Quantum Classical Kernel Combination for ML Accuracy
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Solution Overview
Problem
Existing quantum kernel-based machine learning techniques face challenges such as inefficient kernel selection, high computational costs, overfitting, and scalability issues due to the exponential concentration of kernels as the number of qubits increases.
Innovation Solution
The system employs a combination of multiple quantum and classical kernels by calculating and centering kernels within a feature space, regularizing parameters to combine these kernels, and integrating them classically to create a combined kernel, thereby mitigating overfitting and optimizing resource usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If multiple quantum kernels are calculated and combined, then the accuracy of quantum kernel learning models is improved, but the computational cost increases
Solution Approach 1:
The patent divides the feature space into multiple subsets and calculates kernels for each subset separately on quantum systems. This segmentation allows parallel computation of multiple kernels, improving accuracy through diverse feature representations while managing computational cost by distributing work across multiple smaller quantum computations rather than one large computation
Solution Approach 2:
The patent combines multiple quantum kernels and classical kernels into a single integrated kernel function. This merging integrates the strengths of different kernel types and feature subsets, achieving improved model accuracy through ensemble learning while using classical computing resources to manage the combination, thereby controlling overall computational cost
2Adaptability or versatility
If the number of qubits increases, then the representational power of quantum kernels is improved, but exponential concentration of kernels occurs leading to scalability issues
Solution Approach 1:
The patent segments the feature map into multiple subsets, each processed by a separate quantum kernel calculation with a limited number of qubits. This approach maintains representational power by covering diverse feature subsets while avoiding exponential concentration by keeping each individual quantum computation manageable in size
Solution Approach 2:
The patent transitions from relying on increasing qubit count in a single kernel to achieving representational power through multiple kernels operating in a different dimension - the dimension of kernel diversity. This dimensional shift allows scaling by adding more kernel computations rather than increasing qubit count, avoiding the exponential concentration problem
3Loss of information
If quantum kernels are calculated for all features, then the completeness of feature representation is improved, but the computational time increases
Solution Approach 1:
The patent segments the complete feature set into multiple subsets and calculates quantum kernels for each subset. This ensures comprehensive feature representation is achieved through the union of all subset kernels while reducing computational time by parallelizing the calculation across multiple smaller subsets rather than processing all features in a single computation
Solution Approach 2:
The patent calculates kernels for multiple feature subsets, which may overlap or cover the feature space more extensively than a single kernel would. This partial redundancy ensures complete feature representation while the selective subset approach prevents unnecessary computation on all possible feature combinations, optimizing the time-completeness tradeoff
Data Source
AI summary
A system to train multiple combined quantum classical kernels can comprise a memory that stores, and a processor that executes, computer executable components that perform operations comprising determining a set of kernel bandwidths, calculating a plurality of kernels, based on the kernel bandwidths, for subsets of features of a feature map, centering the plurality of kernels within a feature space of the feature map, regularizing parameters to combine the plurality of kernels, and combining the plurality of kernels into a combined kernel. Feature subsampling and data subsampling can be employed to compute a finite set subsampled kernels. Furthermore, the finite set of subsampled kernels can be combined classically to create a combined kernel that can represent an arbitrary target kernel function of a target dataset.