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1. Algorithmic reconstruction of the fiber of persistent homology on cell complexes

   https://doi.org/10.1007/s41468-024-00165-w  

   Leygonie, Jacob ; Henselman-Petrusek, Gregory ( April 2024 , Journal of Applied and Computational Topology)

   Let Kbe a finite simplicial, cubical, delta or CW complex. The persistence map $$\textrm{PH}$$$\text{PH}$takes a filter $$f:K\rightarrow \mathbb {R}$$$f:K\to R$as input and returns the barcodes of the sublevel set persistent homology of fin each dimension. We address the inverse problem: given target barcodes D, computing the fiber $$\textrm{PH}^{-1}(D)$$${\text{PH}}^{-1}\left(D\right)$. For this, we use the fact that $$\textrm{PH}^{-1}(D)$$${\text{PH}}^{-1}\left(D\right)$decomposes as a polyhedral complex when Kis a simplicial complex, and we generalise this result to arbitrary based chain complexes. We then design and implement a depth-first search that recovers the polytopes forming the fiber $$\textrm{PH}^{-1}(D)$$${\text{PH}}^{-1}\left(D\right)$. As an application, we solve a corpus of 120 sample problems, providing a first insight into the statistical structure of these fibers, for general CW complexes.

    

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2. Plasmonically enhanced mid-IR light source based on tunable spectrally and directionally selective thermal emission from nanopatterned graphene

   https://doi.org/10.1038/s41598-020-73582-3  

   Shabbir, Muhammad Waqas ; Leuenberger, Michael N. ( October 2020 , Scientific Reports)

   We present a proof of concept for a spectrally selective thermal mid-IR source based on nanopatterned graphene (NPG) with a typical mobility of CVD-grown graphene (up to 3000$$\hbox {cm}^2\,\hbox {V}^{-1}\,\hbox {s}^{-1}$$${\text{cm}}^2{\text{V}}^{-1}{\text{s}}^{-1}$), ensuring scalability to large areas. For that, we solve the electrostatic problem of a conducting hyperboloid with an elliptical wormhole in the presence of anin-planeelectric field. The localized surface plasmons (LSPs) on the NPG sheet, partially hybridized with graphene phonons and surface phonons of the neighboring materials, allow for the control and tuning of the thermal emission spectrum in the wavelength regime from$$\lambda =3$$$\lambda =3$to 12$$\upmu$$$\mu$m by adjusting the size of and distance between the circular holes in a hexagonal or square lattice structure. Most importantly, the LSPs along with an optical cavity increase the emittance of graphene from about 2.3% for pristine graphene to 80% for NPG, thereby outperforming state-of-the-art pristine graphene light sources operating in the near-infrared by at least a factor of 100. According to our COMSOL calculations, a maximum emission power per area of$$11\times 10^3$$$11\times {10}^3$W/$$\hbox {m}^2$$${\text{m}}^2$at$$T=2000$$$T=2000$K for a bias voltage of$$V=23$$$V=23$V is achieved by controlling the temperature of the hot electrons through the Joule heating. By generalizing Planck’s theory to any grey body and deriving the completely general nonlocal fluctuation-dissipation theorem with nonlocal response of surface plasmons in the random phase approximation, we show that the coherence length of the graphene plasmons and the thermally emitted photons can be as large as 13$$\upmu$$$\mu$m and 150$$\upmu$$$\mu$m, respectively, providing the opportunity to create phased arrays made of nanoantennas represented by the holes in NPG. The spatial phase variation of the coherence allows for beamsteering of the thermal emission in the range between$$12^\circ$$${12}^{\circ }$and$$80^\circ$$${80}^{\circ }$by tuning the Fermi energy between$$E_F=1.0$$$E_F=1.0$eV and$$E_F=0.25$$$E_F=0.25$eV through the gate voltage. Our analysis of the nonlocal hydrodynamic response leads to the conjecture that the diffusion length and viscosity in graphene are frequency-dependent. Using finite-difference time domain calculations, coupled mode theory, and RPA, we develop the model of a mid-IR light source based on NPG, which will pave the way to graphene-based optical mid-IR communication, mid-IR color displays, mid-IR spectroscopy, and virus detection.

    

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3. Borexino’s search for low-energy neutrinos associated with gravitational wave events from GWTC-3 database: Borexino Collaboration

   https://doi.org/10.1140/epjc/s10052-023-11688-4  

   Basilico, D. ; Bellini, G. ; Benziger, J. ; Biondi, R. ; Caccianiga, B. ; Calaprice, F. ; Caminata, A. ; Chepurnov, A. ; D’Angelo, D. ; Derbin, A. ; et al ( June 2023 , The European Physical Journal C)

   The search for neutrino events in correlation with gravitational wave (GW) events for three observing runs (O1, O2 and O3) from 09/2015 to 03/2020 has been performed using the Borexino data-set of the same period. We have searched for signals of neutrino-electron scattering and inverse beta-decay (IBD) within a time window of$$\pm \, 1000$$$\pm 1000$ s centered at the detection moment of a particular GW event. The search was done with three visible energy thresholds of 0.25, 0.8 and 3.0 MeV. Two types of incoming neutrino spectra were considered: the mono-energetic line and the supernova-like spectrum. GW candidates originated by merging binaries of black holes (BHBH), neutron stars (NSNS) and neutron star and black hole (NSBH) were analyzed separately. Additionally, the subset of most intensive BHBH mergers at closer distances and with larger radiative mass than the rest was considered. In total, follow-ups of 74 out of 93 gravitational waves reported in the GWTC-3 catalog were analyzed and no statistically significant excess over the background was observed. As a result, the strongest upper limits on GW-associated neutrino and antineutrino fluences for all flavors ($$\nu _e, \nu _\mu , \nu _\tau $$${\nu }_e,{\nu }_{\mu },{\nu }_{\tau }$) at the level$$10^9{-}10^{15}~\textrm{cm}^{-2}\,\textrm{GW}^{-1}$$${10}^9-{10}^{15}{\text{cm}}^{-2}{\text{GW}}^{-1}$have been obtained in the 0.5–5 MeV neutrino energy range.

