Bond distortion effects and electric orders in spiral multiferroic magnets

We study in this paper bond distortion effect on electric polarization in spiral multiferroic magnets based on cluster and chain models. The bond distortion break inversion symmetry and modify the $d$-$p$ hybridization. Consequently, it will affect electric polarization which can be divided into spin-current part and lattice-mediated part. The spin-current polarization can be written in terms of $\vec{e}_{i,j}\times(\vec{e}_{i}\times\vec{e}_{j})$ and the lattice-mediated polarization exists only when the M-O-M bond is distorted. The electric polarization for three-atom M-O-M and four-atom M-O$_{2}$-M clusters is calculated. We also study possible electric ordering in three kinds of chains made of different clusters. We apply our theory to multiferroics cuprates and find that the results are in agreement with experimental observations.Comment: 14 pages, 11 figure

Scalable and Flexible Classical Shadow Tomography with Tensor Networks

Classical shadow tomography is a powerful randomized measurement protocol for predicting many properties of a quantum state with few measurements. Two classical shadow protocols have been extensively studied in the literature: the single-qubit (local) Pauli measurement, which is well suited for predicting local operators but inefficient for large operators; and the global Clifford measurement, which is efficient for low-rank operators but infeasible on near-term quantum devices due to the extensive gate overhead. In this work, we demonstrate a scalable classical shadow tomography approach for generic randomized measurements implemented with finite-depth local Clifford random unitary circuits, which interpolates between the limits of Pauli and Clifford measurements. The method combines the recently proposed locally-scrambled classical shadow tomography framework with tensor network techniques to achieve scalability for computing the classical shadow reconstruction map and evaluating various physical properties. The method enables classical shadow tomography to be performed on shallow quantum circuits with superior sample efficiency and minimal gate overhead and is friendly to noisy intermediate-scale quantum (NISQ) devices. We show that the shallow-circuit measurement protocol provides immediate, exponential advantages over the Pauli measurement protocol for predicting quasi-local operators. It also enables a more efficient fidelity estimation compared to the Pauli measurement.Comment: 15 pages + 1 page appendix, 10 figure

Measurement-Induced Criticality is Tomographically Optimal

We develop a classical shadow tomography protocol utilizing the randomized measurement scheme based on hybrid quantum circuits, which consist of layers of two-qubit random unitary gates mixed with single-qubit random projective measurements. Unlike conventional protocols that perform all measurements by the end of unitary evolutions, our protocol allows measurements to occur at any spacetime position throughout the quantum evolution. We provide a universal classical post-processing strategy to approximately reconstruct the original quantum state from intermittent measurement outcomes given the corresponding random circuit realizations over repeated experiments. We investigated the sample complexity for estimating different observables at different measurement rates of the hybrid quantum circuits. Our result shows that the sample complexity has an optimal scaling at the critical measurement rate when the hybrid circuit undergoes the measurement-induced transition.Comment: 6 pages, 4 figures + 13 pages appendice

Effect of Zicao ointment on second-degree burns in rats

Purpose: To investigate the healing effect of Zicao Ointment (ZCO) on second-degree burns in rats.Methods: Male Sprague Dawley (SD) rats, weighing 200 – 220 g, were subjected to deep seconddegree skin burns by electrical scald instrument. The animals were divided into three groups as follows: (1) second-degree burns (control) group, (2) burns treated with 1 % silver sulfadiazine (SSD) group, and (3) second-degree burns treated with ZCO group. On days 3, 7 and 14 following administration of thedrug or ZCO, wound area and histopathological changes of rat epidermis were evaluated for the various groups.Results: On day 14, mean wound area of ZCO treatment group (0.28 ± 0.04 cm2) was significantly smaller than that of the control rats (2.63 ± 0.19 cm2, p < 0.01). Histological results indicate that inflammatory cells disappeared and were replaced by new granulation tissue by day 14 in the group treated with ZCO. Compared with SSD group rats, the inflammatory cells decreased and fibroblast and granulation tissues increased significantly in burnt rats treated with ZCO.Conclusion: Zicao Ointment is effective for the treatment of second-degree burns in rats and may be suitable for clinical therapy of second-degree burns.Keywords: Zicao ointment, Second-degree burns, Healing, Rat epidermis, Silver sulfadiazin