Online learning of a panoply of quantum objects

• URL: http://arxiv.org/abs/2406.04245v2
• Date: Sun, 06 Oct 2024 21:13:14 GMT
• Title: Online learning of a panoply of quantum objects
• Authors: Akshay Bansal, Ian George, Soumik Ghosh, Jamie Sikora, Alice Zheng,
• Abstract summary: In many quantum tasks, there is an unknown quantum object that one wishes to learn. We prove a sublinear regret bound for learning over general subsets of positive semidefinite matrices. Our bound applies to many other quantum objects with compact, convex representations.
• Score: 0.873811641236639
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In many quantum tasks, there is an unknown quantum object that one wishes to learn. An online strategy for this task involves adaptively refining a hypothesis to reproduce such an object or its measurement statistics. A common evaluation metric for such a strategy is its regret, or roughly the accumulated errors in hypothesis statistics. We prove a sublinear regret bound for learning over general subsets of positive semidefinite matrices via the regularized-follow-the-leader algorithm and apply it to various settings where one wishes to learn quantum objects. For concrete applications, we present a sublinear regret bound for learning quantum states, effects, channels, interactive measurements, strategies, co-strategies, and the collection of inner products of pure states. Our bound applies to many other quantum objects with compact, convex representations. In proving our regret bound, we establish various matrix analysis results useful in quantum information theory. This includes a generalization of Pinsker's inequality for arbitrary positive semidefinite operators with possibly different traces, which may be of independent interest and applicable to more general classes of divergences.

Related papers

• Few measurement shots challenge generalization in learning to classify entanglement [0.0]
  This paper focuses on hybrid quantum learning techniques where classical machine-learning methods are paired with quantum algorithms. We show that, in some settings, the uncertainty coming from a few measurement shots can be the dominant source of errors. We introduce an estimator based on classical shadows that performs better in the big data, few copy regime.
  arXiv  Detail & Related papers  (2024-11-10T21:20:21Z)
• Efficient Learning for Linear Properties of Bounded-Gate Quantum Circuits [63.733312560668274]
  Given a quantum circuit containing d tunable RZ gates and G-d Clifford gates, can a learner perform purely classical inference to efficiently predict its linear properties? We prove that the sample complexity scaling linearly in d is necessary and sufficient to achieve a small prediction error, while the corresponding computational complexity may scale exponentially in d. We devise a kernel-based learning model capable of trading off prediction error and computational complexity, transitioning from exponential to scaling in many practical settings.
  arXiv  Detail & Related papers  (2024-08-22T08:21:28Z)
• Separable Power of Classical and Quantum Learning Protocols Through the Lens of No-Free-Lunch Theorem [70.42372213666553]
  The No-Free-Lunch (NFL) theorem quantifies problem- and data-independent generalization errors regardless of the optimization process. We categorize a diverse array of quantum learning algorithms into three learning protocols designed for learning quantum dynamics under a specified observable. Our derived NFL theorems demonstrate quadratic reductions in sample complexity across CLC-LPs, ReQu-LPs, and Qu-LPs. We attribute this performance discrepancy to the unique capacity of quantum-related learning protocols to indirectly utilize information concerning the global phases of non-orthogonal quantum states.
  arXiv  Detail & Related papers  (2024-05-12T09:05:13Z)
• Bounds and guarantees for learning and entanglement [0.0]
  Information theory provides tools to predict the performance of a learning algorithm on a given dataset. This work first extends this relationship by demonstrating that a small conditional entropy is also sufficient for successful learning. This connection between information theory and learning suggests that we might similarly apply quantum information theory to characterize learning tasks involving quantum systems.
  arXiv  Detail & Related papers  (2024-04-10T18:09:22Z)
• Information-theoretic generalization bounds for learning from quantum data [5.0739329301140845]
  We propose a general mathematical formalism for describing quantum learning by training on classical-quantum data. We prove bounds on the expected generalization error of a quantum learner in terms of classical and quantum information-theoretic quantities. Our work lays a foundation for a unifying quantum information-theoretic perspective on quantum learning.
  arXiv  Detail & Related papers  (2023-11-09T17:21:38Z)
• Quantum algorithms: A survey of applications and end-to-end complexities [90.05272647148196]
  The anticipated applications of quantum computers span across science and industry. We present a survey of several potential application areas of quantum algorithms. We outline the challenges and opportunities in each area in an "end-to-end" fashion.
  arXiv  Detail & Related papers  (2023-10-04T17:53:55Z)
• Analysing quantum systems with randomised measurements [0.4179230671838898]
  We present the advancements made in utilising randomised measurements in various scenarios of quantum information science. We describe how to detect and characterise different forms of entanglement, including genuine multipartite entanglement and bound entanglement. We also present an overview on the estimation of non-linear functions of quantum states and shadow tomography from randomised measurements.
  arXiv  Detail & Related papers  (2023-07-03T18:00:01Z)
• The Quantum Path Kernel: a Generalized Quantum Neural Tangent Kernel for Deep Quantum Machine Learning [52.77024349608834]
  Building a quantum analog of classical deep neural networks represents a fundamental challenge in quantum computing. Key issue is how to address the inherent non-linearity of classical deep learning. We introduce the Quantum Path Kernel, a formulation of quantum machine learning capable of replicating those aspects of deep machine learning.
  arXiv  Detail & Related papers  (2022-12-22T16:06:24Z)
• Scalable approach to many-body localization via quantum data [69.3939291118954]
  Many-body localization is a notoriously difficult phenomenon from quantum many-body physics. We propose a flexible neural network based learning approach that circumvents any computationally expensive step. Our approach can be applied to large-scale quantum experiments to provide new insights into quantum many-body physics.
  arXiv  Detail & Related papers  (2022-02-17T19:00:09Z)
• Experimental violations of Leggett-Garg's inequalities on a quantum computer [77.34726150561087]
  We experimentally observe the violations of Leggett-Garg-Bell's inequalities on single and multi-qubit systems. Our analysis highlights the limits of nowadays quantum platforms, showing that the above-mentioned correlation functions deviate from theoretical prediction as the number of qubits and the depth of the circuit grow.
  arXiv  Detail & Related papers  (2021-09-06T14:35:15Z)
• Universal compiling and (No-)Free-Lunch theorems for continuous variable quantum learning [1.2891210250935146]
  We motivate several, closely related, short depth continuous variable algorithms for quantum compilation. We analyse the trainability of our proposed cost functions and demonstrate our algorithms by learning arbitrary numerically Gaussian operations. We make connections between this framework and quantum learning theory in the continuous variable setting by deriving No-Free-Lunch theorems.
  arXiv  Detail & Related papers  (2021-05-03T17:50:04Z)
• A Unified Framework for Quantum Supervised Learning [0.7366405857677226]
  We present an embedding-based framework for supervised learning with trainable quantum circuits. The aim of these approaches is to map data from different classes to separated locations in the Hilbert space via the quantum feature map. We establish an intrinsic connection between the explicit approach and other quantum supervised learning models.
  arXiv  Detail & Related papers  (2020-10-25T18:43:13Z)

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.