Paramagnetic Materials and Practical Algorithmic Cooling for NMR Quantum Computing

Algorithmic Cooling is a method that uses novel data compression techniques and simplecquantum computing devices to improve NMR spectroscopy, and to offer scalable NMR quantum computers. The algorithm recursively employs two steps. A reversible entropy compression of the computation quantum-bits (qubits) of the system and an irreversible heat transfer from the system to the environment through a set of reset qubits that reach thermal relaxation rapidly. Is it possible to experimentally demonstrate algorithmic cooling using existing technology? To allow experimental algorithmic cooling, the thermalization time of the reset qubits must be much shorter than the thermalization time of the computation qubits. However such thermalization-times ratios have yet to be reported. We investigate here the effect of a paramagnetic salt on the thermalization-times ratio of computation qubits (carbons) and a reset qubit (hydrogen). We show that the thermalization-times ratio is improved by approximately three-fold. Based on this result, an experimental demonstration of algorithmic cooling by thermalization and magnetic ions is currently performed by our group and collaborators.Comment: 5 pages, A conference version of this paper appeared in SPIE, volume 5105, pages 185-194 (2003

New, Highly Accurate Propagator for the Linear and Nonlinear Schr\"odinger Equation

A propagation method for the time dependent Schr\"odinger equation was studied leading to a general scheme of solving ode type equations. Standard space discretization of time-dependent pde's usually results in system of ode's of the form u_t -Gu = s where G is a operator (matrix) and u is a time-dependent solution vector. Highly accurate methods, based on polynomial approximation of a modified exponential evolution operator, had been developed already for this type of problems where G is a linear, time independent matrix and s is a constant vector. In this paper we will describe a new algorithm for the more general case where s is a time-dependent r.h.s vector. An iterative version of the new algorithm can be applied to the general case where G depends on t or u. Numerical results for Schr\"odinger equation with time-dependent potential and to non-linear Schr\"odinger equation will be presented.Comment: 14 page

Chaotic Quivering of Micron-Scaled On-Chip Resonators Excited by Centrifugal Optical Pressure

Opto-mechanical chaotic oscillation of an on-chip resonator is excited by the radiation-pressure nonlinearity. Continuous optical input, with no external feedback or modulation, excites chaotic vibrations in very different geometries of the cavity (both tori and spheres) and shows that opto-mechanical chaotic oscillations are an intrinsic property of optical microcavities. Measured phenomena include period doubling, a spectral continuum, aperiodic oscillations, and complex trajectories. The rate of exponential divergence from a perturbed initial condition (Lyapunov exponent) is calculated. Continuous improvements in cavities mean that such chaotic oscillations can be expected in the future with many other platforms, geometries, and frequency spans

Pinpointing the massive black hole in the Galactic Center with gravitationally lensed stars

A new statistical method for pinpointing the massive black hole (BH) in the Galactic Center on the IR grid is presented and applied to astrometric IR observations of stars close to the BH. This is of interest for measuring the IR emission from the BH, in order to constrain accretion models; for solving the orbits of stars near the BH, in order to measure the BH mass and to search for general relativistic effects; and for detecting the fluctuations of the BH away from the dynamical center of the stellar cluster, in order to study the stellar potential. The BH lies on the line connecting the two images of any background source it gravitationally lenses, and so the intersection of these lines fixes its position. A combined search for a lensing signal and for the BH shows that the most likely point of intersection coincides with the center of acceleration of stars orbiting the BH. This statistical detection of lensing by the BH has a random probability of ~0.01. It can be verified by deep IR stellar spectroscopy, which will determine whether the most likely lensed image pair candidates (listed here) have identical spectra.Comment: 4 pages, 2 figures, submitted to ApJ

Algorithmic Cooling of Spins: A Practicable Method for Increasing Polarization

An efficient technique to generate ensembles of spins that are highly polarized by external magnetic fields is the Holy Grail in Nuclear Magnetic Resonance (NMR) spectroscopy. Since spin-half nuclei have steady-state polarization biases that increase inversely with temperature, spins exhibiting high polarization biases are considered cool, even when their environment is warm. Existing spin-cooling techniques are highly limited in their efficiency and usefulness. Algorithmic cooling is a promising new spin-cooling approach that employs data compression methods in open systems. It reduces the entropy of spins on long molecules to a point far beyond Shannon's bound on reversible entropy manipulations (an information-theoretic version of the 2nd Law of Thermodynamics), thus increasing their polarization. Here we present an efficient and experimentally feasible algorithmic cooling technique that cools spins to very low temperatures even on short molecules. This practicable algorithmic cooling could lead to breakthroughs in high-sensitivity NMR spectroscopy in the near future, and to the development of scalable NMR quantum computers in the far future. Moreover, while the cooling algorithm itself is classical, it uses quantum gates in its implementation, thus representing the first short-term application of quantum computing devices.Comment: 24 pages (with annexes), 3 figures (PS). This version contains no major content changes: fixed bibliography & figures, modified acknowledgement

Deep Functional Maps: Structured Prediction for Dense Shape Correspondence

We introduce a new framework for learning dense correspondence between deformable 3D shapes. Existing learning based approaches model shape correspondence as a labelling problem, where each point of a query shape receives a label identifying a point on some reference domain; the correspondence is then constructed a posteriori by composing the label predictions of two input shapes. We propose a paradigm shift and design a structured prediction model in the space of functional maps, linear operators that provide a compact representation of the correspondence. We model the learning process via a deep residual network which takes dense descriptor fields defined on two shapes as input, and outputs a soft map between the two given objects. The resulting correspondence is shown to be accurate on several challenging benchmarks comprising multiple categories, synthetic models, real scans with acquisition artifacts, topological noise, and partiality.Comment: Accepted for publication at ICCV 201

Hidden Convexity in Partially Separable Optimization

The paper identifies classes of nonconvex optimization problems whose convex relaxations have optimal solutions which at the same time are global optimal solutions of the original nonconvex problems. Such a hidden convexity property was so far limited to quadratically constrained quadratic problems with one or two constraints. We extend it here to problems with some partial separable structure. Among other things, the new hidden convexity results open up the possibility to solve multi-stage robust optimization problems using certain nonlinear decision rules.convex relaxation of nonconvex problems;hidden convexity;partially separable functions;robust optimization

Erbium-doped and Raman microlasers on a silicon chip fabricated by the sol–gel process

We report high-Q sol–gel microresonators on silicon chips, fabricated directly from a sol–gel layer deposited onto a silicon substrate. Quality factors as high as 2.5×10^7 at 1561 nm were obtained in toroidal microcavities formed of silica sol–gel, which allowed Raman lasing at absorbed pump powers below 1 mW. Additionally, Er3+-doped microlasers were fabricated from Er3+-doped sol–gel layers with control of the laser dynamics possible by varying the erbium concentration of the starting sol–gel material. Continuous lasing with a threshold of 660 nW for erbium-doped microlaser was also obtained