Introduction to QuantumKNN #
QuantumKNN (QKNN) stands for Q-Kernel-based Nearest Neighbor is a quantum-enhanced classification algorithm that brings together the advantages of quantum computing with the classical k-Nearest Neighbors (kNN) method. Rather than computing Euclidean distances directly between data points, QKNN leverages quantum circuits to estimate the similarity between quantum state representations of data vectors, utilizing the swap test. This approach aims to exploit quantum parallelism and interference to reduce the overall time complexity of distance evaluations while enabling a richer mapping of high-dimensional features into a quantum Hilbert space.
Presenting here with a short video tour of how the Quantum Veto Algorithm is implemented and runs in Qniverse
How QuantumKNN Differs from Classical KNN? #
Classical kNN assigns a label to a test point by calculating its Euclidean distance to all training points and voting among the k closest neighbors. In contrast, QKNN differs from the classical algorithm in these critical ways:
• Quantum State Encoding:
Classical data vectors are encoded into quantum states by methods such as amplitude encoding or angle encoding. These methods compress high-dimensional data into quantum states that live in an exponentially large Hilbert space [4]. This mapping can capture intricate data correlations that may not be evident in classical representations.
• Swap Test Distance Estimation:
Instead of relying solely on Euclidean distance, QKNN uses the swap test to compute the squared inner product between quantum states. The swap test is a quantum subroutine where an ancilla qubit is prepared in state |0⟩, manipulated with a Hadamard gate, and then used to control a swap between two registers containing the encoded states. After a final Hadamard gate on the ancilla and measurement, the probability of obtaining |0⟩ provides an estimate of the fidelity |⟨x|y⟩|² [6]. This fidelity, combined with the classical norms of the original vectors, allows one to compute a quantum-inspired distance metric using the cosine law:
D(x,y) = √(|x|² + |y|² − 2|x||y| • |⟨x|y⟩|)
• Hybrid Quantum-Classical Framework:
While the swap test and quantum state encoding accelerate the similarity computation, cluster (or class) assignment is still handled by classical routines such as majority voting. The algorithm combines the rapid parallel distance estimation on a quantum device with reliable classical techniques for updating decisions and tuning parameters
How QuantumKNN Can Be Implemented? #
Implementing QuantumKNN involves several stages that blend both quantum subroutines and classical operations. The following outline details each step:
1. Data Normalization and Preparation
- Normalization:
Every data point—represented as a real-valued vector—is normalized so it lies on the unit sphere, ensuring it can be faithfully mapped to a quantum state [3]. - Data Formatting:
The normalized vectors are arranged into a format amenable to quantum state encoding [4].
2. Quantum State Encoding
- Encoding Techniques:
Data is encoded into quantum states by mapping its features as amplitudes (amplitude encoding) or as angles (angle encoding) for quantum rotation gates such as RY or RX [4][5]. - State Preparation:
Through this process, each classical vector is transformed into a quantum state |ψ⟩ that preserves its essential information in the quantum domain [1].
3. Distance Computation Using the Swap Test
- Swap Test Overview:
To compute the similarity between a test vector and a training vector’s quantum state, the swap test is used. An ancilla qubit is initialized in |0⟩, passed through a Hadamard gate to create a superposition, and then used in a controlled-SWAP (CSWAP) between the two quantum states [6]. - Measurement and Calculation:
A final Hadamard gate is applied to the ancilla before measurement; the probability of measuring |0⟩ is directly related to the squared inner product |⟨x|y⟩|². This output, when combined with the classical norms of the vectors, is used to determine a quantum-enhanced distance metric as described above [7].
4. Nearest Neighbors Search and Voting
- Neighbor Identification:
For each test data point, the quantum-enhanced distance is computed concerning all training data. The k smallest distances are identified, and the corresponding labels form the basis for prediction [8]. - Majority Voting:
A classical majority vote among the k nearest neighbors determines the final class assignment for the test point.
5. Iteration and Convergence
- Iterative Process:
The assignment and voting steps can be repeated iteratively if the algorithm is embedded within a broader optimization framework. Convergence is determined when the assignment of test points stabilizes or after a maximum number of iterations. - Convergence Check:
Stability of labels or minimal change in distance metrics can serve as the convergence criteria [8].
6. Evaluation and Hyperparameter Tuning
- Performance Metrics:
Metrics such as accuracy, precision, recall, the Adjusted Rand Index (ARI), and Normalized Mutual Information (NMI) are used to evaluate the classification performance [9]. - Hyperparameter Tuning:
Techniques like cross-validation or the elbow method can be employed to determine the optimal number of neighbors (k).
Advantages and Disadvantages Compared to Classical KNN #
Advantages #
- Enhanced Feature Representation:
Encoding data into quantum states allows the capture of complex and high-dimensional features more naturally than classical methods [4][5]. - Quantum Parallelism:
Quantum circuits, such as the swap test, compute similarities for all training samples simultaneously, providing a potential speedup over classical distance computations [6][7]. - Hybrid Efficiency:
The combination of fast quantum subroutines and classical decision-making can improve performance, especially in high-dimensional or large-scale datasets [8].
