Scrambling Ability of Quantum Neural Networks Architectures

Abstract

In this letter we propose a general principle for how to build up a quantum neural network with high learning efficiency. Our stratagem is based on the equivalence between extracting information from input state to readout qubit and scrambling information from the readout qubit to input qubits. We characterize the quantum information scrambling by operator size growth, and by Haar random averaging over operator sizes, we propose an averaged operator size to describe the information scrambling ability for a given quantum neural network architectures, and argue this quantity is positively correlated with the learning efficiency of this architecture. As examples, we compute the averaged operator size for several different architectures, and we also consider two typical learning tasks, which are a regression task of a quantum problem and a classification task on classical images, respectively. In both cases, we find that, for the architecture with a larger averaged operator size, the loss function decreases faster or the prediction accuracy in the testing dataset increases faster as the training epoch increases, which means higher learning efficiency. Our results can be generalized to more complicated quantum versions of machine learning algorithms.

References in corpus (47)

• Quantum Computing in the NISQ era and beyond
• Quantum Machine Learning
• Topological entanglement entropy
• A bound on chaos
• Barren plateaus in quantum neural network training landscapes
• Detecting topological order in a ground state wave function
• Quantum Circuit Learning
• Black holes and the butterfly effect
• Quantum Convolutional Neural Networks
• Circuit-centric quantum classifiers
• Operator Spreading in Random Unitary Circuits
• Chaos in quantum channels
• Efficient Learning for Deep Quantum Neural Networks
• Localized shocks
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Quantum autoencoders for efficient compression of quantum data
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Two-dimensional conformal field theory and the butterfly effect
• A generative modeling approach for benchmarking and training shallow quantum circuits
• Hierarchical quantum classifiers
• The Expressive Power of Parameterized Quantum Circuits
• Towards Quantum Machine Learning with Tensor Networks
• Diffusive hydrodynamics of out-of-time-ordered correlators with charge conservation
• Out-of-Time-Order Correlation for Many-Body Localization
• Differentiable Learning of Quantum Circuit Born Machine
• Operator growth in the SYK model
• Quantum Epidemiology: Operator Growth, Thermal Effects, and SYK
• Quantum autoencoders to denoise quantum data
• Locality, Quantum Fluctuations, and Scrambling
• Quantum-Assisted Learning of Hardware-Embedded Probabilistic Graphical Models
• Accessing scrambling using matrix product operators
• Experimental Realization of a Quantum Autoencoder: The Compression of Qutrits via Machine Learning
• Unitary quantum perceptron as efficient universal approximator
• Learning and Inference on Generative Adversarial Quantum Circuits
• Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information
• A Universal Training Algorithm for Quantum Deep Learning
• Information Scrambling in Quantum Neural Networks
• Operator size at finite temperature and Planckian bounds on quantum dynamics
• Quantum machine learning and quantum biomimetics: A perspective
• Realising and compressing quantum circuits with quantum reservoir computing
• Operator scrambling and quantum chaos
• Making Trotters Sprint: A Variational Imaginary Time Ansatz for Quantum Many-body Systems
• Entanglement structures in qubit systems
• Creating and concentrating quantum resource states in noisy environments using a quantum neural network
• Recurrent Quantum Neural Networks
• Size of bulk fermions in the SYK model
• The Quantum Cocktail Party Problem

Cited by in corpus (17)

• Resource theory of quantum scrambling
• Imaginary components of out-of-time correlators and information scrambling for navigating the learning landscape of a quantum machine learning model
• Quantum Information Scrambling in Quantum Many-body Scarred Systems
• Dynamical Transition of Operator Size Growth in Quantum Systems Embedded in an Environment
• Barren plateaus from learning scramblers with local cost functions
• Randomness-enhanced expressivity of quantum neural networks
• Operator Size Distribution in Large $N$ Quantum Mechanics of Majorana Fermions
• Subsystem Information Capacity in Random Circuits and Hamiltonian Dynamics
• Adversarial Robustness Guarantees for Quantum Classifiers
• Information scrambling and entanglement in quantum approximate optimization algorithm circuits
• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Quantum Annealing Formulation for Binary Neural Networks
• Information scrambling in quantum walks: Discrete-time formulation of Krylov complexity
• Optimal quantum reservoir learning in proximity to universality
• Benchmarking of quantum fidelity kernels for Gaussian process regression
• A graph-theoretic approach to chaos and complexity in quantum systems
• Fast suppression of classification error in variational quantum circuits