Finding the ground states of the Ising Hamiltonian [1] maps to various combinatorial optimization problems in biology, medicine, wireless communications, artificial intelligence, and social network. So far no efficient classical and quantum algorithm
is known for these problems, and intensive research is focused on creating physical systems - Ising machines - capable of finding the absolute or approximate ground states of the Ising Hamiltonian [2-6]. Here we report a novel Ising machine using a network of degenerate optical parametric oscillators (OPOs). Spins are represented with above-threshold binary phases of the OPOs and the Ising couplings are realized by mutual injections [7]. The network is implemented in a single OPO ring cavity with multiple trains of femtosecond pulses and configurable mutual couplings, and operates at room temperature. We programed the smallest non-deterministic polynomial time (NP)- hard Ising problem on the machine, and in 1000 runs of the machine no computational error was detected.
Magnetic excitations in the isostructural spin-dimer systems Sr3Cr2O8 and Ba3Cr2O8 are probed by means of high-field electron spin resonance at sub-terahertz frequencies. Three types of magnetic modes were observed. One mode is gapless and correspond
s to transitions within excited states, while two other sets of modes are gapped and correspond to transitions from the ground to the first excited states. The selection rules of the gapped modes are analyzed in terms of a dynamical Dzyaloshinskii-Moriya interaction, suggesting the presence of phonon-assisted effects in the low-temperature spin dynamics of Sr3Cr2O8 and Ba3Cr2O8
We report on optical transmission spectroscopy of the Cr-based frustrated triangular antiferromagnets CuCrO2 and alpha-CaCr2O4, and the spinels CdCr2O4 and ZnCr2O4 in the near-infrared to visible-light frequency range. We explore the possibility to s
earch for spin correlations far above the magnetic ordering temperature and for anomalies in the magnon lifetime in the magnetically ordered state by probing exciton-magnon sidebands of the spin-forbidden crystal-field transitions of the Cr3+ ions (spin S = 3/2). In CuCrO2 and alpha-CaCr2O4 the appearance of fine structures below T_N is assigned to magnon sidebands by comparison with neutron scattering results. The temperature dependence of the line width of the most intense sidebands in both compounds can be described by an Arrhenius law. For CuCrO2 the sideband associated with the 4A2 -> 2T2 transition can be observed even above T_N. Its line width does not show a kink at the magnetic ordering temperature and can alternatively be described by a Z2 vortex scenario proposed previously for similar materials. The exciton-magnon features in alpha-CaCr2O4 are more complex due to the orthorhombic distortion. While for CdCr2O4 magnon sidebands are identified below T_N and one sideband excitation is found to persist across the magnetic ordering transition, only a weak fine structure related to magnetic ordering has been observed in ZnCr2O4.
We report clear observations of the magnetic Meissner effect in arrays of superconducting 4 {AA} carbon nanotubes grown in the linear channels of AlPO4-5 (AFI) zeolite single crystals. Both bulk magnetization and magnetic torque experiments show a cl
ear signature of the lower critical Hc1 transition, a pronounced difference in zero-field cooled and field cooled branches during temperature sweeps below 6K, and signatures of 1D superconducting fluctuations below ~15-18 K. These experiments extend the magnetic phase diagram we obtained previously by resistive experiments [Z. Wang et al., Phys. Rev. B 81, 174530 (2010)] towards low magnetic fields and within the range of zero resistance.
We present a joint source-channel multiple description (JSC-MD) framework for resource-constrained network communications (e.g., sensor networks), in which one or many deprived encoders communicate a Markov source against bit errors and erasure error
s to many heterogeneous decoders, some powerful and some deprived. To keep the encoder complexity at minimum, the source is coded into K descriptions by a simple multiple description quantizer (MDQ) with neither entropy nor channel coding. The code diversity of MDQ and the path diversity of the network are exploited by decoders to correct transmission errors and improve coding efficiency. A key design objective is resource scalability: powerful nodes in the network can perform JSC-MD distributed estimation/decoding under the criteria of maximum a posteriori probability (MAP) or minimum mean-square error (MMSE), while primitive nodes resort to simpler MD decoding, all working with the same MDQ code. The application of JSC-MD to distributed estimation of hidden Markov models in a sensor network is demonstrated. The proposed JSC-MD MAP estimator is an algorithm of the longest path in a weighted directed acyclic graph, while the JSC-MD MMSE decoder is an extension of the well-known forward-backward algorithm to multiple descriptions. Both algorithms simultaneously exploit the source memory, the redundancy of the fixed-rate MDQ, and the inter-description correlations. They outperform the existing hard-decision MDQ decoders by large margins (up to 8dB). For Gaussian Markov sources, the complexity of JSC-MD distributed MAP sequence estimation can be made as low as that of typical single description Viterbi-type algorithms.
