Generalization Metrics for Practical Quantum Advantage in Generative Models

• URL: http://arxiv.org/abs/2201.08770v3
• Date: Thu, 11 May 2023 12:14:43 GMT
• Title: Generalization Metrics for Practical Quantum Advantage in Generative Models
• Authors: Kaitlin Gili, Marta Mauri, Alejandro Perdomo-Ortiz
• Abstract summary: Generative modeling is a widely accepted natural use case for quantum computers. We construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Our simulation results show that our quantum-inspired models have up to a $68 times$ enhancement in generating unseen unique and valid samples.
• Score: 68.8204255655161
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: As the quantum computing community gravitates towards understanding the practical benefits of quantum computers, having a clear definition and evaluation scheme for assessing practical quantum advantage in the context of specific applications is paramount. Generative modeling, for example, is a widely accepted natural use case for quantum computers, and yet has lacked a concrete approach for quantifying success of quantum models over classical ones. In this work, we construct a simple and unambiguous approach to probe practical quantum advantage for generative modeling by measuring the algorithm's generalization performance. Using the sample-based approach proposed here, any generative model, from state-of-the-art classical generative models such as GANs to quantum models such as Quantum Circuit Born Machines, can be evaluated on the same ground on a concrete well-defined framework. In contrast to other sample-based metrics for probing practical generalization, we leverage constrained optimization problems (e.g., cardinality-constrained problems) and use these discrete datasets to define specific metrics capable of unambiguously measuring the quality of the samples and the model's generalization capabilities for generating data beyond the training set but still within the valid solution space. Additionally, our metrics can diagnose trainability issues such as mode collapse and overfitting, as we illustrate when comparing GANs to quantum-inspired models built out of tensor networks. Our simulation results show that our quantum-inspired models have up to a $68 \times$ enhancement in generating unseen unique and valid samples compared to GANs, and a ratio of 61:2 for generating samples with better quality than those observed in the training set. We foresee these metrics as valuable tools for rigorously defining practical quantum advantage in the domain of generative modeling.

Related papers

• 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)
• Bayesian Modelling Approaches for Quantum States -- The Ultimate Gaussian Process States Handbook [0.0]
  This thesis discusses novel tools and techniques for the (classical) modelling of quantum many-body wavefunctions. It is outlined how synergies with standard machine learning approaches can be exploited to enable an automated inference of the most relevant intrinsic characteristics. The resulting model carries a high degree of interpretability and offers an easily applicable tool for study of quantum systems.
  arXiv  Detail & Related papers  (2023-08-15T09:37:58Z)
• A Framework for Demonstrating Practical Quantum Advantage: Racing Quantum against Classical Generative Models [62.997667081978825]
  We build over a proposed framework for evaluating the generalization performance of generative models. We establish the first comparative race towards practical quantum advantage (PQA) between classical and quantum generative models. Our results suggest that QCBMs are more efficient in the data-limited regime than the other state-of-the-art classical generative models.
  arXiv  Detail & Related papers  (2023-03-27T22:48:28Z)
• 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)
• Generative model for learning quantum ensemble via optimal transport loss [0.9404723842159504]
  We propose a quantum generative model that can learn quantum ensemble. The proposed model paves the way for a wide application such as the health check of quantum devices.
  arXiv  Detail & Related papers  (2022-10-19T17:35:38Z)
• Provably efficient variational generative modeling of quantum many-body systems via quantum-probabilistic information geometry [3.5097082077065003]
  We introduce a generalization of quantum natural gradient descent to parameterized mixed states. We also provide a robust first-order approximating algorithm, Quantum-Probabilistic Mirror Descent. Our approaches extend previously sample-efficient techniques to allow for flexibility in model choice.
  arXiv  Detail & Related papers  (2022-06-09T17:58:15Z)
• On Quantum Circuits for Discrete Graphical Models [1.0965065178451106]
  We provide the first method that allows one to provably generate unbiased and independent samples from general discrete factor models. Our method is compatible with multi-body interactions and its success probability does not depend on the number of variables. Experiments with quantum simulation as well as actual quantum hardware show that our method can carry out sampling and parameter learning on quantum computers.
  arXiv  Detail & Related papers  (2022-06-01T11:03:51Z)
• Quantum Machine Learning with SQUID [64.53556573827525]
  We present the Scaled QUantum IDentifier (SQUID), an open-source framework for exploring hybrid Quantum-Classical algorithms for classification problems. We provide examples of using SQUID in a standard binary classification problem from the popular MNIST dataset.
  arXiv  Detail & Related papers  (2021-04-30T21:34:11Z)
• Error mitigation and quantum-assisted simulation in the error corrected regime [77.34726150561087]
  A standard approach to quantum computing is based on the idea of promoting a classically simulable and fault-tolerant set of operations. We show how the addition of noisy magic resources allows one to boost classical quasiprobability simulations of a quantum circuit.
  arXiv  Detail & Related papers  (2021-03-12T20:58:41Z)
• Enhancing Generative Models via Quantum Correlations [1.6099403809839032]
  Generative modeling using samples drawn from the probability distribution constitutes a powerful approach for unsupervised machine learning. We show theoretically that such quantum correlations provide a powerful resource for generative modeling. We numerically test this separation on standard machine learning data sets and show that it holds for practical problems.
  arXiv  Detail & Related papers  (2021-01-20T22:57:22Z)

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.