Quantum Feature Map Evaluation via Density Matrices
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Solution Overview
Problem
Current methods for evaluating quantum feature maps rely on arbitrarily chosen reference kernels and are based on traditional support vector machine algorithms, leading to variations in evaluation and limitations in predictive performance.
Innovation Solution
A computer-implemented method and system that generate a metric for evaluating a quantum feature map using quantum density matrices, which computes quantum wave functions, projection operators, and density operators to assess the feature map's effectiveness.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If quantum feature map evaluation relies on arbitrarily chosen reference kernels, then the evaluation process becomes simpler, but the evaluation results vary and lack consistency
Solution Approach 1:
The quantum feature map evaluates itself by computing quantum kernels between data points and comparing them with classical kernels, eliminating the need for external reference kernels. The system uses its own quantum mechanical properties to generate evaluation metrics, making the process self-contained and consistent without arbitrary external references
Solution Approach 2:
The patent replaces the classical mechanical approach of choosing reference kernels with a quantum mechanical approach where quantum kernels are computed from actual quantum state representations. This substitution of evaluation methodology eliminates arbitrariness by grounding the evaluation in quantum physics principles
2Adaptability or versatility
If quantum feature map evaluation is based on support vector machine algorithms, then the evaluation can leverage existing machine learning frameworks, but the evaluation is limited by the predictive performance of SVM
Solution Approach 1:
The patent extracts the quantum kernel computation from the SVM framework, separating the quantum feature map evaluation from dependence on SVM's predictive performance. By isolating the quantum kernel computation as an independent evaluation metric, the system can assess quantum feature maps without being constrained by SVM algorithm limitations
Solution Approach 2:
The quantum kernel-based evaluation metric is designed to be universally applicable to different quantum feature maps and machine learning algorithms. The evaluation framework can assess various quantum circuits and feature maps regardless of the specific algorithm used, making it more versatile than SVM-dependent methods
3Loss of information
If quantum feature maps use quantum mechanical representations, then new insights into data can be obtained through entanglement, but the translation from classical to quantum representation is complex
Solution Approach 1:
The quantum kernel acts as an intermediary that bridges classical data and quantum mechanical representations. By computing quantum kernels from quantum states and comparing them with classical kernels, the system provides a structured translation pathway that manages complexity while preserving quantum mechanical insights about the data
Data Source
AI summary
A computing device including a memory and a processor is disclosed. The processor is programmed to: (i) generate a quantum feature map and compute a quantum wave function and a plurality of projection operators for each quantum wave function corresponding to each classical data input; (ii) generate a respective quantum density operator for a positive class and a negative class; (iii) evaluate a difference between a first expectation value corresponding to the positive class for the respective quantum density operator and a second expectation value corresponding to the negative class for the respective quantum density operator; and/or (iv) compute a first average value and a second average value of the difference between the first expectation value and the second expectation value for each classical data point in the positive class and in the negative class, respectively, for generating a metric value.