Universal expressiveness of variational quantum classifiers and quantum kernels for support vector machines
| Autor: | Jonas Jäger, Roman V. Krems |
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| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Quantum Physics Computer Science - Machine Learning Multidisciplinary ComputerSystemsOrganization_MISCELLANEOUS General Physics and Astronomy FOS: Physical sciences General Chemistry Quantum Physics (quant-ph) General Biochemistry Genetics and Molecular Biology Machine Learning (cs.LG) |
| DOI: | 10.48550/arxiv.2207.05865 |
| Popis: | Machine learning is considered to be one of the most promising applications of quantum computing. Therefore, the search for quantum advantage of the quantum analogues of machine learning models is a key research goal. Here, we show that variational quantum classifiers and support vector machines with quantum kernels can solve a classification problem based on the $k$-Forrelation problem, which is known to be PromiseBQP-complete. Because the PromiseBQP complexity class includes all Bounded-Error Quantum Polynomial-Time (BQP) decision problems, our results imply that there exists a feature map and a quantum kernel that make variational quantum classifiers and quantum kernel support vector machines efficient solvers for any BQP problem. Hence, this work implies that their feature map and quantum kernel, respectively, can be designed to have a quantum advantage for any classification problem that cannot be classically solved in polynomial time but contrariwise by a quantum computer. Comment: 6 pages, 2 figures |
| Databáze: | OpenAIRE |
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