Disadvantages #
- Hardware Limitations:
Current quantum devices are limited by qubit count and noise levels. As a result, many QKNN implementations must run on simulators, which may reduce potential speedups [9]. - Quantum Overhead:
The process of state preparation, gate operations, and repeated measurements to gather sufficient statistics imposes significant overhead [8]. - Integration Complexity:
Combining probabilistic quantum routines with deterministic classical algorithms introduces extra layers of complexity for debugging and error mitigation [8]. - Scalability Challenges:
While theoretical models suggest polylogarithmic scaling, practical implementations on current hardware may face scalability issues due to increased circuit depth and error accumulation [9].
Real-World Applications #
QuantumKNN holds promise across various sectors where classical kNN may fall short:
- Pattern Recognition and Image Classification:
High-dimensional image data can benefit from the quantum-enhanced similarity measures, potentially improving object or facial recognition tasks. - Medical Diagnostics:
Complex biomedical datasets (e.g., genomics, radiology) can be analyzed with improved sensitivity to subtle feature variations. - Financial Forecasting and Fraud Detection:
Rapid processing of large-scale financial or transactional data can leverage quantum parallelism to spot anomalies more quickly [8]. - Cybersecurity:
QuantumKNN can assist in real-time network anomaly detection due to its advanced similarity evaluation. - Scientific Data Analysis:
Clustering and classification of high-dimensional experimental data in domains like astrophysics or quantum chemistry could be enhanced through quantum techniques.
Overview #
The QuantumKNN (QKNN) module implements a quantum-enhanced k-nearest neighbors (k-NN) classifier that leverages quantum circuit simulations to compute distances between data points. It integrates quantum state encoding and quantum distance computations with classical data preprocessing and parallelized prediction workflows. QKNN offers a hybrid approach where quantum swap tests are used as the basis for measuring similarities in an otherwise classical k-NN framework.
Key Features
- Hybrid Quantum-Classical Architecture:
QKNN embeds classical feature vectors into quantum states using amplitude encoding. - It combines quantum simulation (for computing distances via the swap test) with classical operations such as normalization, one-hot encoding, and standard evaluation metrics.
- Quantum Distance Computation via Swap Test:
Quantum Encoding:
Converts input vectors to normalized quantum amplitudes, including padding vectors to the next power of 2 when necessary.
• Swap Test Circuit:
Implements a swap test using an ancilla qubit and controlled-SWAP (CSWAP) gates to estimate the fidelity (overlap) between two quantum states.
• Distance Metric:
Transforms the computed fidelity into a Euclidean-like distance metric for k-NN classification. - QNode Caching for Efficiency:
The module caches compiled QNodes (quantum circuits) based on the number of qubits and simulation shots, greatly reducing re-compilation overhead during repeated distance computations.
• A global simulation lock is used to ensure thread-safe quantum simulation calls, especially in multi-threaded environments. - Backend Flexibility and Parallel Processing:
Supports multi-threading through the use of Python’s threading and joblib’s Parallel for accelerated prediction across large datasets.
• While primarily targeting classical CPU execution in a simulated quantum environment, its design is modular enough to allow future integration with GPU-enabled quantum simulators. - Extensive Preprocessing Pipeline:
Accepts diverse input types (CSV files, pandas DataFrames, NumPy arrays) and automatically handles categorical data with one-hot encoding.
• Provides utilities to normalize and standardize data, ensuring each feature vector is correctly prepared for amplitude encoding. - Robust Model Evaluation:
The module computes standard classification metrics, including accuracy, precision, recall, and F1 score, and produces both a confusion matrix and a detailed classification report.
Offers functions to perform hyperparameter tuning, such as k-selection using cross-validation or the elbow method, adapting the k parameter based on the dataset.
Workflow Summary #
- Data Preprocessing:
- Input data is processed through methods that convert to NumPy arrays, apply one-hot encoding where necessary, and perform vector normalization and padding to prepare for quantum state embedding.
- Quantum State Encoding and QNode Construction:
- Each data point is converted into a quantum state using amplitude encoding.
- A swap test QNode is constructed (or retrieved from a cache) to evaluate the similarity (distance) between quantum states.
- Distance Computation and k-NN Prediction:
- For a given test sample, the module computes the swap test-based distance to all training samples.
- Nearest neighbors are identified by sorting these distances, and majority voting determines the final class prediction.
- Hyperparameter Tuning:
- Optional k-selection methods (cross-validation and the elbow method) are provided to automatically determine the optimal number of neighbors based on performance on validation splits.
- Model Training and Evaluation:
- The training workflow includes reading the dataset, splitting into training and test sets, fitting the model via precomputing quantum state encodings, and finally evaluating predictions on the test set using standard metrics.
- Visualization:
- A dedicated plotting function enables visualization of loss versus k, helping to analyze the impact of the k parameter on classification performance.
This comprehensive approach makes the QuantumKNN module an effective tool for researchers and developers exploring quantum-inspired classification methods, offering a unique blend of quantum simulation and classical machine learning techniques.