Following the discovery of long-range antiferromagnetic order in the parent compounds of high-transition-temperature (high-Tc) copper oxides, there have been efforts to understand the role of magnetism in the superconductivity that occurs when mobile ‘electrons’ or ‘holes’ are doped into the antiferromagnetic parent compounds. Superconductivity in the newly discovered rare-earth iron-based oxide systems ROFeAs (R, rare-earth metal) also arises from either electron or hole doping of their non-superconducting parent compounds. The parent material LaOFeAs is metallic but shows anomalies near 150 K in both resistivity and d.c. magnetic susceptibility. Although optical conductivity and theoretical calculations suggest that LaOFeAs exhibits a spin-density-wave (SDW) instability that is suppressed by doping with electrons to induce superconductivity, there has been no direct evidence of SDW order. Here we report neutron-scattering experiments that demonstrate that LaOFeAs undergoes an abrupt structural distortion below 155 K, changing the symmetry from tetragonal (space group P4/nmm) to monoclinic (space group P112/n) at low temperatures, and then, at ∼137 K, develops long-range SDW-type antiferromagnetic order with a small moment but simple magnetic structure. Doping the system with fluorine suppresses both the magnetic order and the structural distortion in favour of superconductivity. Therefore, like high-Tc copper oxides, the superconducting regime in these iron-based materials occurs in close proximity to a long-range-ordered antiferromagnetic ground state.
In this paper, we construct a generalized Darboux transformation for the nonlinear Schrödinger equation. The associated N-fold Darboux transformation is given in terms of both a summation formula and determinants. As applications, we obtain compact representations for the Nth-order rogue wave solutions of the focusing nonlinear Schrödinger equation and Hirota equation. In particular, the dynamics of the general third-order rogue wave is discussed and shown to exhibit interesting structures.
This primer serves two functions: (1) It is a simplified introduction to Q methodology, covering the topics of concourse, Q samples, Q sorting, correlation, factor analysis, theoretical rotation, factor scores, and factor interpretation. (2) It also illustrates different conceptions of Q methodology by taking the concept of "Q methodology" as the subject matter of the study. The factor results show how current understandings about Q are traceable to debates among Stephenson, Burt, and others in the 1930s, '40s, and '50s.
Subwavelength confinement of light with plasmonics is promising for nanophotonics and optoelectronics. However, it is nontrivial to obtain narrow plasmonic resonances due to the intrinsically high optical losses and radiative damping in metallic structures. In this review, a thorough summary of the recent research progress on achieving high‐quality (high‐Q) factor plasmonic resonances is provided, emphasizing the fundamentals and six resonant mode types, including surface lattice resonances, multipolar resonances, plasmonic Fano resonances, plasmon‐induced transparency, guided‐mode resonances, and Tamm plasmon resonances. The applications of high‐Q plasmonic resonances in spectrally selective thermal emission, sensing, single‐photon emission, filtering, and band‐edge lasing are also discussed.
Iordanis Kerenidis, Jonas Landman, Alessandro Luongo
et al.
Quantum machine learning is one of the most promising applications of a full-scale quantum computer. Over the past few years, many quantum machine learning algorithms have been proposed that can potentially offer considerable speedups over the corresponding classical algorithms. In this paper, we introduce q-means, a new quantum algorithm for clustering which is a canonical problem in unsupervised machine learning. The $q$-means algorithm has convergence and precision guarantees similar to $k$-means, and it outputs with high probability a good approximation of the $k$ cluster centroids like the classical algorithm. Given a dataset of $N$ $d$-dimensional vectors $v_i$ (seen as a matrix $V \in \mathbb{R}^{N \times d})$ stored in QRAM, the running time of q-means is $\widetilde{O}\left( k d \frac{\eta}{\delta^2}\kappa(V)(\mu(V) + k \frac{\eta}{\delta}) + k^2 \frac{\eta^{1.5}}{\delta^2} \kappa(V)\mu(V) \right)$ per iteration, where $\kappa(V)$ is the condition number, $\mu(V)$ is a parameter that appears in quantum linear algebra procedures and $\eta = \max_{i} ||v_{i}||^{2}$. For a natural notion of well-clusterable datasets, the running time becomes $\widetilde{O}\left( k^2 d \frac{\eta^{2.5}}{\delta^3} + k^{2.5} \frac{\eta^2}{\delta^3} \right)$ per iteration, which is linear in the number of features $d$, and polynomial in the rank $k$, the maximum square norm $\eta$ and the error parameter $\delta$. Both running times are only polylogarithmic in the number of datapoints $N$. Our algorithm provides substantial savings compared to the classical $k$-means algorithm that runs in time $O(kdN)$ per iteration, particularly for the case of large datasets.
Takuya Hiraoka, Takahisa Imagawa, Taisei Hashimoto
et al.
Randomized ensembled double Q-learning (REDQ) (Chen et al., 2021b) has recently achieved state-of-the-art sample efficiency on continuous-action reinforcement learning benchmarks. This superior sample efficiency is made possible by using a large Q-function ensemble. However, REDQ is much less computationally efficient than non-ensemble counterparts such as Soft Actor-Critic (SAC) (Haarnoja et al., 2018a). To make REDQ more computationally efficient, we propose a method of improving computational efficiency called DroQ, which is a variant of REDQ that uses a small ensemble of dropout Q-functions. Our dropout Q-functions are simple Q-functions equipped with dropout connection and layer normalization. Despite its simplicity of implementation, our experimental results indicate that DroQ is doubly (sample and computationally) efficient. It achieved comparable sample efficiency with REDQ, much better computational efficiency than REDQ, and comparable computational efficiency with that of SAC.
Abstract By examining asymptotic behavior of certain infinite basic (q-) hypergeometric sums at roots of unity (that is, at a ‘q-microscopic’ level) we prove polynomial congruences for their truncations. The latter reduce to non-trivial (super)congruences for truncated ordinary hypergeometric sums, which have been observed numerically and proven rarely. A typical example includes derivation, from a q-analogue of Ramanujan's formula ∑ n = 0 ∞ ( 4 n 2 n ) ( 2 n n ) 2 2 8 n 3 2 n ( 8 n + 1 ) = 2 3 π , of the two supercongruences S ( p − 1 ) ≡ p ( − 3 p ) ( mod p 3 ) and S ( p − 1 2 ) ≡ p ( − 3 p ) ( mod p 3 ) , valid for all primes p > 3 , where S ( N ) denotes the truncation of the infinite sum at the N-th place and ( − 3 ⋅ ) stands for the quadratic character modulo 3.