Hybrid Quantum-Classical Classification Using Gram Matrix Proxies
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Solution Overview
Problem
Classical computing devices face challenges in performing multiclass classification of quantum datasets due to exponentially sized computations, while quantum computing devices are cost-prohibitive for large-scale implementations.
Innovation Solution
A hybrid classical-quantum computing system uses a quantum computing device to generate a Gram matrix, and a classical computing device to determine operators as proxies for quantum dataset datums, enabling efficient multiclass classification through semi-definite programs.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If quantum computing devices are used to perform multiclass classification, then computation efficiency and accuracy are improved, but cost increases significantly
Solution Approach 1:
The classification task is divided into two segments: (1) quantum computing device generates Gram matrix from quantum dataset, (2) classical computing device performs multiclass classification using the Gram matrix. This segmentation allows leveraging quantum computational advantages for matrix generation while using cost-effective classical devices for the classification task.
Solution Approach 2:
The Gram matrix serves as an intermediary representation that bridges quantum and classical computing systems. It captures quantum computational advantages (through efficient generation from quantum states) while being compatible with classical classification algorithms, thus enabling hybrid processing.
2Device complexity
If classical computing devices are used to perform multiclass classification, then cost is reduced, but computation time increases due to exponential complexity
Solution Approach 1:
The quantum computing device performs preliminary action by generating the Gram matrix from the quantum dataset. This pre-processing step transforms the quantum data into a form that classical devices can efficiently process, reducing the computational burden and time for subsequent classification tasks.
3Measurement precision
If quantum computing devices are used for multiclass classification, then classification accuracy is improved, but scalability becomes cost-prohibitive
Solution Approach 1:
The system segments the classification workflow such that quantum devices handle data representation and Gram matrix generation (where quantum advantages provide accuracy), while classical devices handle the classification decision-making (where cost-effectiveness and scalability are prioritized). This segmentation enables accurate classification without the full cost burden of quantum-only solutions.
Data Source
AI summary
A method may include obtaining a multi-dimensional training dataset that includes multiple datums. Each of the datums may correspond to a number of quantum bits (qubits) and may represent a quantum state. The method may also include generating, using a quantum computing device, a Gram matrix based on the multiple datums. In addition, the method may include determining, using a classical computing device, multiple operators according to a constraint defined by the Gram matrix. Each of the operators may be configured as a proxy for a corresponding datum. Further, the method may include assigning, using the classical computing device, each of the operators to a label.