Unifying (Quantum) Statistical and Parametrized (Quantum) Algorithms

• URL: http://arxiv.org/abs/2310.17716v1
• Date: Thu, 26 Oct 2023 18:23:21 GMT
• Title: Unifying (Quantum) Statistical and Parametrized (Quantum) Algorithms
• Authors: Alexander Nietner
• Abstract summary: We take inspiration from Kearns' SQ oracle and Valiant's weak evaluation oracle. We introduce an extensive yet intuitive framework that yields unconditional lower bounds for learning from evaluation queries.
• Score: 65.268245109828
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Kearns' statistical query (SQ) oracle (STOC'93) lends a unifying perspective for most classical machine learning algorithms. This ceases to be true in quantum learning, where many settings do not admit, neither an SQ analog nor a quantum statistical query (QSQ) analog. In this work, we take inspiration from Kearns' SQ oracle and Valiant's weak evaluation oracle (TOCT'14) and establish a unified perspective bridging the statistical and parametrized learning paradigms in a novel way. We explore the problem of learning from an evaluation oracle, which provides an estimate of function values, and introduce an extensive yet intuitive framework that yields unconditional lower bounds for learning from evaluation queries and characterizes the query complexity for learning linear function classes. The framework is directly applicable to the QSQ setting and virtually all algorithms based on loss function optimization. Our first application is to extend prior results on the learnability of output distributions of quantum circuits and Clifford unitaries from the SQ to the (multi-copy) QSQ setting, implying exponential separations between learning stabilizer states from (multi-copy) QSQs versus from quantum samples. Our second application is to analyze some popular quantum machine learning (QML) settings. We gain an intuitive picture of the hardness of many QML tasks which goes beyond existing methods such as barren plateaus and the statistical dimension, and contains crucial setting-dependent implications. Our framework not only unifies the perspective of cost concentration with that of the statistical dimension in a unified language but exposes their connectedness and similarity.

Related papers

• Benchmarking Quantum Generative Learning: A Study on Scalability and Noise Resilience using QUARK [0.3624329910445628]
  This paper investigates the scalability and noise resilience of quantum generative learning applications. We employ rigorous benchmarking techniques to track progress and identify challenges in scaling QML algorithms. We show that QGANs are not as affected by the curse of dimensionality as QCBMs and to which extent QCBMs are resilient to noise.
  arXiv  Detail & Related papers  (2024-03-27T15:05:55Z)
• Learning unitaries with quantum statistical queries [0.0]
  We propose several algorithms for learning unitary operators from quantum statistical queries (QSQs) Our methods hinge on a novel technique for estimating the Fourier mass of a unitary on a subset of Pauli strings with a single quantum statistical query. We show that quantum statistical queries lead to an exponentially larger sample complexity for certain tasks, compared to separable measurements to the Choi-Jamiolkowski state.
  arXiv  Detail & Related papers  (2023-10-03T17:56:07Z)
• Variational Quantum Approximate Spectral Clustering for Binary Clustering Problems [0.7550566004119158]
  We introduce the Variational Quantum Approximate Spectral Clustering (VQASC) algorithm. VQASC requires optimization of fewer parameters than the system size, N, traditionally required in classical problems. We present numerical results from both synthetic and real-world datasets.
  arXiv  Detail & Related papers  (2023-09-08T17:54:42Z)
• Quantum Imitation Learning [74.15588381240795]
  We propose quantum imitation learning (QIL) with a hope to utilize quantum advantage to speed up IL. We develop two QIL algorithms, quantum behavioural cloning (Q-BC) and quantum generative adversarial imitation learning (Q-GAIL) Experiment results demonstrate that both Q-BC and Q-GAIL can achieve comparable performance compared to classical counterparts.
  arXiv  Detail & Related papers  (2023-04-04T12:47:35Z)
• 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)
• End-to-end resource analysis for quantum interior point methods and portfolio optimization [63.4863637315163]
  We provide a complete quantum circuit-level description of the algorithm from problem input to problem output. We report the number of logical qubits and the quantity/depth of non-Clifford T-gates needed to run the algorithm.
  arXiv  Detail & Related papers  (2022-11-22T18:54:48Z)
• Oracle separations of hybrid quantum-classical circuits [68.96380145211093]
  Two models of quantum computation: CQ_d and QC_d. CQ_d captures the scenario of a d-depth quantum computer many times; QC_d is more analogous to measurement-based quantum computation. We show that, despite the similarities between CQ_d and QC_d, the two models are intrinsically, i.e. CQ_d $nsubseteq$ QC_d and QC_d $nsubseteq$ CQ_d relative to an oracle.
  arXiv  Detail & Related papers  (2022-01-06T03:10:53Z)
• Quantum agents in the Gym: a variational quantum algorithm for deep Q-learning [0.0]
  We introduce a training method for parametrized quantum circuits (PQCs) that can be used to solve RL tasks for discrete and continuous state spaces. We investigate which architectural choices for quantum Q-learning agents are most important for successfully solving certain types of environments.
  arXiv  Detail & Related papers  (2021-03-28T08:57:22Z)
• Momentum Q-learning with Finite-Sample Convergence Guarantee [49.38471009162477]
  This paper analyzes a class of momentum-based Q-learning algorithms with finite-sample guarantee. We establish the convergence guarantee for MomentumQ with linear function approximations and Markovian sampling. We demonstrate through various experiments that the proposed MomentumQ outperforms other momentum-based Q-learning algorithms.
  arXiv  Detail & Related papers  (2020-07-30T12:27:03Z)
• Quantum statistical query learning [6.434862450258459]
  We propose a learning model called the quantum statistical learning QSQ model. Our model can be seen as a restriction of the quantum PAC learning model. We show that learnability in QSQ model implies learnability in quantum private PAC model.
  arXiv  Detail & Related papers  (2020-02-19T15:36:57Z)

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.