Abstract
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed quantum states encoding the training data, while the model training is processed on a classical computer. Our two-photon proposal encodes data points in a discrete, eight-dimensional feature Hilbert space. In order to maximize the application range of the deployable kernels, we optimize feature maps towards the resulting kernels’ ability to separate points, i.e., their “resolution,” under the constraint of finite, fixed Hilbert space dimension. Implementing these kernels, our setup delivers viable decision boundaries for standard nonlinear supervised classification tasks in feature space. We demonstrate such kernel-based quantum machine learning using specialized multiphoton quantum optical circuits. The deployed kernel exhibits exponentially better scaling in the required number of qubits than a direct generalization of kernels described in the literature.
Highlights
We implement an all-optical setup demonstrating kernel-based quantum machine learning for twodimensional classification problems
Kernel-based Quantum ML (QML) (KQML)is attractive to be implemented on linear-optics platforms, as quantum memories are not required
We report on the first experimental implementation of supervised QML for solving a nonlinear multidimensional classification problem with clusters of points which are not trivially separated in the feature space
Summary
We implement an all-optical setup demonstrating kernel-based quantum machine learning for twodimensional classification problems. In order to maximize the application range of the deployable kernels, we optimize feature maps towards the resulting kernels’ ability to separate points, i.e., their “resolution,” under the constraint of finite, fixed Hilbert space dimension Implementing these kernels, our setup delivers viable decision boundaries for standard nonlinear supervised classification tasks in feature space. We investigate the prospect of KQML with multiphoton quantum optical circuits To this end, we propose kernels that scale exponentially better in the number of required qubits than a direct generalization of kernels previously discussed in the literature[12]. We propose kernels that scale exponentially better in the number of required qubits than a direct generalization of kernels previously discussed in the literature[12] We realize this scheme in a proof-of-principle experiment demonstrating its suitability on the platform of linear optics, proving its practical applicability with current state of quantum technologies.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have