    

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4. Approximate Unitary t-Designs by Short Random Quantum Circuits Using Nearest-Neighbor and Long-Range Gates

   https://doi.org/10.1007/s00220-023-04675-z  

   Harrow, Aram W. ; Mehraban, Saeed ( May 2023 , Communications in Mathematical Physics)

   We prove that$${{\,\textrm{poly}\,}}(t) \cdot n^{1/D}$$$\text{poly}\left(t\right)·n^{1/D}$-depth local random quantum circuits with two qudit nearest-neighbor gates on aD-dimensional lattice withnqudits are approximatet-designs in various measures. These include the “monomial” measure, meaning that the monomials of a random circuit from this family have expectation close to the value that would result from the Haar measure. Previously, the best bound was$${{\,\textrm{poly}\,}}(t)\cdot n$$$\text{poly}\left(t\right)·n$due to Brandão–Harrow–Horodecki (Commun Math Phys 346(2):397–434, 2016) for$$D=1$$$D=1$. We also improve the “scrambling” and “decoupling” bounds for spatially local random circuits due to Brown and Fawzi (Scrambling speed of random quantum circuits, 2012). One consequence of our result is that assuming the polynomial hierarchy ($${{\,\mathrm{\textsf{PH}}\,}}$$$\mathrm{PH}$) is infinite and that certain counting problems are$$\#{\textsf{P}}$$$\#P$-hard “on average”, sampling within total variation distance from these circuits is hard for classical computers. Previously, exact sampling from the outputs of even constant-depth quantum circuits was known to be hard for classical computers under these assumptions. However the standard strategy for extending this hardness result to approximate sampling requires the quantum circuits to have a property called “anti-concentration”, meaning roughly that the output has near-maximal entropy. Unitary 2-designs have the desired anti-concentration property. Our result improves the required depth for this level of anti-concentration from linear depth to a sub-linear value, depending on the geometry of the interactions. This is relevant to a recent experiment by the Google Quantum AI group to perform such a sampling task with 53 qubits on a two-dimensional lattice (Arute in Nature 574(7779):505–510, 2019; Boixo et al. in Nate Phys 14(6):595–600, 2018) (and related experiments by USTC), and confirms their conjecture that$$O(\sqrt{n})$$$O\left(\sqrt{n}\right)$depth suffices for anti-concentration. The proof is based on a previous construction oft-designs by Brandão et al. (2016), an analysis of how approximate designs behave under composition, and an extension of the quasi-orthogonality of permutation operators developed by Brandão et al. (2016). Different versions of the approximate design condition correspond to different norms, and part of our contribution is to introduce the norm corresponding to anti-concentration and to establish equivalence between these various norms for low-depth circuits. For random circuits with long-range gates, we use different methods to show that anti-concentration happens at circuit size$$O(n\ln ^2 n)$$$O\left(n{ln}^{2}n\right)$corresponding to depth$$O(\ln ^3 n)$$$O\left({ln}^{3}n\right)$. We also show a lower bound of$$\Omega (n \ln n)$$$\Omega (nlnn)$for the size of such circuit in this case. We also prove that anti-concentration is possible in depth$$O(\ln n \ln \ln n)$$$O(lnnlnlnn)$(size$$O(n \ln n \ln \ln n)$$$O(nlnnlnlnn)$) using a different model.

    

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5. 3D Mirror Symmetry for Instanton Moduli Spaces

   https://doi.org/10.1007/s00220-023-04831-5  

   Koroteev, Peter ; Zeitlin, Anton M. ( September 2023 , Communications in Mathematical Physics)

   We prove that the Hilbert scheme ofkpoints on$${\mathbb {C}}^2$$$C^2$($$\hbox {Hilb}^k[{\mathbb {C}}^2]$$${\text{Hilb}}^k\left[C^2\right]$) is self-dual under three-dimensional mirror symmetry using methods of geometry and integrability. Namely, we demonstrate that the corresponding quantum equivariant K-theory is invariant upon interchanging its Kähler and equivariant parameters as well as inverting the weight of the$${\mathbb {C}}^\times _\hbar $$$C_{ħ}^{\times }$-action. First, we find a two-parameter family$$X_{k,l}$$$X_{k,l}$of self-mirror quiver varieties of type A and study their quantum K-theory algebras. The desired quantum K-theory of$$\hbox {Hilb}^k[{\mathbb {C}}^2]$$${\text{Hilb}}^k\left[C^2\right]$is obtained via direct limit$$l\longrightarrow \infty $$$l⟶\infty$and by imposing certain periodic boundary conditions on the quiver data. Throughout the proof, we employ the quantum/classical (q-Langlands) correspondence between XXZ Bethe Ansatz equations and spaces of twisted$$\hbar $$$ħ$-opers. In the end, we propose the 3d mirror dual for the moduli spaces of torsion-free rank-Nsheaves on$${\mathbb {P}}^2$$$P^2$with the help of a different (three-parametric) family of type A quiver varieties with known mirror dual.

    

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