Quantum Similarity Matrix for High-Dimensional Data Clustering
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Solution Overview
Problem
Classical computers face difficulties in accurately clustering high-dimensional data, particularly in fields like pharmaceuticals and biosciences, due to the inaccessibility of quantum distances and chaotic nonlinear data, which requires advanced methods to effectively group similar data points.
Innovation Solution
A hybrid quantum-classical system is employed, utilizing a quantum processor with qubits corresponding to feature dimensions to execute a quantum circuit with feature map and backward feature map template circuits, outputting similarity measures for data points, which are then used to create a similarity matrix for classical clustering algorithms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If classical clustering algorithms are used on high-dimensional data, then the algorithm is simple to implement, but the clustering accuracy deteriorates due to inaccessibility of quantum distances and chaotic nonlinear data
Solution Approach 1:
The patent introduces a quantum processor as an intermediary component between the classical data and clustering algorithm. The quantum processor executes quantum circuits that compute similarity measures between data points, which are then fed back to the classical system for clustering. This intermediary quantum system enables access to quantum distances and handles chaotic nonlinear data that classical algorithms cannot process effectively.
Solution Approach 2:
The system is segmented into distinct quantum and classical components. The quantum processor handles the computationally intensive similarity measurement task using quantum circuits with feature map template circuits, while the classical processor handles the clustering algorithm. This segmentation allows each component to operate in its optimal domain, improving overall clustering accuracy without requiring the entire system to be quantum.
2Measurement precision
If quantum circuits with feature map template circuits are executed to compute similarity measures, then clustering accuracy improves, but the computational time and resource requirements increase
Solution Approach 1:
The quantum feature map template circuits compute similarity measures with higher precision than classical methods, potentially using more quantum operations than minimally required. This partial excess in computational effort in the quantum domain translates to significant time savings and accuracy improvements in the overall clustering task, especially for high-dimensional data where classical methods struggle.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
This approach enables accurate clustering of data sets that are challenging for classical computers, achieving 100% accuracy in identifying clusters, as demonstrated by simulated and experimental results, particularly outperforming classical algorithms in complex data sets.
Implementation Method 1
The feature map template circuit and the backward feature map template circuit each use quantum properties of superposition and entanglement of the qubits of the quantum processor
Implementation Method 2
The feature map template circuit and the backward feature map template circuit each use quantum properties of superposition and entanglement of the qubits of the quantum processor
Data Source
AI summary
A method of performing unsupervised clustering of data points includes determining a number of qubits to include in a quantum processor based on feature dimensions of each data point. The method includes, for each pair of data points, executing a quantum circuit on a quantum processor having the determined number of qubits. The quantum circuit includes a feature map template circuit parameterized with a first plurality of rotations, a backward feature map template circuit parameterized with a second plurality of rotations, and a measurement circuit that outputs a similarity measure. The method includes creating a similarity matrix based on the similarity measure for each pair of data points, and inputting the similarity matrix to a classical clustering algorithm to cluster the data points. The feature map template circuit and the backward feature map template circuit each use quantum properties of superposition and entanglement of the qubits of the quantum processor.