Prospects and Limitations of Algorithmic Cooling

Heat-bath algorithmic cooling (AC) of spins is a theoretically powerful effective cooling approach, that (ideally) cools spins with low polarization exponentially better than cooling by reversible entropy manipulations alone. Here, we investigate the limitations and prospects of AC. For non-ideal and semioptimal AC, we study the impact of finite relaxation times of reset and computation spins on the achievable effective cooling. We derive, via simulations, the attainable cooling levels for given ratios of relaxation times using two semioptimal practicable algorithms. We expect this analysis to be valuable for the planning of future experiments. For ideal and optimal AC, we make use of lower bounds on the number of required reset steps, based on entropy considerations, to present important consequences of using AC as a tool for improving signal-to-noise ratio in liquid-state magnetic resonance spectroscopy. We discuss the potential use of AC for noninvasive clinical diagnosis and drug monitoring, where it may have significantly lower specific absorption rate (SAR) with respect to currently used methods.Comment: 12 pages, 5 figure

Semi-optimal Practicable Algorithmic Cooling

Algorithmic Cooling (AC) of spins applies entropy manipulation algorithms in open spin-systems in order to cool spins far beyond Shannon's entropy bound. AC of nuclear spins was demonstrated experimentally, and may contribute to nuclear magnetic resonance (NMR) spectroscopy. Several cooling algorithms were suggested in recent years, including practicable algorithmic cooling (PAC) and exhaustive AC. Practicable algorithms have simple implementations, yet their level of cooling is far from optimal; Exhaustive algorithms, on the other hand, cool much better, and some even reach (asymptotically) an optimal level of cooling, but they are not practicable. We introduce here semi-optimal practicable AC (SOPAC), wherein few cycles (typically 2-6) are performed at each recursive level. Two classes of SOPAC algorithms are proposed and analyzed. Both attain cooling levels significantly better than PAC, and are much more efficient than the exhaustive algorithms. The new algorithms are shown to bridge the gap between PAC and exhaustive AC. In addition, we calculated the number of spins required by SOPAC in order to purify qubits for quantum computation. As few as 12 and 7 spins are required (in an ideal scenario) to yield a mildly pure spin (60% polarized) from initial polarizations of 1% and 10%, respectively. In the latter case, about five more spins are sufficient to produce a highly pure spin (99.99% polarized), which could be relevant for fault-tolerant quantum computing.Comment: 13 pages, 5 figure

Extreme 3D Face Reconstruction: Seeing Through Occlusions

Existing single view, 3D face reconstruction methods can produce beautifully detailed 3D results, but typically only for near frontal, unobstructed viewpoints. We describe a system designed to provide detailed 3D reconstructions of faces viewed under extreme conditions, out of plane rotations, and occlusions. Motivated by the concept of bump mapping, we propose a layered approach which decouples estimation of a global shape from its mid-level details (e.g., wrinkles). We estimate a coarse 3D face shape which acts as a foundation and then separately layer this foundation with details represented by a bump map. We show how a deep convolutional encoder-decoder can be used to estimate such bump maps. We further show how this approach naturally extends to generate plausible details for occluded facial regions. We test our approach and its components extensively, quantitatively demonstrating the invariance of our estimated facial details. We further provide numerous qualitative examples showing that our method produces detailed 3D face shapes in viewing conditions where existing state of the art often break down.Comment: Accepted to CVPR'18. Previously titled: "Extreme 3D Face Reconstruction: Looking Past Occlusions

Decision-Making and the Newsvendor Problem – An Experimental Study

This paper investigates repetitive purchase decisions of perishable items in the face of uncertain demand (the newsvendor problem). The experimental design includes: high, or low profit levels; and uniform, or normal demand distributions. The results show that in all cases both learning and convergence occur and are effected by: (1) the mean demand; (2) the order-size of the maximal expected profit; and (3) the demand level of the immediately preceding round. In all cases of the experimental design, the purchase order converges to a value between the mean demand and the quantity for maximizing the expected profit.Inventory, Learning, Behavior, Management, Optimization

