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 (3)

• Quantum machine learning and quantum biomimetics: A perspective
• Creating and concentrating quantum resource states in noisy environments using a quantum neural network
• Recurrent Quantum Neural Networks

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