Interpretable Quantum Advantage in Neural Sequence Learning

Abstract

Quantum neural networks have been widely studied in recent years, given their potential practical utility and recent results regarding their ability to efficiently express certain classical data. However, analytic results to date rely on assumptions and arguments from complexity theory. Due to this, there is little intuition as to the source of the expressive power of quantum neural networks or for which classes of classical data any advantage can be reasonably expected to hold. Here, we study the relative expressive power between a broad class of neural network sequence models and a class of recurrent models based on Gaussian operations with non-Gaussian measurements. We explicitly show that quantum contextuality is the source of an unconditional memory separation in the expressivity of the two model classes. Additionally, as we are able to pinpoint quantum contextuality as the source of this separation, we use this intuition to study the relative performance of our introduced model on a standard translation data set exhibiting linguistic contextuality. In doing so, we demonstrate that our introduced quantum models are able to outperform state of the art classical models even in practice.

arXiv comment30 pages, 9 figures

References in corpus (37)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum Machine Learning
• Quantum information with continuous variables
• Supervised learning with quantum enhanced feature spaces
• Quantum computational advantage using photons
• Barren plateaus in quantum neural network training landscapes
• Circuit Quantum Electrodynamics
• Quantum machine learning in feature Hilbert spaces
• Encoding a qubit in an oscillator
• Improved Simulation of Stabilizer Circuits
• An introduction to quantum machine learning
• Strong quantum computational advantage using a superconducting quantum processor
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Quantum generative adversarial learning
• A rigorous and robust quantum speed-up in supervised machine learning
• Positive Wigner functions render classical simulation of quantum computation efficient
• Phase-Programmable Gaussian Boson Sampling Using Stimulated Squeezed Light
• Quantum Simulation of Electronic Structure with Linear Depth and Connectivity
• Efficient Classical Simulation of Continuous Variable Quantum Information Processes
• Continuous-variable quantum neural networks
• Quantum Boltzmann Machine
• The Expressive Power of Parameterized Quantum Circuits
• Opportunities and challenges for quantum-assisted machine learning in near-term quantum computers
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Graphical calculus for Gaussian pure states
• All-Gaussian universality and fault tolerance with the Gottesman-Kitaev-Preskill code
• Quantum generative adversarial learning in a superconducting quantum circuit
• Non-Gaussian quantum states of a multimode light field
• The Born Supremacy: Quantum Advantage and Training of an Ising Born Machine
• Quantum Circuits with Unbounded Fan-out
• On the Quantum versus Classical Learnability of Discrete Distributions
• Enhancing Generative Models via Quantum Correlations
• Fault-tolerant preparation of approximate GKP states
• The power of one qumode for quantum computation
• State-independent quantum contextuality for continuous variables
• Near-Term Quantum-Classical Associative Adversarial Networks

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