Quantum Convolutional Neural Networks are Effectively Classically Simulable

Abstract

Quantum Convolutional Neural Networks (QCNNs) are widely regarded as a promising model for Quantum Machine Learning (QML). In this work we tie their heuristic success to two facts. First, that when randomly initialized, they can only operate on the information encoded in low-bodyness measurements of their input states. And second, that they are commonly benchmarked on "locally-easy'' datasets whose states are precisely classifiable by the information encoded in these low-bodyness observables subspace. We further show that the QCNN's action on this subspace can be efficiently classically simulated by a classical algorithm equipped with Pauli shadows on the dataset. Indeed, we present a shadow-based simulation of QCNNs on up-to $1024$ qubits for phases of matter classification. Our results can then be understood as highlighting a deeper symptom of QML: Models could only be showing heuristic success because they are benchmarked on simple problems, for which their action can be classically simulated. This insight points to the fact that non-trivial datasets are a truly necessary ingredient for moving forward with QML. To finish, we discuss how our results can be extrapolated to classically simulate other architectures.

12 + 15 pages , 6 + 7 figures, 1 table, updated to published version

References in corpus (78)

• Deep Learning in Neural Networks: An Overview
• Quantum entanglement
• Quantum Machine Learning
• The density-matrix renormalization group in the age of matrix product states
• Variational Quantum Algorithms
• Barren plateaus in quantum neural network training landscapes
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Noisy intermediate-scale quantum (NISQ) algorithms
• Improved Simulation of Stabilizer Circuits
• Quantum Convolutional Neural Networks
• Predicting Many Properties of a Quantum System from Very Few Measurements
• Cost Function Dependent Barren Plateaus in Shallow Parametrized Quantum Circuits
• Expressibility and entangling capability of parameterized quantum circuits for hybrid quantum-classical algorithms
• Power of data in quantum machine learning
• Challenges and Opportunities in Quantum Machine Learning
• Exact and Approximate Unitary 2-Designs: Constructions and Applications
• Connecting ansatz expressibility to gradient magnitudes and barren plateaus
• Hybrid quantum-classical algorithms and quantum error mitigation
• Generalization in quantum machine learning from few training data
• Training variational quantum algorithms is NP-hard
• Quantum convolutional neural network for classical data classification
• Complete universal quantum gate set approaching fault-tolerant thresholds with superconducting qubits
• The randomized measurement toolbox
• Quantum-assisted quantum compiling
• Random Quantum Circuits are Approximate 2-designs
• Local random quantum circuits are approximate polynomial-designs
• Provably efficient machine learning for quantum many-body problems
• Beyond Barren Plateaus: Quantum Variational Algorithms Are Swamped With Traps
• Diagnosing Barren Plateaus with Tools from Quantum Optimal Control
• Barren Plateaus in Variational Quantum Computing
• Matchgates and classical simulation of quantum circuits
• Exploiting symmetry in variational quantum machine learning
• Group-Invariant Quantum Machine Learning
• Efficient classical simulation of random shallow 2D quantum circuits
• Equivalence of quantum barren plateaus to cost concentration and narrow gorges
• A Lie Algebraic Theory of Barren Plateaus for Deep Parameterized Quantum Circuits
• Introduction to Haar Measure Tools in Quantum Information: A Beginner's Tutorial
• Higher Order Derivatives of Quantum Neural Networks with Barren Plateaus
• Realizing Quantum Convolutional Neural Networks on a Superconducting Quantum Processor to Recognize Quantum Phases
• Quantum Machine Learning in High Energy Physics
• Theory for Equivariant Quantum Neural Networks
• Theoretical Guarantees for Permutation-Equivariant Quantum Neural Networks
• Fermionic Gaussian states: an introduction to numerical approaches
• Random quantum circuits are approximate unitary $t$-designs in depth $O\left(n{t}^{5+o(1)}\right)$
• Multiclass classification using quantum convolutional neural networks with hybrid quantum-classical learning
• Does provable absence of barren plateaus imply classical simulability?
• A polynomial-time classical algorithm for noisy random circuit sampling
• Analyzing the barren plateau phenomenon in training quantum neural networks with the ZX-calculus
• Understanding quantum machine learning also requires rethinking generalization
• Symbolic integration with respect to the Haar measure on the unitary group
• Learning many-body Hamiltonians with Heisenberg-limited scaling
• On the practical usefulness of the Hardware Efficient Ansatz
• Hamiltonian variational ansatz without barren plateaus
• Shadows of quantum machine learning
• The Adjoint Is All You Need: Characterizing Barren Plateaus in Quantum Ansätze
• Synergy Between Quantum Circuits and Tensor Networks: Short-cutting the Race to Practical Quantum Advantage
• Classical-to-quantum convolutional neural network transfer learning
• Quantum Machine Learning for Digital Health? A Systematic Review
• The Presence and Absence of Barren Plateaus in Tensor-network Based Machine Learning
• Classical surrogates for quantum learning models
• Quantum phase detection generalisation from marginal quantum neural network models
• Trainability barriers and opportunities in quantum generative modeling
• Provably Trainable Rotationally Equivariant Quantum Machine Learning
• Model-Independent Learning of Quantum Phases of Matter with Quantum Convolutional Neural Networks
• Trainability Enhancement of Parameterized Quantum Circuits via Reduced-Domain Parameter Initialization
• Non-trivial symmetries in quantum landscapes and their resilience to quantum noise
• Quantum Deep Hedging
• Tight and Efficient Gradient Bounds for Parameterized Quantum Circuits
• Learning shallow quantum circuits
• Classically estimating observables of noiseless quantum circuits
• Lie-algebraic classical simulations for quantum computing
• Isometric tensor network optimization for extensive Hamiltonians is free of barren plateaus
• Quantum neural networks form Gaussian processes
• Computing exact moments of local random quantum circuits via tensor networks
• Approximately Equivariant Quantum Neural Network for $p4m$ Group Symmetries in Images
• Trainability and Expressivity of Hamming-Weight Preserving Quantum Circuits for Machine Learning
• Improving Gradient Methods via Coordinate Transformations: Applications to Quantum Machine Learning
• Error-tolerant quantum convolutional neural networks for symmetry-protected topological phases

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• Barren Plateaus in Variational Quantum Computing
• Quantum Machine Learning in Drug Discovery: Applications in Academia and Pharmaceutical Industries
• Tensor networks for quantum computing
• Simulating quantum circuits with arbitrary local noise using Pauli Propagation
• Efficient quantum-enhanced classical simulation for patches of quantum landscapes
• Uncovering Quantum Many-body Scars with Quantum Machine Learning
• Quantum Neural Networks in Practice: A Comparative Study with Classical Models from Standard Data Sets to Industrial Images
• Optimal quantum reservoir learning in proximity to universality
• A graph-theoretic approach to chaos and complexity in quantum systems
• Variational decision diagrams for quantum-inspired machine learning applications
• Benchmarking quantum devices beyond classical capabilities