Gradients and frequency profiles of quantum re-uploading models

• URL: http://arxiv.org/abs/2311.10822v2
• Date: Fri, 08 Nov 2024 16:20:00 GMT
• Title: Gradients and frequency profiles of quantum re-uploading models
• Authors: Alice Barthe, Adrián Pérez-Salinas,
• Abstract summary: We prove bounds for the differences between gradients of the better-studied data-less parameterized quantum circuits and re-uploading models. For the expressivity, we prove that quantum re-uploading models output functions with vanishing high-frequency components and upper-bounded derivatives with respect to data.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum re-uploading models have been extensively investigated as a form of machine learning within the context of variational quantum algorithms. Their trainability and expressivity are not yet fully understood and are critical to their performance. In this work, we address trainability through the lens of the magnitude of the gradients of the cost function. We prove bounds for the differences between gradients of the better-studied data-less parameterized quantum circuits and re-uploading models. We coin the concept of {\sl absorption witness} to quantify such difference. For the expressivity, we prove that quantum re-uploading models output functions with vanishing high-frequency components and upper-bounded derivatives with respect to data. As a consequence, such functions present limited sensitivity to fine details, which protects against overfitting. We performed numerical experiments extending the theoretical results to more relaxed and realistic conditions. Overall, future designs of quantum re-uploading models will benefit from the strengthened knowledge delivered by the uncovering of absorption witnesses and vanishing high frequencies.

Related papers

• Minimal Quantum Reservoirs with Hamiltonian Encoding [72.27323884094953]
  We investigate a minimal architecture for quantum reservoir computing based on Hamiltonian encoding.<n>This approach circumvents many of the experimental overheads typically associated with quantum machine learning.
  arXiv  Detail & Related papers  (2025-05-28T16:50:05Z)
• An Efficient Quantum Classifier Based on Hamiltonian Representations [50.467930253994155]
  Quantum machine learning (QML) is a discipline that seeks to transfer the advantages of quantum computing to data-driven tasks. We propose an efficient approach that circumvents the costs associated with data encoding by mapping inputs to a finite set of Pauli strings. We evaluate our approach on text and image classification tasks, against well-established classical and quantum models.
  arXiv  Detail & Related papers  (2025-04-13T11:49:53Z)
• Quantum Latent Diffusion Models [65.16624577812436]
  We propose a potential version of a quantum diffusion model that leverages the established idea of classical latent diffusion models. This involves using a traditional autoencoder to reduce images, followed by operations with variational circuits in the latent space. The results demonstrate an advantage in using a quantum version, as evidenced by obtaining better metrics for the images generated by the quantum version.
  arXiv  Detail & Related papers  (2025-01-19T21:24:02Z)
• Entanglement-induced provable and robust quantum learning advantages [0.0]
  We rigorously establish a noise-robust, unconditional quantum learning advantage in terms of expressivity, inference speed, and training efficiency. Our proof is information-theoretic and pinpoints the origin of this advantage.
  arXiv  Detail & Related papers  (2024-10-04T02:39:07Z)
• Fourier Neural Operators for Learning Dynamics in Quantum Spin Systems [77.88054335119074]
  We use FNOs to model the evolution of random quantum spin systems. We apply FNOs to a compact set of Hamiltonian observables instead of the entire $2n$ quantum wavefunction.
  arXiv  Detail & Related papers  (2024-09-05T07:18:09Z)
• Towards Efficient Quantum Hybrid Diffusion Models [68.43405413443175]
  We propose a new methodology to design quantum hybrid diffusion models. We propose two possible hybridization schemes combining quantum computing's superior generalization with classical networks' modularity.
  arXiv  Detail & Related papers  (2024-02-25T16:57:51Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Trainability barriers and opportunities in quantum generative modeling [0.0]
  We investigate the barriers to the trainability of quantum generative models. We show that using implicit generative models with explicit losses leads to a new flavour of barren plateau. We propose a new local quantum fidelity-type loss which, by leveraging quantum circuits, is both faithful and enjoys trainability guarantees.
  arXiv  Detail & Related papers  (2023-05-04T14:45:02Z)
• A didactic approach to quantum machine learning with a single qubit [68.8204255655161]
  We focus on the case of learning with a single qubit, using data re-uploading techniques. We implement the different proposed formulations in toy and real-world datasets using the qiskit quantum computing SDK.
  arXiv  Detail & Related papers  (2022-11-23T18:25:32Z)
• Generalization despite overfitting in quantum machine learning models [0.0]
  We provide a characterization of benign overfitting in quantum models. We show how a class of quantum models exhibits analogous features. We intuitively explain these features according to the ability of the quantum model to interpolate noisy data with locally "spiky" behavior.
  arXiv  Detail & Related papers  (2022-09-12T18:08:45Z)
• Improved Quantum Algorithms for Fidelity Estimation [77.34726150561087]
  We develop new and efficient quantum algorithms for fidelity estimation with provable performance guarantees. Our algorithms use advanced quantum linear algebra techniques, such as the quantum singular value transformation. We prove that fidelity estimation to any non-trivial constant additive accuracy is hard in general.
  arXiv  Detail & Related papers  (2022-03-30T02:02:16Z)
• Variational Quantum Policy Gradients with an Application to Quantum Control [0.0]
  Quantum Machine Learning models are composed by Variational Quantum Circuits (VQCs) in a very natural way. In this work, we consider Policy Gradients using a hardware-efficient ansatz. We prove that the complexity of obtaining an epsilon-approximation of the gradient using quantum hardware scales only logarithmically with the number of parameters.
  arXiv  Detail & Related papers  (2022-03-20T16:14:49Z)
• Quantum-tailored machine-learning characterization of a superconducting qubit [50.591267188664666]
  We develop an approach to characterize the dynamics of a quantum device and learn device parameters. This approach outperforms physics-agnostic recurrent neural networks trained on numerically generated and experimental data. This demonstration shows how leveraging domain knowledge improves the accuracy and efficiency of this characterization task.
  arXiv  Detail & Related papers  (2021-06-24T15:58:57Z)
• The effect of data encoding on the expressive power of variational quantum machine learning models [0.7734726150561088]
  Quantum computers can be used for supervised learning by treating parametrised quantum circuits as models that map data inputs to predictions. Here we investigate how the strategy with which data is encoded into the model influences the expressive power of parametrised quantum circuits as function approximators.
  arXiv  Detail & Related papers  (2020-08-19T18:00:11Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.