, we will simulate how the quantum autoencoder behaves with normal and anomalous data.

# Simulate normal data
normal_counts = {'000': 512, '111': 512}

# Simulate anomalous data
anomalous_counts = {'001': 512, '110': 512}

# Define a threshold for anomaly detection
threshold = 100

# Detect anomalies based on the counts
def detect_anomaly(counts, threshold):
    anomaly_score = sum(counts.get(key, 0) for key in ['001', '010', '011', '100', '101', '110'])
    return anomaly_score > threshold

# Check normal data
is_anomaly = detect_anomaly(normal_counts, threshold)
print(f'Normal data anomaly detected: {is_anomaly}')

# Check anomalous data
is_anomaly = detect_anomaly(anomalous_counts, threshold)
print(f'Anomalous data anomaly detected: {is_anomaly}')

Explanation

Quantum Autoencoder Circuit:
- The quantum autoencoder circuit is designed with a small number of qubits (3 in this case).
- The encoder section applies Hadamard and CNOT gates to create an entangled state.
- The decoder section reverses the encoding process.
- Finally, the circuit measures the qubits.
Anomaly Detection:
- we simulate normal and anomalous data using predefined counts.
- A simple function checks if the counts for certain states exceed a threshold to detect anomalies.

Running on Real Quantum Hardware

To run this code on real quantum hardware, I will need access to IBM Quantum Experience and replace the simulator with a real quantum device. Here are the steps:

Set up IBM Quantum Experience Account:

from qiskit import IBMQ
IBMQ.save_account('my_IBM_QUANTUM_API_TOKEN')
IBMQ.load_account()
provider = IBMQ.get_provider('ibm-q')
backend = provider.get_backend('ibmq_quito')  # Replace with my preferred backend

Execute on Real Quantum Device:

qc = transpile(qc, backend)
job = execute(qc, backend, shots=1024)
job_monitor(job)
result = job.result()
counts = result.get_counts(qc)
print(counts)
plot_histogram(counts)
plt.show()

Replace 'my_IBM_QUANTUM_API_TOKEN' with my actual IBM Quantum Experience API token.

This example provides a basic introduction to running a quantum autoencoder for anomaly detection. The current quantum hardware limitations mean that more complex and practical quantum machine learning models are still in the research phase.

The paper “Anomaly Detection Using Quantum Autoencoders” presents a framework for anomaly detection using quantum autoencoders. While we don’t have access to the specific implementation details from the paper, I can provide a similar example based on the concepts discussed.

The example will use qiskit to build a quantum autoencoder and run it on a quantum simulator. we’ll follow these steps:

Set up the environment.
Define the quantum autoencoder circuit.
Train the quantum autoencoder.
Use the autoencoder for anomaly detection.

Step 1: Setup and Import Libraries

set up the environment and import the necessary libraries.

# Install necessary libraries
!pip install qiskit

# Import libraries
from qiskit import QuantumCircuit, transpile, Aer, execute
from qiskit.visualization import plot_histogram
import numpy as np
import matplotlib.pyplot as plt

# Set up a quantum simulator
backend = Aer.get_backend('qasm_simulator')

Step 2: Define the Quantum Autoencoder Circuit

we’ll define a quantum circuit for the autoencoder.

# Define a simple quantum autoencoder circuit
def quantum_autoencoder():
    qc = QuantumCircuit(3, 3)
    
    # Encoder: Apply Hadamard and CNOT gates
    qc.h(0)
    qc.cx(0, 1)
    qc.cx(1, 2)
    
    # Decoder: Reverse the encoding process
    qc.cx(1, 2)
    qc.cx(0, 1)
    qc.h(0)
    
    # Measurement
    qc.measure([0, 1, 2], [0, 1, 2])
    
    return qc

# Create the circuit
qc = quantum_autoencoder()

# Transpile the circuit for the simulator
qc = transpile(qc, backend)

# Execute the circuit
job = execute(qc, backend, shots=1024)
result = job.result()

# Get the counts
counts = result.get_counts(qc)
print(counts)

# Plot the results
plot_histogram(counts)
plt.show()

Step 3: Simulating Anomaly Detection

For the purpose of anomaly detection, we’ll simulate how the quantum autoencoder behaves with normal and anomalous data.

# Simulate normal data
normal_counts = {'000': 512, '111': 512}

# Simulate anomalous data
anomalous_counts = {'001': 512, '110': 512}

# Define a threshold for anomaly detection
threshold = 100

# Detect anomalies based on the counts
def detect_anomaly(counts, threshold):
    anomaly_score = sum(counts.get(key, 0) for key in ['001', '010', '011', '100', '101', '110'])
    return anomaly_score > threshold

# Check normal data
is_anomaly = detect_anomaly(normal_counts, threshold)
print(f'Normal data anomaly detected: {is_anomaly}')

# Check anomalous data
is_anomaly = detect_anomaly(anomalous_counts, threshold)
print(f'Anomalous data anomaly detected: {is_anomaly}')

Explanation

Quantum Autoencoder Circuit:
- The quantum autoencoder circuit is designed with a small number of qubits (3 in this case).
- The encoder section applies Hadamard and CNOT gates to create an entangled state.
- The decoder section reverses the encoding process.
- Finally, the circuit measures the qubits.
Anomaly Detection:
- we simulate normal and anomalous data using predefined counts.
- A simple function checks if the counts for certain states exceed a threshold to detect anomalies.

