Learning the tensor network model of a quantum state using a few single-qubit measurements

The constantly increasing dimensionality of artificial quantum systems demands for highly efficient methods for their characterization and benchmarking. Conventional quantum tomography fails for larger systems due to the exponential growth of the required number of measurements. The conceptual solution for this dimensionality curse relies on a simple idea - a complete description of a quantum state is excessive and can be discarded in favor of experimentally accessible information about the system. The probably approximately correct (PAC) learning theory has been recently successfully applied to a problem of building accurate predictors for the measurement outcomes using a dataset which scales only linearly with the number of qubits. Here we present a constructive and numerically efficient protocol which learns a tensor network model of an unknown quantum system. We discuss the limitations and the scalability of the proposed method.Comment: 10 pages, 11 figure

Time-domain Hong-Ou-Mandel interference of quasi-thermal fields and its application in linear optical circuit characterization

We study temporal correlations of interfering quasi-thermal fields, obtained by scattering laser radiation on a rotating ground glass disk. We show that the Doppler effect causes oscillations in temporal cross-correlation function. Furthermore, we propose how to use Hong-Ou-Mandel interference of quasi-thermal fields in the time domain to characterize linear optical circuits.Comment: 8 pages, 5 figures (main), 4 pages, 1 figure (supplemental

Employee skills for circular business model implementation: A taxonomy

A growing body of scholarship has examined circular business models as a pathway towards sustainability. However, employee skills to support such business models have been largely overlooked. Addressing this research gap, this article proposes a comprehensive skill taxonomy for start-ups embracing circular economy transition. As the first large-N effort to develop a comprehensive skill taxonomy for circular business model implementation, this study uses a clustering analysis of self-reported skill profiles for 2407 staff working in circular start-ups. The taxonomy outlines 40 skills across six categories: business innovation, operations, social dimensions, systems, digitization, and technical issues. Findings suggest that circular business model implementation requires a set of general, sustainable, and circular skills, but some of these skills have been neglected in scholarship. Promoting circular narratives as a framing device for skill development can help advance CE towards mainstream uptake, and this study's taxonomy offers a practical framework for using talent to accelerate CE transition

Observation of edge solitons in topological trimer arrays

We report the experimental observation of nonlinear light localization and edge soliton formation at the edges of fs-laser written trimer waveguide arrays, where transition from nontopological to topological phases is controlled by the spacing between neighboring trimers. We found that, in the former regime, edge solitons occur only above a considerable power threshold, whereas in the latter one they bifurcate from linear states. Edge solitons are observed in a broad power range where their propagation constant falls into one of the topological gaps of the system, while partial delocalization is observed when considerable nonlinearity drives the propagation constant into an allowed band, causing coupling with bulk modes. Our results provide direct experimental evidence of the coexistence and selective excitation in the same or in different topological gaps of two types of topological edge solitons with different internal structures, which can rarely be observed even in nontopological systems. This also constitutes the first experimental evidence of formation of topological solitons in a nonlinear system with more than one topological gap.The authors acknowledge funding of this study by RSF (grant 21‐12‐00096). Also, support by CEX2019‐000910‐S [funded by MCIN/AEI/10.13039/501100011033], Fundació Cellex, Fundació Mir‐Puig, and Generalitat de Catalunya (CERCA) is acknowledged.Peer ReviewedPostprint (author's final draft

Observation of π\pi solitons in oscillating waveguide arrays

Floquet systems with periodically varying in time parameters enable realization of unconventional topological phases that do not exist in static systems with constant parameters and that are frequently accompanied by appearance of novel types of the topological states. Among such Floquet systems are the Su-Schrieffer-Heeger lattices with periodically-modulated couplings that can support at their edges anomalous $\pi$ modes of topological origin despite the fact that the lattice spends only half of the evolution period in topologically nontrivial phase, while during other half-period it is topologically trivial. Here, using Su-Schrieffer-Heeger arrays composed from periodically oscillating waveguides inscribed in transparent nonlinear optical medium, we report experimental observation of photonic anomalous $\pi$ modes residing at the edge or in the corner of the one- or two-dimensional arrays, respectively, and demonstrate a new class of topological $\pi$ solitons bifurcating from such modes in the topological gap of the Floquet spectrum at high powers. $\pi$ solitons reported here are strongly oscillating nonlinear Floquet states exactly reproducing their profiles after each longitudinal period of the structure. They can be dynamically stable in both one- and two-dimensional oscillating waveguide arrays, the latter ones representing the first realization of the Floquet photonic higher-order topological insulator, while localization properties of such $\pi$ solitons are determined by their power.Comment: 10 pages, 6 figures, to appear in Science Bulleti

Observation of linear and nonlinear light localization at the edges of moiré arrays

We observe linear and nonlinear light localization at the edges and in the corners of truncated moiré arrays created by the superposition of periodic mutually twisted at Pythagorean angles square sublattices. Experimentally exciting corner linear modes in the femtosecond-laser written moiré arrays we find drastic differences in their localization properties in comparison with the bulk excitations. We also address the impact of nonlinearity on the corner and bulk modes and experimentally observe the crossover from linear quasilocalized states to the surface solitons emerging at the higher input powers. Our results constitute the first experimental demonstration of localization phenomena induced by truncation of periodic moiré structures in photonic systems.This research is funded by the research Project No. FFUU- 2021-0003 of the Institute of Spectroscopy of the Russian Academy of Sciences and partially funded by the RSF Grant No. 21-12-00096. F. Y. acknowledges support from Shanghai Outstanding Academic Leaders Plan (Grant No. 20XD1402000) and the NSFC (Grant No. 91950120). S. K. I. and L. T. acknowledge support by Grants No. CEX2019-000910-S and No. PGC2018-097035-B-I00 funded by MCIN/AEI/10.13039/501100011033/FEDER, Fundació Cellex, Fundació Mir-Puig, and Generalitat de Catalunya (CERCA).Peer ReviewedPostprint (published version