Introduction to Quantum Data Encoding and ML
Since its inception in the 1980s, the field of quantum computing has advanced significantly and quickly. Quantum computers store information in qubits, which are a superposition of digital zeroes and ones that enable operations through probability manipulation. The field is currently in the NISQ (Noisy Intermediate-Scale Quantum) era, which is marked by noise and limited qubits, despite the promise that quantum computers will be able to execute computations beyond classical capacity.
Machine learning (ML) is a clear method to take advantage of the extra processing capability that quantum computing offers. Owing to existing constraints, hybrid quantum-classical methods, such as Variational Quantum Algorithms, which employ a feedback loop that blends quantum learning layers with classical parameter modification, are more practical.
Quantum encoding is required to transform conventional data into quantum states for any general application, such as machine learning or quantum chemistry. The conversion of classical input data into quantum states is an essential step that has a significant impact on later machine learning performance, affecting measures like accuracy and runtime. In essence, the encoding strategy selection is a hyperparameter that drastically alters machine learning results.
Quantum Data Encoding Techniques
Three fundamental encoding techniques, basis, rotation, and amplitude, are investigated in a number of hybrid quantum-classical machine learning studies.
Basis Encoding
In general, the simplest method in terms of computing is basis encoding. This approach maps classical bits directly to the qubits’ computational basis states. Each binary digit is stored in a qubit after data points are first transformed into integers and then into binary. This method works well with discrete data types, such as integer or binary numbers. The three primary methods, basis encoding is frequently regarded as the least space-efficient; it takes n times m qubits to encode data points, each of which comprises m binary digits.
Rotation (Angle) Encoding
Classical feature values are stored in qubit rotation angles in rotation or angle encoding. Quantum states are manipulated to represent the input via rotation gates across the y- and z-axes, with angles determined by the data. A richer mapping appropriate for continuous data is produced by this method. Rotation encoding, like base encoding, necessitates the encoding of n data points into n qubits and typically leads to a large circuit depth.
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Amplitude Encoding
The best space efficiency may be possible with amplitude encoding. The quantum state’s probability amplitudes are encoded with classical information. This approach, which makes use of the exponential representation provided by the Hilbert space, is extremely compact. Amplitude encoding results in a low circuit depth and enables the encoding of n data points into log(n) qubits. Amplitude encoding works well with continuous data, just like rotation encoding. Amplitude-encoded state preparation can be computationally expensive, which could be a disadvantage.
Experimental Findings on Accuracy and Performance
The effectiveness and effects of applying various encoding techniques in machine learning scenarios have been well studied.
Hybrid Quantum-Classical Network Performance
QuClassi hybrid deep neural network architecture was used to test the three encoding techniques for binary classification of the “3” and “6” digits from the MNIST dataset. One of the three encoding techniques was used to normalize and convert the raw images into quantum states after they had been compressed into four dimensions using Principal Component Analysis.
Accuracy Results: Rotation encoding had the best classification accuracy, achieving almost 95%, across a number of machines and simulators used in the studies. Amplitude encoding, on the other hand, showed the most consistency, achieving nearly 86% accuracy over several trials.
Noise Resistance: It seemed that amplitude encoding was the most noise-resistant. Even without using error mitigation, amplitude encoding performed on the IBM_Torino quantum computer with an accuracy comparable to the optimal outcome from the simulator.
Error Mitigation: All three encoding techniques’ accuracy was successfully increased on real quantum hardware using the dynamical decoupling error mitigation methodology, making them more similar to the ideal simulator findings.
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Effectiveness in Traditional Machine Learning Frameworks
Another study used a telecommunications customer churn dataset to incorporate quantum data embedding techniques into solely classical machine learning algorithms, such as ensemble methods, K-Nearest Neighbors (KNN), Support Vector Machines (SVM), and logistic regression.
Overall Improvement: Compared to using solely classical data, the study discovered that quantum data embedding generally increased classification accuracy and F1 scores for numerous ML algorithms. This improvement was especially noticeable in models that are inherently better at representing features.
Encoding Comparison: Quantum Basis Encoding continuously showed competitive or better results than classical encoding techniques, such as Principal Component Analysis (PCA), across a variety of classical models studied. Using quantum-encoded data improved the accuracy and precision of the KNN, Decision Tree, and Logistic Regression models.
Computational Implications
There is a computational cost associated with using quantum encoding. Depending on the machine learning technique employed, the effect on running time is complex and varies greatly.
- Low-Complexity Models: The quantum encoding procedure only slightly increased the running time of models with comparatively low complexity, like KNN and logistic regression
- High-Complexity Models: When non-linear kernels were applied to quantum-encoded data, processing times for more computationally demanding models, specifically SVMs, rose more noticeably.
- Ensemble Methods: Random Forest, LightGBM, AdaBoost, and CatBoost are examples of ensemble methods that showed a good balance between performance gains and unreasonably long running times. This implies that the slight computational increase for these models might be justified by the improvements in accuracy and F1 score.
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