On Face Segmentation, Face Swapping, and Face Perception

We show that even when face images are unconstrained and arbitrarily paired, face swapping between them is actually quite simple. To this end, we make the following contributions. (a) Instead of tailoring systems for face segmentation, as others previously proposed, we show that a standard fully convolutional network (FCN) can achieve remarkably fast and accurate segmentations, provided that it is trained on a rich enough example set. For this purpose, we describe novel data collection and generation routines which provide challenging segmented face examples. (b) We use our segmentations to enable robust face swapping under unprecedented conditions. (c) Unlike previous work, our swapping is robust enough to allow for extensive quantitative tests. To this end, we use the Labeled Faces in the Wild (LFW) benchmark and measure the effect of intra- and inter-subject face swapping on recognition. We show that our intra-subject swapped faces remain as recognizable as their sources, testifying to the effectiveness of our method. In line with well known perceptual studies, we show that better face swapping produces less recognizable inter-subject results. This is the first time this effect was quantitatively demonstrated for machine vision systems

Experimental Heat-Bath Cooling of Spins

Algorithmic cooling (AC) is a method to purify quantum systems, such as ensembles of nuclear spins, or cold atoms in an optical lattice. When applied to spins, AC produces ensembles of highly polarized spins, which enhance the signal strength in nuclear magnetic resonance (NMR). According to this cooling approach, spin-half nuclei in a constant magnetic field are considered as bits, or more precisely, quantum bits, in a known probability distribution. Algorithmic steps on these bits are then translated into specially designed NMR pulse sequences using common NMR quantum computation tools. The $algorithmic$ cooling of spins is achieved by alternately combining reversible, entropy-preserving manipulations (borrowed from data compression algorithms) with $selective$ $reset$, the transfer of entropy from selected spins to the environment. In theory, applying algorithmic cooling to sufficiently large spin systems may produce polarizations far beyond the limits due to conservation of Shannon entropy. Here, only selective reset steps are performed, hence we prefer to call this process "heat-bath" cooling, rather than algorithmic cooling. We experimentally implement here two consecutive steps of selective reset that transfer entropy from two selected spins to the environment. We performed such cooling experiments with commercially-available labeled molecules, on standard liquid-state NMR spectrometers. Our experiments yielded polarizations that $bypass$ $Shannon's$ $entropy$-$conservation$ $bound$, so that the entire spin-system was cooled. This paper was initially submitted in 2005, first to Science and then to PNAS, and includes additional results from subsequent years (e.g. for resubmission in 2007). The Postscriptum includes more details.Comment: 20 pages, 8 figures, replaces quant-ph/051115

The Effects of Fault Roughness on the Earthquake Nucleation Process

We study numerically the effects of fault roughness on the nucleation process during earthquake sequences. The faults are governed by a rate and state friction law. The roughness introduces local barriers that complicate the nucleation process and result in asymmetric expansion of the rupture, nonmonotonic increase in the slip rates on the fault, and the generation of multiple slip pulses. These complexities are reflected as irregular fluctuations in the moment rate. There is a large difference between first slip events in the sequences and later events. In the first events, for roughness amplitude b_r ≤ 0.002, there is a large increase in the nucleation length with increasing br. For larger values of b_r, slip is mostly aseismic. For the later events there is a trade-off between the effects of the finite fault length and the fault roughness. For b_r ≤ 0.002, the finite length is a more dominant factor and the nucleation length barely changes with br. For larger values of b_r, the roughness plays a larger role and the nucleation length increases significantly with b_r. Using an energy balance approach, where the roughness is accounted for in the fault stiffness, we derive an approximate solution for the nucleation length on rough faults. The solution agrees well with the main trends observed in the simulations for the later events and provides an estimate of the frictional and roughness properties under which faults experience a transition between seismic and aseismic slip