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Efficient training of photonic quantum generative models

Felix Gottlieb, Rawad Mezher, Brian Ventura, Shane Mansfield, Alexia Salavrakos

TL;DR

This work proposes an efficient training procedure for photon-native quantum generative models based on the maximum mean discrepancy, where the deployment of the model corresponds to the task of boson sampling.

Abstract

The topic of generative learning has gained traction within the field of quantum machine learning, in particular with the advent of train-on-classical, deploy-on-quantum methods. This approach exploits the properties of intermediate-complexity circuits whose training can be simulated classically efficiently, but that generally require quantum hardware for the corresponding sampling problem. Quantum linear optics possess similar properties, which allows us to propose an efficient training procedure for photon-native quantum generative models based on the maximum mean discrepancy, where the deployment of the model corresponds to the task of boson sampling. We provide numerical results, propose datasets, and we also explore how initialization strategies and ansatz choice affect the training.

Efficient training of photonic quantum generative models

TL;DR

This work proposes an efficient training procedure for photon-native quantum generative models based on the maximum mean discrepancy, where the deployment of the model corresponds to the task of boson sampling.

Abstract

The topic of generative learning has gained traction within the field of quantum machine learning, in particular with the advent of train-on-classical, deploy-on-quantum methods. This approach exploits the properties of intermediate-complexity circuits whose training can be simulated classically efficiently, but that generally require quantum hardware for the corresponding sampling problem. Quantum linear optics possess similar properties, which allows us to propose an efficient training procedure for photon-native quantum generative models based on the maximum mean discrepancy, where the deployment of the model corresponds to the task of boson sampling. We provide numerical results, propose datasets, and we also explore how initialization strategies and ansatz choice affect the training.
Paper Structure (17 sections, 1 theorem, 34 equations, 2 figures)

This paper contains 17 sections, 1 theorem, 34 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Discrete variable linear optical quantum computing
  4. Generative model
  5. Estimating the MMD loss in linear optics
  6. MMD observable
  7. Classical estimation procedure
  8. Ansätze and initialization strategies in linear optical circuits
  9. Interferometer choice
  10. Input state
  11. Warm starts and initialization strategies
  12. Datasets and applications
  13. Boson sampling datasets
  14. User preference datasets
  15. Bioinformatics datasets
  16. ...and 2 more sections

Key Result

Proposition 1

The MMD loss function for distributions $p, q$ defined on $\Tilde{\mathcal{X}}_{m, n}$ can be computed with the linear optical observable in the no-collision regime.

Figures (2)

  • Figure 1: Estimation of the MMD observable.
  • Figure 2: Subfigures (a) and (b) compare the MMD loss curve for different sizes of sets $\mathcal{K}$ and $\mathcal{Z}$ from the estimation procedure: when the sets are smaller, the loss has slightly larger variations. Subfigures (c) - (f) display the value of the MMD on the test set for the quantum model and the classical benchmarks, for different datasets. In (c), different choices of interferometers are displayed, and in (d) - (f) different choices of bandwidth $\sigma$ are shown. The best performance of the quantum model is observed for the boson sampling dataset. Error bars are obtained from repeating the simulations five times each, and in the case of the test-to-test MMD, by shuffling the test set.

Theorems & Definitions (2)

  • Proposition 1
  • proof