Typical Machine Learning Datasets as Low-Depth Quantum Circuits

Abstract

Quantum machine learning (QML) is an emerging field that investigates the capabilities of quantum computers for learning tasks. While QML models can theoretically offer advantages such as exponential speed-ups, challenges in data loading and the ability to scale to relevant problem sizes have prevented demonstrations of such advantages on practical problems. In particular, the encoding of arbitrary classical data into quantum states usually comes at a high computational cost, either in terms of qubits or gate count. However, real-world data typically exhibits some inherent structure (such as image data) which can be leveraged to load them with a much smaller cost on a quantum computer. This work further develops an efficient algorithm for finding low-depth quantum circuits to load classical image data as quantum states. To evaluate its effectiveness, we conduct systematic studies on the MNIST, Fashion-MNIST, CIFAR-10, and Imagenette datasets. The corresponding circuits for loading the full large-scale datasets are available publicly as PennyLane datasets and can be used by the community for their own benchmarks. We further analyze the performance of various quantum classifiers, such as quantum kernel methods, parameterized quantum circuits, and tensor-network classifiers, and we compare them to convolutional neural networks. In particular, we focus on the performance of the quantum classifiers as we introduce nonlinear functions of the input state, e.g., by letting the circuit parameters depend on the input state.

References in corpus (58)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• Supervised learning with quantum enhanced feature spaces
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Quantum machine learning in feature Hilbert spaces
• Quantum Circuit Learning
• Universal Quantum Computation with ideal Clifford gates and noisy ancillas
• Circuit-centric quantum classifiers
• The effect of data encoding on the expressive power of variational quantum machine learning models
• Power of data in quantum machine learning
• Data re-uploading for a universal quantum classifier
• A rigorous and robust quantum speed-up in supervised machine learning
• Quantum convolutional neural network for classical data classification
• Sequential generation of entangled multi-qubit states
• Quantum-state preparation with universal gate decompositions
• Algorithms for entanglement renormalization
• Variational quantum algorithms for nonlinear problems
• Hierarchical quantum classifiers
• Towards Quantum Machine Learning with Tensor Networks
• Quantum Circuits for Isometries
• Quantum machine learning beyond kernel methods
• Real- and imaginary-time evolution with compressed quantum circuits
• MQT Bench: Benchmarking Software and Design Automation Tools for Quantum Computing
• Encoding of Matrix Product States into Quantum Circuits of One- and Two-Qubit Gates
• Sequential Generation of Matrix-Product States in Cavity QED
• A Quantum Inspired Approach to Exploit Turbulence Structures
• Crossing a topological phase transition with a quantum computer
• Parallel Quantum Simulation of Large Systems on Small Quantum Computers
• Learning Feynman Diagrams with Tensor Trains
• Universal Approximation Property of Quantum Machine Learning Models in Quantum-Enhanced Feature Spaces
• On the Quantum versus Classical Learnability of Discrete Distributions
• Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning
• Quasioptimality of maximum-volume cross interpolation of tensors
• Parallel cross interpolation for high-precision calculation of high-dimensional integrals
• Hamiltonian variational ansatz without barren plateaus
• Riemannian optimization of isometric tensor networks
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
• Quantics Tensor Cross Interpolation for High-Resolution, Parsimonious Representations of Multivariate Functions in Physics and Beyond
• Quantum classification of the MNIST dataset with Slow Feature Analysis
• QUARK: A Framework for Quantum Computing Application Benchmarking
• The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning
• Multigrid Renormalization
• Quantum pixel representations and compression for $N$-dimensional images
• Absence of barren plateaus in finite local-depth circuits with long-range entanglement
• Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization
• Fourier expansion in variational quantum algorithms
• Variational quantum simulation: a case study for understanding warm starts
• Drastic Circuit Depth Reductions with Preserved Adversarial Robustness by Approximate Encoding for Quantum Machine Learning
• Quantum Transfer Learning with Adversarial Robustness for Classification of High-Resolution Image Datasets
• Approximate encoding of quantum states using shallow circuits
• A super-polynomial quantum-classical separation for density modelling
• Quantum-Inspired Fluid Simulation of 2D Turbulence with GPU Acceleration
• Efficient MPS representations and quantum circuits from the Fourier modes of classical image data
• Benchmarking Quantum Generative Learning: A Study on Scalability and Noise Resilience using QUARK
• Digital-analog quantum learning on Rydberg atom arrays
• Absence of barren plateaus and scaling of gradients in the energy optimization of isometric tensor network states
• Gradients and frequency profiles of quantum re-uploading models

Cited by in corpus (1)

• Quantum feature-map learning with reduced resource overhead