Covariant quantum kernels for data with group structure

Abstract

The use of kernel functions is a common technique to extract important features from data sets. A quantum computer can be used to estimate kernel entries as transition amplitudes of unitary circuits. Quantum kernels exist that, subject to computational hardness assumptions, cannot be computed classically. It is an important challenge to find quantum kernels that provide an advantage in the classification of real-world data. We introduce a class of quantum kernels that can be used for data with a group structure. The kernel is defined in terms of a unitary representation of the group and a fiducial state that can be optimized using a technique called kernel alignment. We apply this method to a learning problem on a coset-space that embodies the structure of many essential learning problems on groups. We implement the learning algorithm with $27$ qubits on a superconducting processor.

arXiv comment18 pages, 8 figures

References in corpus (13)

• Supervised learning with quantum enhanced feature spaces
• Quantum machine learning in feature Hilbert spaces
• Quantum Circuit Learning
• Error mitigation for short-depth quantum circuits
• Parameterized quantum circuits as machine learning models
• Circuit-centric quantum classifiers
• Extending the computational reach of a noisy superconducting quantum processor
• Power of data in quantum machine learning
• A rigorous and robust quantum speed-up in supervised machine learning
• Mitigating measurement errors in multi-qubit experiments
• Hierarchical quantum classifiers
• Hadamard-free circuits expose the structure of the Clifford group
• Classical algorithms for quantum mean values

Cited by in corpus (21)

• The Future of Quantum Computing with Superconducting Qubits
• Semisupervised Anomaly Detection using Support Vector Regression with Quantum Kernel
• Neural quantum kernels: training quantum kernels with quantum neural networks
• Solving The Vehicle Routing Problem via Quantum Support Vector Machines
• Efficient Parameter Optimisation for Quantum Kernel Alignment: A Sub-sampling Approach in Variational Training
• Quantum Gaussian process model of potential energy surface for a polyatomic molecule
• Reinforcement learning-based architecture search for quantum machine learning
• Direct implementation of a perceptron in superconducting circuit quantum hardware
• Quantum Kernel Learning for Small Dataset Modeling in Semiconductor Fabrication: Application to Ohmic Contact
• Self-Adaptive Quantum Kernel Principal Components Analysis for Compact Readout of Chemiresistive Sensor Arrays
• Efficient simulation of parametrized quantum circuits under non-unital noise through Pauli backpropagation
• Quantum Kernel Machine Learning With Continuous Variables
• Realizing a Continuous Set of Two-Qubit Gates Parameterized by an Idle Time
• Security Analysis of Ensemble-Based Quantum Token Protocol Under Advanced Attacks
• Ensemble-Based Quantum Token Protocol Benchmarked on IBM Quantum Processors
• On the similarity of bandwidth-tuned quantum kernels and classical kernels
• Quantum enhanced stratification of Breast Cancer: exploring quantum expressivity for real omics data
• Quantum Kernel Methods: Convergence Theory, Separation Bounds and Applications to Marketing Analytics
• Mitigating exponential concentration in covariant quantum kernels for subspace and real-world data
• Quantum Gates via Dynamical Decoupling of Central Qubit on IBMQ and 15NV Center in Diamond
• Equivalence between exponential concentration in quantum machine learning kernels and barren plateaus in variational algorithms