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1. 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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2. Optomechanical inertial sensors

   https://doi.org/10.1364/AO.393061  

   Hines, Adam ; Richardson, Logan ; Wisniewski, Hayden ; Guzman, Felipe ( June 2020 , Applied Optics)

   We present a performance analysis of compact monolithic optomechanical inertial sensors that describes their key fundamental limits and overall acceleration noise floor. Performance simulations for low-frequency gravity-sensitive inertial sensors show attainable acceleration noise floors on the order of$1\times <\#comment/>{10}^{-<\#comment/>11}\mathrm{m}/{\mathrm{s}}^2\sqrt{\mathrm{H}\mathrm{z}}$. Furthermore, from our performance models, we devised an optimization approach for our sensor designs, sensitivity, and bandwidth trade space. We conducted characterization measurements of these compact mechanical resonators, demonstrating$\mathit{\text{mQ}}$-products at levels of 250 kg, which highlight their exquisite acceleration sensitivity.

    

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3. Distributed quantum sensing enhanced by continuous-variable error correction

   https://doi.org/10.1088/1367-2630/ab7257  

   Zhuang, Quntao ; Preskill, John ; Jiang, Liang ( February 2020 , New Journal of Physics)

   A distributed sensing protocol uses a network of local sensing nodes to estimate a global feature of the network, such as a weighted average of locally detectable parameters. In the noiseless case, continuous-variable (CV) multipartite entanglement shared by the nodes can improve the precision of parameter estimation relative to the precision attainable by a network without shared entanglement; for an entangled protocol, the root mean square estimation error scales like 1/Mwith the numberMof sensing nodes, the so-called Heisenberg scaling, while for protocols without entanglement, the error scales like$1/\sqrt{M}$. However, in the presence of loss and other noise sources, although multipartite entanglement still has some advantages for sensing displacements and phases, the scaling of the precision withMis less favorable. In this paper, we show that using CV error correction codes can enhance the robustness of sensing protocols against imperfections and reinstate Heisenberg scaling up to moderate values ofM. Furthermore, while previous distributed sensing protocols could measure only a single quadrature, we construct a protocol in which both quadratures can be sensed simultaneously. Our work demonstrates the value of CV error correction codes in realistic sensing scenarios.

    

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4. A Mach-Zehnder Fabry-Perot hybrid fiber-optic interferometer operating at the thermal noise limit

   https://doi.org/10.1038/s41598-022-16474-y  

   Hoque, Nabil Md Rakinul ; Duan, Lingze ( July 2022 , Scientific Reports)

   A new type of interferometric fiber sensor based on a Mach-Zehnder Fabry-Perot hybrid scheme has been experimentally demonstrated. The interferometer combines the benefits of both a double-path configuration and an optical resonator, leading to record-high strain and phase resolutions limited only by the intrinsic thermal noise in optical fibers across a broad frequency range. Using only off-the-shelf components, the sensor is able to achieve noise-limited strain resolutions of 40 f$$\varepsilon $$$\epsilon$/$$\sqrt{(}Hz)$$$\sqrt{(}Hz)$at 10 Hz and 1 f$$\varepsilon $$$\epsilon$/$$\sqrt{(}Hz)$$$\sqrt{(}Hz)$at 100 kHz. With a proper scale-up, atto-strain resolutions are believed to be within reach in the ultrasonic frequency range with such interferometers.

    

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5. HERA Phase I Limits on the Cosmic 21 cm Signal: Constraints on Astrophysics and Cosmology during the Epoch of Reionization

   https://doi.org/10.3847/1538-4357/ac2ffc  

   Abdurashidova, Zara ; Aguirre, James E. ; Alexander, Paul ; Ali, Zaki S. ; Balfour, Yanga ; Barkana, Rennan ; Beardsley, Adam P. ; Bernardi, Gianni ; Billings, Tashalee S. ; Bowman, Judd D. ; et al ( January 2022 , The Astrophysical Journal)

   Recently, the Hydrogen Epoch of Reionization Array (HERA) has produced the experiment’s first upper limits on the power spectrum of 21 cm fluctuations atz∼ 8 and 10. Here, we use several independent theoretical models to infer constraints on the intergalactic medium (IGM) and galaxies during the epoch of reionization from these limits. We find that the IGM must have been heated above the adiabatic-cooling threshold byz∼ 8, independent of uncertainties about IGM ionization and the radio background. Combining HERA limits with complementary observations constrains the spin temperature of thez∼ 8 neutral IGM to 27 K$〈{\overline{T}}_S〉$630 K (2.3 K$〈{\overline{T}}_S〉$640 K) at 68% (95%) confidence. They therefore also place a lower bound on X-ray heating, a previously unconstrained aspects of early galaxies. For example, if the cosmic microwave background dominates thez∼ 8 radio background, the new HERA limits imply that the first galaxies produced X-rays more efficiently than local ones. Thez∼ 10 limits require even earlier heating if dark-matter interactions cool the hydrogen gas. If an extra radio background is produced by galaxies, we rule out (at 95% confidence) the combination of high radio and low X-ray luminosities ofL_r,ν/SFR > 4 × 10²⁴W Hz⁻¹$M_{\odot }^{-1}$yr andL_X/SFR < 7.6 × 10³⁹erg s⁻¹$M_{\odot }^{-1}$yr. The new HERA upper limits neither support nor disfavor a cosmological interpretation of the recent Experiment to Detect the Global EOR Signature (EDGES) measurement. The framework described here provides a foundation for the interpretation of future HERA results.

    

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