Fock State-enhanced Expressivity of Quantum Machine Learning Models

Abstract

The data-embedding process is one of the bottlenecks of quantum machine learning, potentially negating any quantum speedups. In light of this, more effective data-encoding strategies are necessary. We propose a photonic-based bosonic data-encoding scheme that embeds classical data points using fewer encoding layers and circumventing the need for nonlinear optical components by mapping the data points into the high-dimensional Fock space. The expressive power of the circuit can be controlled via the number of input photons. Our work shed some light on the unique advantages offers by quantum photonics on the expressive power of quantum machine learning models. By leveraging the photon-number dependent expressive power, we propose three different noisy intermediate-scale quantum-compatible binary classification methods with different scaling of required resources suitable for different supervised classification tasks.

16 pages, 7 figures

References in corpus (22)

• Quantum algorithm for solving linear systems of equations
• Photonics for artificial intelligence and neuromorphic computing
• Kernel methods in machine learning
• Quantum random access memory
• Quantum Data Fitting
• Boson sampling with 20 input photons in 60-mode interferometers at $10^{14}$ state spaces
• General parameter-shift rules for quantum gradients
• Supervised quantum machine learning models are kernel methods
• Generalization in Quantum Machine Learning: a Quantum Information Perspective
• Linear Optical Quantum Metrology with Single Photons: Exploiting Spontaneously Generated Entanglement to Beat the Shot-Noise Limit
• Towards understanding the power of quantum kernels in the NISQ era
• Recent advances for quantum classifiers
• One qubit as a Universal Approximant
• Further Compactifying Linear Optical Unitaries
• Training Gaussian Boson Sampling Distributions
• Quantum machine learning with adaptive linear optics
• Summability of Multi-Dimensional Trigonometric Fourier Series
• Classical and Quantum Algorithms for Orthogonal Neural Networks
• Natural Gradient Optimization for Optical Quantum Circuits
• Non-Classical Kernels in Continuous Variable Systems
• Encoding-dependent generalization bounds for parametrized quantum circuits
• Exponential Error Convergence in Data Classification with Optimized Random Features: Acceleration by Quantum Machine Learning

Cited by in corpus (10)

• Quantum machine learning with Adaptive Boson Sampling via post-selection
• Multidimensional Fourier series with quantum circuits
• An exponentially-growing family of universal quantum circuits
• Variational approach to photonic quantum circuits via the parameter shift rule
• Photonic quantum generative adversarial networks for classical data
• Expressive Quantum Supervised Machine Learning using Kerr-nonlinear Parametric Oscillators
• Quantum kernel learning Model constructed with small data
• Quantum Kernel Evaluation via Hong-Ou-Mandel Interference
• Error-mitigated photonic quantum circuit Born machine
• Mitigating photon loss in linear optical quantum circuits