Preparing thermal states of quantum systems by dimension reduction

We present an algorithm that prepares thermal Gibbs states of one dimensional quantum systems on a quantum computer without any memory overhead, and in a time significantly shorter than other known alternatives. Specifically, the time complexity is dominated by the quantity $N^{\|h\|/ T}$, where $N$ is the size of the system, $\|h\|$ is a bound on the operator norm of the local terms of the Hamiltonian (coupling energy), and $T$ is the temperature. Given other results on the complexity of thermalization, this overall scaling is likely optimal. For higher dimensions, our algorithm lowers the known scaling of the time complexity with the dimension of the system by one.Comment: Published version. Minor editorial changes, one new reference added. 4 pages, 1 figur

Secrecy Capacity of a Class of Broadcast Channels with an Eavesdropper

We study the security of communication between a single transmitter and multiple receivers in a broadcast channel in the presence of an eavesdropper. We consider several special classes of channels. As the first model, we consider the degraded multi-receiver wiretap channel where the legitimate receivers exhibit a degradedness order while the eavesdropper is more noisy with respect to all legitimate receivers. We establish the secrecy capacity region of this channel model. Secondly, we consider the parallel multi-receiver wiretap channel with a less noisiness order in each sub-channel, where this order is not necessarily the same for all sub-channels. We establish the common message secrecy capacity and sum secrecy capacity of this channel. Thirdly, we study a special class of degraded parallel multi-receiver wiretap channels and provide a stronger result. In particular, we study the case with two sub-channels two users and one eavesdropper, where there is a degradedness order in each sub-channel such that in the first (resp. second) sub-channel the second (resp. first) receiver is degraded with respect to the first (resp. second) receiver, while the eavesdropper is degraded with respect to both legitimate receivers in both sub-channels. We determine the secrecy capacity region of this channel. Finally, we focus on a variant of this previous channel model where the transmitter can use only one of the sub-channels at any time. We characterize the secrecy capacity region of this channel as well.Comment: Submitted to EURASIP Journal on Wireless Communications and Networking (Special Issue on Wireless Physical Layer Security

Range separated hybrid exchange-correlation functional analyses of W and/or N(S) (co)doped anatase TiO_2

Electronic properties and atomic structures of W, N, S, W/N, and W/S dopings of anatase TiO_2 have been systematically investigated using the density functional theory (DFT). The exchange and correlation effects have been treated with Heyd, Scuseria and Ernzerhof (HSE) hybrid functional. Mixing traditional semi-local and non-local screened Hartree-Fock (HF) exchange energies, the HSE method corrects the band gap and also improves the description of anion/cation derived gap states. Enhanced charge carrier dynamics, observed for W/N codoped titania, can partly be explained by the passivative modifications of N 2p and W 5d states on its electronic structure. Following this trend we have found an apparent band gap narrowing of 1.03 eV for W/S codoping. This is due to the large dispersion of S 3p states at the valance band (VB) top extending its edge to higher energies and Ti--S--W hybridized states appearing at the bottom of the conduction band (CB). W/S-TiO_2 might show strong visible light response comparable to W/N codoped anatase catalysts.Comment: 8 pages, 5 figures and 3 table

Anyonic entanglement renormalization

We introduce a family of variational ansatz states for chains of anyons which optimally exploits the structure of the anyonic Hilbert space. This ansatz is the natural analog of the multi-scale entanglement renormalization ansatz for spin chains. In particular, it has the same interpretation as a coarse-graining procedure and is expected to accurately describe critical systems with algebraically decaying correlations. We numerically investigate the validity of this ansatz using the anyonic golden chain and its relatives as a testbed. This demonstrates the power of entanglement renormalization in a setting with non-abelian exchange statistics, extending previous work on qudits, bosons and fermions in two dimensions.Comment: 19 pages, 10 figures, v2: extended, updated to match published versio

Coarse grained belief propagation for simulation of interacting quantum systems at all temperatures

We continue our numerical study of quantum belief propagation initiated in [Phys. Rev. A, 77 (2008), p. 052318]. We demonstrate how the method can be expressed in terms of an effective thermal potential that materializes when the system presents quantum correlations, but is insensitive to classical correlations. The thermal potential provides an efficient means to assess the precision of belief propagation on graphs with no loops. We illustrate these concepts using the one-dimensional quantum Ising model and compare our results with exact solutions. We also use the method to study the transverse field quantum Ising spin glass for which we obtain a phase diagram that is largely in agreement with the one obtained in [arXiv:0706.4391] using a different approach. Finally, we introduce the coarse grained belief propagation (CGBP) algorithm to improve belief propagation at low temperatures. This method combines the reliability of belief propagation at high temperatures with the ability of entanglement renormalization to efficiently describe low energy subspaces of quantum systems with local interactions. With CGBP, thermodynamic properties of quantum systems can be calculated with a high degree of accuracy at all temperatures.Comment: updated references and acknowledgement