# Effects of quantum resources on the statistical complexity of quantum circuits

@article{Bu2021EffectsOQ, title={Effects of quantum resources on the statistical complexity of quantum circuits}, author={Kaifeng Bu and Dax Enshan Koh and Lu Li and Qingxian Luo and Yaobo Zhang}, journal={ArXiv}, year={2021}, volume={abs/2102.03282} }

Kaifeng Bu,1, ∗ Dax Enshan Koh,2, † Lu Li,3, 4 Qingxian Luo,4, 5 and Yaobo Zhang6, 7 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 2Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), 1 Fusionopolis Way, #16-16 Connexis, Singapore 138632, Singapore 3Department of Mathematics, Zhejiang Sci-Tech University, Hangzhou, Zhejiang 310018, China 4School of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027…

## 8 Citations

### Rademacher complexity of noisy quantum circuits

- Education, Materials Science
- 2021

Kaifeng Bu,1, ∗ Dax Enshan Koh,2, † Lu Li,3, 4 Qingxian Luo,4, 5 and Yaobo Zhang6, 7 1Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA 2Institute of High Performance…

### Complexity of quantum circuits via sensitivity, magic, and coherence

- Physics, Computer ScienceArXiv
- 2022

This work defines the set of unitaries with vanishing sensitivity and shows that it coincides with the family of matchgates, and proves that sensitivity is necessary for a quantum speedup.

### Encoding-dependent generalization bounds for parametrized quantum circuits

- Computer ScienceQuantum
- 2021

These results facilitate the selection of optimal data-encoding strategies via structural risk minimization, a mathematically rigorous framework for model selection, by bounding the complexity of PQC-based models as measured by the Rademacher complexity and the metric entropy, two complexity measures from statistical learning theory.

### Learning Quantum Processes and Hamiltonians via the Pauli Transfer Matrix

- PhysicsArXiv
- 2022

Learning about physical systems from quantum-enhanced experiments, relying on a quantum memory and quantum processing, can outperform learning from experiments in which only classical memory and…

### Accelerating variational quantum algorithms with multiple quantum processors

- Computer ScienceArXiv
- 2021

An efficient distributed optimization scheme, called QUDIO, that can be readily mixed with other advanced VQAs-based techniques to narrow the gap between the state of the art and applications with quantum advantage.

### Learning bounds for quantum circuits in the agnostic setting

- Computer ScienceQuantum Information Processing
- 2021

This paper investigates the learnability of some hypothesis sets for regression and binary classification defined by quantum circuits and compares the current bounds with others found in the literature and discusses their implications for classification and regression on quantum data.

### Structural risk minimization for quantum linear classifiers

- Computer ScienceQuantum
- 2023

This paper proves that two model parameters closely control the models' complexity and therefore its generalization performance, and gives rise to new options for structural risk minimization for QML models.

### Generalization in quantum machine learning from few training data

- Computer ScienceNature Communications
- 2022

This work provides a comprehensive study of generalization performance in QML after training on a limited number N of training data points, and reports rigorous bounds on the generalisation error in variational QML, confirming how known implementable models generalize well from an efficient amount ofTraining data.

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