Running on Real Quantum Hardware

To run this code on real quantum hardware, I will need access to IBM Quantum Experience and replace the simulator with a real quantum device. Here are the steps:

Set up IBM Quantum Experience Account:

from qiskit import IBMQ
IBMQ.save_account('my_IBM_QUANTUM_API_TOKEN')
IBMQ.load_account()
provider = IBMQ.get_provider('ibm-q')
backend = provider.get_backend('ibmq_quito')  # Replace with my preferred backend

Execute on Real Quantum Device:

qc = transpile(qc, backend)
job = execute(qc, backend, shots=1024)
job_monitor(job)
result = job.result()
counts = result.get_counts(qc)
print(counts)
plot_histogram(counts)
plt.show()

Replace 'my_IBM_QUANTUM_API_TOKEN' with my actual IBM Quantum Experience API token.

Applying the McPhaul Quantum Pathway Algorithm (MQPA) concept to the quantum autoencoder involves dynamically adjusting the gates based on the state of the qubits. This example will illustrate a simple form of MQPA by modifying the quantum autoencoder circuit to include conditional operations.

Step 1: Setup and Import Libraries

Ensure I have the necessary libraries installed and imported.

!pip install qiskit

from qiskit import QuantumCircuit, transpile, Aer, execute
from qiskit.visualization import plot_histogram
import numpy as np
import matplotlib.pyplot as plt
from qiskit.providers.aer import AerSimulator

Step 2: Define the MQPA-inspired Quantum Autoencoder Circuit

we define a quantum circuit that uses dynamic gate applications based on the current state of the qubits.

# Define the MQPA-inspired quantum autoencoder circuit
def mqpa_quantum_autoencoder():
    qc = QuantumCircuit(3, 3)
    
    # Encoder: Apply Hadamard and CNOT gates
    qc.h(0)
    qc.cx(0, 1)
    qc.cx(1, 2)
    
    # Dynamic gate application based on qubit state (simplified example)
    qc.h(2)  # Example dynamic operation
    
    # Decoder: Reverse the encoding process
    qc.cx(1, 2)
    qc.cx(0, 1)
    qc.h(0)
    
    # Measurement
    qc.measure([0, 1, 2], [0, 1, 2])
    
    return qc

# Create the circuit
qc = mqpa_quantum_autoencoder()

# Transpile the circuit for the simulator
backend = AerSimulator()
qc = transpile(qc, backend)

# Execute the circuit
job = execute(qc, backend, shots=1024)
result = job.result()

# Get the counts
counts = result.get_counts(qc)
print(counts)

# Plot the results
plot_histogram(counts)
plt.show()

Step 3: Simulating Anomaly Detection

For the purpose of anomaly detection, we’ll simulate how the MQPA-inspired quantum autoencoder behaves with normal and anomalous data.

# Simulate normal data
normal_counts = {'000': 512, '111': 512}

# Simulate anomalous data
anomalous_counts = {'001': 512, '110': 512}

# Define a threshold for anomaly detection
threshold = 100

# Detect anomalies based on the counts
def detect_anomaly(counts, threshold):
    anomaly_score = sum(counts.get(key, 0) for key in ['001', '010', '011', '100', '101', '110'])
    return anomaly_score > threshold

# Check normal data
is_anomaly_normal = detect_anomaly(normal_counts, threshold)
print(f'Normal data anomaly detected: {is_anomaly_normal}')

# Check anomalous data
is_anomaly_anomalous = detect_anomaly(anomalous_counts, threshold)
print(f'Anomalous data anomaly detected: {is_anomaly_anomalous}')

mqpa

Jessica McPhaUL

2024-07-19

The Real-World Inspiration

Layman’s Terms

In Nature

Enter:

MQPA: A Quantum Leap in Thinking

How MQPA Works

Why MQPA Matters

The Road Ahead

Step 1: Setup and Import Libraries

Step 2: Load and Preprocess the QM9 Dataset

Step 3: Define the Autoencoder Model

Step 4: Train the Autoencoder

Step 5: Evaluate the Autoencoder and Detect Anomalies

Step 6: Integrating MQPA-inspired Dynamic Gate Application

Expected Output Description

Running the Code Locally

Expected Output Description

Running the Code Locally

Step 1: Setup and Import Libraries

Step 2: Define the Quantum Autoencoder Circuit

Step 3: Simulating Anomaly Detection

Explanation

Running on Real Quantum Hardware

Step 1: Setup and Import Libraries

Step 2: Define the Quantum Autoencoder Circuit

Step 3: Simulating Anomaly Detection

Explanation

Running on Real Quantum Hardware

Step 1: Setup and Import Libraries

Step 2: Define the MQPA-inspired Quantum Autoencoder Circuit

Step 3: Simulating Anomaly Detection