Variable Hyperparameterized Gaussian Kernel using Displaced Squeezed Vacuum State (2403.11560v1)
Abstract: There are schemes for realizing different types of kernels by quantum states of light. It is particularly interesting to realize the Gaussian kernel due to its wider applicability. A multimode coherent state can generate the Gaussian kernel with a constant value of hyperparameter. This constant hyperparameter has limited the application of the Gaussian kernel when it is applied to complex learning problems. We realize the variable hyperparameterized Gaussian kernel with a multimode-displaced squeezed vacuum state. The learning capacity of this kernel is tested with the support vector machines over some synthesized data sets as well as public benchmark data sets. We establish that the proposed variable hyperparameterized Gaussian kernel offers better accuracy over the constant Gaussian kernel.
- Ahmed, Shahnawaz, et al “Classification and reconstruction of optical quantum states with deep neural networks.” Physical Review Research 3, 3 (2021): 033278.
- Luo, Yi-Jun, Jin-Ming Liu, and Chengjie Zhang. “Detecting genuine multipartite entanglement via machine learning.” Physical Review A 108, 5 (2023): 052424.
- Zhang, Lifeng, Zhihua Chen, and Shao-Ming Fei. “Entanglement verification with deep semisupervised machine learning.” Physical Review A 108, 2 (2023): 022427.
- Rebentrost, Patrick, Masoud Mohseni, and Seth Lloyd. “Quantum support vector machine for big data classification.” Physical Review Letters 113, 13 (2014): 130503.
- Schuld, Maria, Mark Fingerhuth, and Francesco Petruccione. “Implementing a distance-based classifier with a quantum interference circuit.” Europhysics Letters 119, 6 (2017): 60002.
- Park, Daniel K., Carsten Blank, and Francesco Petruccione. “The theory of the quantum kernel-based binary classifier.” Physics Letters A 384, 21 (2020): 126422.
- Schuld, Maria. “Supervised quantum machine learning models are kernel methods.” arXiv preprint arXiv:2101, 11020 (2021).
- Schuld, Maria, and Nathan Killoran. “Quantum machine learning in feature Hilbert spaces.” Physical Review Letters 122, 4 (2019): 040504.
- Chatterjee, Rupak, and Ting Yu. “Generalized coherent states, reproducing kernels, and quantum support vector machines.” arXiv preprint arXiv:1612, 03713 (2016).
- Li, Long Hin, Dan-Bo Zhang, and Z. D. Wang. “Quantum kernels with Gaussian state encoding for machine learning.” Physics Letters A 436 (2022): 128088.
- Vapnik, Vladimir. “The support vector method of function estimation.” Nonlinear modeling: Advanced black-box techniques. Boston, MA: Springer us, 1998, 55-85.
- Shaydulin, Ruslan, and Stefan M. Wild. “Importance of kernel bandwidth in quantum machine learning.” Physical Review A 106, 4 (2022): 042407.
- Caves, Carlton M. “Quantum-mechanical noise in an interferometer.” Physical Review D 23, 8 (1981): 1693.
- Kim, M. S., F. A. M. De Oliveira, and P. L. Knight. “Properties of squeezed number states and squeezed thermal states.” Physical Review A 40, 5 (1989): 2494.
- Glauber, Roy J. “Coherent and incoherent states of the radiation field.” Physical Review 131, 6 (1963): 2766.
- Caves, Carlton M., and Bonny L. Schumaker. “New formalism for two-photon quantum optics. I. Quadrature phases and squeezed states.” Physical Review A 31, 5 (1985): 3068.
- Schumaker, Bonny L., and Carlton M. Caves. “New formalism for two-photon quantum optics. II. Mathematical foundation and compact notation.” Physical Review A 31, 5 (1985): 3093.
- Schumaker, Bonny L. “Quantum mechanical pure states with Gaussian wave functions.” Physics Reports 135, 6 (1986): 317-408.
- Braunstein, Samuel L. “Squeezing as an irreducible resource.” Physical Review A 71, 5 (2005): 055801.
- Boser, Bernhard E., Isabelle M. Guyon, and Vladimir N. Vapnik. “A training algorithm for optimal margin classifiers.” Proceedings of the fifth annual workshop on Computational learning theory. 1992.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.