Provably Trainable Rotationally Equivariant Quantum Machine Learning

Abstract

Exploiting the power of quantum computation to realise superior machine learning algorithmshas been a major research focus of recent years, but the prospects of quantum machine learning (QML) remain dampened by considerable technical challenges. A particularly significant issue is that generic QML models suffer from so-called barren plateaus in their training landscapes -- large regions where cost function gradients vanish exponentially in the number of qubits employed, rendering large models effectively untrainable. A leading strategy for combating this effect is to build problem-specific models which take into account the symmetries of their data in order to focus on a smaller, relevant subset of Hilbert space. In this work, we introduce a family of rotationally equivariant QML models built upon the quantum Fourier transform, and leverage recent insights from the Lie-algebraic study of QML models to prove that (a subset of) our models do not exhibit barren plateaus. In addition to our analytical results we numerically test our rotationally equivariant models on a dataset of simulated scanning tunnelling microscope images of phosphorus impurities in silicon, where rotational symmetry naturally arises, and find that they dramatically outperform their generic counterparts in practice.

References in corpus (32)

• Quantum Machine Learning
• Supervised learning with quantum enhanced feature spaces
• Barren plateaus in quantum neural network training landscapes
• Quantum machine learning in feature Hilbert spaces
• Quantum Convolutional Neural Networks
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Efficient Learning for Deep Quantum Neural Networks
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• A rigorous and robust quantum speed-up in supervised machine learning
• Quantum advantage in learning from experiments
• The Future of Quantum Computing with Superconducting Qubits
• Quantum algorithms for algebraic problems
• Boundary conditions for the electronic structure of finite-extent, embedded semiconductor nanostructures
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Exploiting symmetry in variational quantum machine learning
• Group-Invariant Quantum Machine Learning
• Nature and Measure of Entanglement in Quantum Phase Transitions
• Hybrid Quantum-Classical Generative Adversarial Network for High Resolution Image Generation
• Theory for Equivariant Quantum Neural Networks
• Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
• Towards quantum enhanced adversarial robustness in machine learning
• Spatial Metrology of Dopants in Silicon with Exact Lattice Site Precision
• Building spatial symmetries into parameterized quantum circuits for faster training
• Reflection Equivariant Quantum Neural Networks for Enhanced Image Classification
• Chen's derivative rule revisited: Role of tip-orbital interference in STM
• Efficient classical algorithms for simulating symmetric quantum systems
• Atomic-level Characterisation of Quantum Computer Arrays by Machine Learning
• Strain and Electric Field Control of Hyperfine Interactions for Donor Spin Qubits in Silicon
• Donor hyperfine Stark shift and the role of central-cell corrections in tight-binding theory
• Permutation Invariant Encodings for Quantum Machine Learning with Point Cloud Data
• Measurements and atomistic theory of electron $g$ factor anisotropy for phosphorus donors in strained silicon
• Influence of sample momentum space features on scanning tunnelling microscope measurements

Cited by in corpus (17)

• Barren Plateaus in Variational Quantum Computing
• Does provable absence of barren plateaus imply classical simulability?
• Drastic Circuit Depth Reductions with Preserved Adversarial Robustness by Approximate Encoding for Quantum Machine Learning
• Quantum Convolutional Neural Networks are Effectively Classically Simulable
• Lie-algebraic classical simulations for quantum computing
• Permutation Invariant Encodings for Quantum Machine Learning with Point Cloud Data
• Stabilizer Tensor Networks with Magic State Injection
• Non-Unitary Quantum Machine Learning
• The role of data embedding in equivariant quantum convolutional neural networks
• Satellite image classification with neural quantum kernels
• Image Classification with Rotation-Invariant Variational Quantum Circuits
• Unitary Designs of Symmetric Local Random Circuits
• Adversarial Robustness Guarantees for Quantum Classifiers
• Permutation-equivariant quantum convolutional neural networks
• Almost fault-tolerant quantum machine learning with drastic overhead reduction
• Towards Improved Quantum Machine Learning for Molecular Force Fields
• A graph-theoretic approach to chaos and complexity in quantum systems