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1. Scaling of the non-phononic spectrum of two-dimensional glasses

   https://doi.org/10.1063/5.0139596  

   Wang, Lijin; Szamel, Grzegorz; Flenner, Elijah (March 2023, The Journal of Chemical Physics)

   Low-frequency vibrational harmonic modes of glasses are frequently used to rationalize their universal low-temperature properties. One well studied feature is the excess low-frequency density of states over the Debye model prediction. Here, we examine the system size dependence of the density of states for two-dimensional glasses. For systems of fewer than 100 particles, the density of states scales with the system size as if all the modes were plane-wave-like. However, for systems greater than 100 particles, we find a different system-size scaling of the cumulative density of states below the first transverse sound mode frequency, which can be derived from the assumption that these modes are quasi-localized. Moreover, for systems greater than 100 particles, we find that the cumulative density of states scales with the frequency as a power law with the exponent that leads to the exponent β = 3.5 for the density of states. For systems whose sizes were investigated, we do not see a size-dependence of exponent β. 

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2. Energy-dependent barren plateau in bosonic variational quantum circuits

   https://doi.org/10.1088/2058-9565/ad80bf  

   Zhang, Bingzhi; Zhuang, Quntao (October 2024, Quantum Science and Technology)

   Abstract Bosonic variational quantum circuits (VQCs) are crucial for information processing in microwave cavities, trapped ions, and optical systems, widely applicable in quantum communication, sensing and error correction. The trainability of such VQCs is less understood, hindered by the lack of theoretical tools such ast-design due to the infinite dimension of the continuous-variable systems involved. We overcome this difficulty to reveal an energy-dependent barren plateau in such VQCs. The variance of the gradient decays as $1/E^{M\nu }$, exponential in the number of modesMbut polynomial in the (per-mode) circuit energyE. The exponentν = 1 for shallow circuits andν = 2 for deep circuits. We prove these results for state preparation of general Gaussian states and number states. We also provide numerical evidence demonstrating that the results extend to general state preparation tasks. As circuit energy is a controllable parameter, we provide a strategy to mitigate the barren plateau in bosonic continuous-variable VQCs. 

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3. Multimode experimental band dynamics of resonant nanophotonic lattices

   https://doi.org/10.1364/OE.495835  

   Razmjooei, Nasrin; Magnusson, Robert (January 2023, Optics Express)

   Subwavelength resonant lattices provide a host of interesting spectral expressions on broadside illumination. The resonance mechanism is based on generation of lateral Bloch modes phase matched to evanescent diffraction orders. The leaky mode structure and mode count determine the spectra and the number of resonance states. Here, we study band flips and bound-state transitions in guided-mode resonant structures supporting multiple resonant modes. We present theoretical simulations and experimental results for a subwavelength silicon-nitride lattice integrated with a liquid film with adjustable boundary. The relatively thick liquid waveguiding region supports additional modes such that the first four transverse-electric (TE) leaky modes are present and generate observable resonance signatures. By varying the duty cycle of the basic lattice in experiment, the 4 bands undergo band transitions and band closures as quantified herein. The experimental results taken in the 1400-1600 nm spectral region agree reasonably well with numerical analysis. 

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4. Spin‐s Dicke States and Their Preparation

   https://doi.org/10.1002/qute.202400057  

   Nepomechie, Rafael I; Ravanini, Francesco; Raveh, David (December 2024, Advanced Quantum Technologies)

   Abstract The notion of spin‐ Dicke states is introduced, which are higher‐spin generalizations of usual (spin‐1/2) Dicke states. These multi‐qudit states can be expressed as superpositions of qudit Dicke states. They satisfy a recursion formula, which is used to formulate an efficient quantum circuit for their preparation, whose size scales as , where is the number of qudits and is the number of times the total spin‐lowering operator is applied to the highest‐weight state. The algorithm is deterministic and does not require ancillary qudits. 

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5. Precision Bounds on Continuous-Variable State Tomography Using Classical Shadows

   https://doi.org/10.1103/PRXQuantum.5.010346  

   Gandhari, Srilekha; Albert, Victor V.; Gerrits, Thomas; Taylor, Jacob M.; Gullans, Michael J. (March 2024, PRX Quantum 5)

   Shadow tomography is a framework for constructing succinct descriptions of quantum states using randomized measurement bases, called “classical shadows,” with powerful methods to bound the estimators used. We recast existing experimental protocols for continuous-variable quantum state tomography in the classical-shadow framework, obtaining rigorous bounds on the number of independent measurements needed for estimating density matrices from these protocols. We analyze the efficiency of homodyne, heterodyne, photon-number-resolving, and photon-parity protocols. To reach a desired precision on the classical shadow of an N-photon density matrix with high probability, we show that homodyne detection requires order O(N4+1/3) measurements in the worst case, whereas photon-number-resolving and photon-parity detection require O(N4) measurements in the worst case (both up to logarithmic corrections). We benchmark these results against numerical simulation as well as experimental data from optical homodyne experiments. We find that numerical and experimental analyses of homodyne tomography match closely with our theoretical predictions. We extend our single-mode results to an efficient construction of multimode shadows based on local measurements. 

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