Gradients and frequency profiles of quantum re-uploading models
- URL: http://arxiv.org/abs/2311.10822v1
- Date: Fri, 17 Nov 2023 19:01:43 GMT
- Title: Gradients and frequency profiles of quantum re-uploading models
- Authors: Alice Barthe, Adri\'an P\'erez-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://arxiv.org/licenses/nonexclusive-distrib/1.0/
- 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
- 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) - Classical-to-Quantum Transfer Learning Facilitates Machine Learning with Variational Quantum Circuit [62.55763504085508]
We prove that a classical-to-quantum transfer learning architecture using a Variational Quantum Circuit (VQC) improves the representation and generalization (estimation error) capabilities of the VQC model.
We show that the architecture of classical-to-quantum transfer learning leverages pre-trained classical generative AI models, making it easier to find the optimal parameters for the VQC in the training stage.
arXiv Detail & Related papers (2023-05-18T03:08:18Z) - 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) - Mixed-Precision Inference Quantization: Radically Towards Faster
inference speed, Lower Storage requirement, and Lower Loss [4.877532217193618]
Existing quantization techniques rely heavily on experience and "fine-tuning" skills.
This study provides a methodology for acquiring a mixed-precise quantization model with a lower loss than the full precision model.
In particular, we will demonstrate that neural networks with massive identity mappings are resistant to the quantization method.
arXiv Detail & Related papers (2022-07-20T10:55:34Z) - 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.