Out-of-distribution generalization for learning quantum dynamics

Abstract

Generalization bounds are a critical tool to assess the training data requirements of Quantum Machine Learning (QML). Recent work has established guarantees for in-distribution generalization of quantum neural networks (QNNs), where training and testing data are drawn from the same data distribution. However, there are currently no results on out-of-distribution generalization in QML, where we require a trained model to perform well even on data drawn from a different distribution to the training distribution. Here, we prove out-of-distribution generalization for the task of learning an unknown unitary. In particular, we show that one can learn the action of a unitary on entangled states having trained only product states. Since product states can be prepared using only single-qubit gates, this advances the prospects of learning quantum dynamics on near term quantum hardware, and further opens up new methods for both the classical and quantum compilation of quantum circuits.

arXiv comment8 pages (main body) + 18 pages (references and appendix); 4+2 figures; V3 includes additional explanations and numerical experiments in the appendix

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• Learning quantum states and unitaries of bounded gate complexity
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• Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix
• Learning shallow quantum circuits
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• Quantum Tensor Product Decomposition from Choi State Tomography
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• Harnessing Quantum Support Vector Machines for Cross-Domain Classification of Quantum States
• Parallel-in-time quantum simulation via Page and Wootters quantum time
• High-fidelity dimer excitations using quantum hardware
• Deep Circuit Compression for Quantum Dynamics via Tensor Networks
• Measurement-based quantum machine learning
• Learning unitaries with quantum statistical queries
• Learning Fourier series with parametrized quantum circuits
• Data-Dependent Generalization Bounds for Parameterized Quantum Models Under Noise
• Out-of-distribution generalisation for learning quantum channels with low-energy coherent states
• Deep Neural Network-assisted improvement of quantum compressed sensing tomography
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• Multi-target quantum compilation algorithm
• Quantum-enhanced learning with a controllable bosonic variational sensor network
• Direct Gradient Computation for Barren Plateaus in Parameterized Quantum Circuits
• Measuring Incompatible Observables with Quantum Neural Networks
• Disentangling quantum autoencoder
• Quantum generative classification with mixed states