2020 NTT Research Summit

The presentation at the NTT meeting was too brief and non-technical to explain these works.
Only three (out of four projects) are very briefly covered in that talk.

Experimental kernel-based quantum machine learning in finite feature space

K. Bartkiewicz, C. Gneiting, A. Cernoch, K. Jirakova, K. Lemr, F. Nori
Scientific Reports 10, 12356 (2020).
　

ABSTRACT
 We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed quantum states encoding the training data, while the model training is processed on a classical computer. Our two-photon proposal encodes data points in a discrete, eight-dimensional feature Hilbert space. In order to maximize the application range of the deployable kernels, we optimize feature maps towards the resulting kernels’ ability to separate points, i.e., their “resolution,” under the constraint of finite, fixed Hilbert space dimension. Implementing these kernels, our setup delivers viable decision boundaries for standard nonlinear supervised classification tasks in feature space. We demonstrate such kernel-based quantum machine learning using specialized multiphoton quantum optical circuits. The deployed kernel exhibits exponentially better scaling in the required number of qubits than a direct generalization of kernels described in the literature.

URL: https://doi.org/10.1038/s41598-020-68911-5

This very interesting work had bad luck with some referees, and we sent it to Sci. Reports just to get it published fast. It includes theory and experiments.

Topological Quantum Phase Transitions Retrieved from Manifold Learning

Yanming Che, Clemens Gneiting, Tao Liu, Franco Nori

Subjects: Computational Physics (physics.comp-ph); Disordered Systems and Neural Networks (cond-mat.dis-nn)

ABSTRACT

 The discovery of topological features of quantum states plays a central role in modern condensed matter physics and various artificial systems. Due to the absence of local order parameters, the detection of topological phase transitions remains a challenge. Machine learning may provide effective methods for identifying topological features. In this work, we show that manifold learning can successfully retrieve topological quantum phase transitions in momentum space. Our results show that the Chebyshev distance (CD) between two data points can successfully capture the main features of topological phase transitions, while the widely used Euclidean distance in general fails. The similarity matrix built upon the CD thus naturally exhibits uncorrelated cluster structures, corresponding to distinct sectors in the topological phase diagram. Then a diffusion map is applied to implement dimensionality reduction and to learn about topological quantum phase transitions in an unsupervised manner. Our demonstrations on the Su-Schrieffer-Heeger (SSH) model, the 2D Qi-Wu-Zhang (QWZ) model, and the quenched SSH model show the capability of generic unsupervised learning, when equipped with a suitable distance metric, in exploring topological quantum phase transitions.

URL: https://arxiv.org/abs/2002.02363

To appear in PRB.

Eigenstate extraction with neural-network tomography

A.Melkani, C. Gneiting, F. Nori

Phys. Rev. A 102, 022412 (2020).
　

ABSTRACT

 We discuss quantum state tomography via a stepwise reconstruction of the eigenstates of the mixed states produced in experiments. Our method is tailored to the experimentally relevant class of nearly pure states, or simple mixed states, which exhibit dominant eigenstates and thus lend themselves to low-rank approximations. The developed scheme is applicable to any pure-state tomography method, promoting it to mixed-state tomography. Here, we demonstrate it with machine learning-inspired pure-state tomography based on neural-network representations of quantum states. The latter have been shown to efficiently approximate generic classes of complex (pure) states of large quantum systems. We test our method by applying it to experimental data from trapped ion experiments with four to eight qubits.

This is listed as “Editors' Suggestion.”

URL: https://doi.org/10.1103/PhysRevA.102.022412

The last one (using Adversarial Neural Networks) is more recent:

 [Submitted on 7 Aug 2020]

Quantum State Tomography with Conditional Generative Adversarial Networks

Shahnawaz Ahmed, Carlos Sánchez Muñoz, Franco Nori, Anton Frisk Kockum

ABSTRACT
 Quantum state tomography (QST) is a challenging task in intermediate-scale quantum devices. Here, we apply conditional generative adversarial networks (CGANs) to QST. In the CGAN framework, two dueling neural networks, a generator and a discriminator, learn multi-modal models from data. We augment a CGAN with custom neural-network layers that enable conversion of output from any standard neural network into a physical density matrix. To reconstruct the density matrix, the generator and discriminator networks train each other on data using standard gradient-based methods. We demonstrate that our QST-CGAN reconstructs optical quantum states with high fidelity orders of magnitude faster, and from less data, than a standard maximum-likelihood method. We also show that the QST-CGAN can reconstruct a quantum state in a single evaluation of the generator network if it has been pre-trained on similar quantum states.

URL: https://arxiv.org/abs/2008.03240

PDF: https://arxiv.org/pdf/2008.03240

The motivation for using these is clearly explained in each Introduction. Also very briefly in the abstract.