Learning to predict arbitrary quantum processes

We present an efficient machine learning (ML) algorithm for predicting any unknown quantum process $\mathcal{E}$ over $n$ qubits. For a wide range of distributions $\mathcal{D}$ on arbitrary $n$-qubit states, we show that this ML algorithm can learn to predict any local property of the output from the unknown process $\mathcal{E}$, with a small average error over input states drawn from $\mathcal{D}$. The ML algorithm is computationally efficient even when the unknown process is a quantum circuit with exponentially many gates. Our algorithm combines efficient procedures for learning properties of an unknown state and for learning a low-degree approximation to an unknown observable. The analysis hinges on proving new norm inequalities, including a quantum analogue of the classical Bohnenblust-Hille inequality, which we derive by giving an improved algorithm for optimizing local Hamiltonians. Overall, our results highlight the potential for ML models to predict the output of complex quantum dynamics much faster than the time needed to run the process itself.Comment: 10 pages, 1 figure + 38-page appendix; v2: Added a figure and fixed a minor formatting issu

Lateralized occipito-temporal N1 responses to images of salient distorted finger postures

For humans as social beings, other people’s hands are highly visually conspicuous. Exceptionally striking are hands in other than natural configuration which have been found to elicit distinct brain activation. Here we studied response strength and lateralization of this activation using event-related potentials (ERPs), in particular, occipitotemporal N1 responses as correlates of activation in extrastriate body area. Participants viewed computer-generated images of hands, half of them showing distorted fingers, the other half showing natural fingers. As control stimuli of similar geometric complexity, images of chairs were shown, half of them with distorted legs, half with standard legs. The contrast of interest was between distorted and natural/standard stimuli. For hands, stronger N1 responses were observed for distorted (vs natural) stimuli from 170 ms post stimulus. Such stronger N1 responses were found for distorted hands and absent for distorted chairs, therefore likely unrelated to visuospatial processing of the unusual distorted shapes. Rather, N1 modulation over both hemispheres - but robustly right-lateralized - could reflect distorted hands as emotionally laden stimuli. The results are in line with privileged visual processing of hands as highly salient body parts, with distortions engaging neural resources that are especially activated for biological stimuli in social perception

Retraction and Generalized Extension of Computing with Words

Fuzzy automata, whose input alphabet is a set of numbers or symbols, are a formal model of computing with values. Motivated by Zadeh's paradigm of computing with words rather than numbers, Ying proposed a kind of fuzzy automata, whose input alphabet consists of all fuzzy subsets of a set of symbols, as a formal model of computing with all words. In this paper, we introduce a somewhat general formal model of computing with (some special) words. The new features of the model are that the input alphabet only comprises some (not necessarily all) fuzzy subsets of a set of symbols and the fuzzy transition function can be specified arbitrarily. By employing the methodology of fuzzy control, we establish a retraction principle from computing with words to computing with values for handling crisp inputs and a generalized extension principle from computing with words to computing with all words for handling fuzzy inputs. These principles show that computing with values and computing with all words can be respectively implemented by computing with words. Some algebraic properties of retractions and generalized extensions are addressed as well.Comment: 13 double column pages; 3 figures; to be published in the IEEE Transactions on Fuzzy System

Gender differences in ankylosing spondylitis-associated cumulative healthcare utilization: a population-based cohort study

BACKGROUND: Ankylosing spondylitis (AS) is one of the most common rheumatic diseases with gender differences in prevalence and clinical presentation. This study aimed to examine whether such gender differences are correlated with cumulative healthcare utilization in Taiwan. METHODS: The National Health Insurance Research Database supplied claim records of one million individuals from 1996 to 2007. Selected cases included patients aged >16 years. Certified rheumatologists diagnosed the patients in three or more visits and gave prescriptions for AS. Multivariate adjusted logistic regression analyses were used to calculate the influence of gender on cumulative healthcare utilization associated with AS. RESULTS: The study included 228 women and 636 men. After adjustment for potential confounding factors, men had more cumulative outpatient visits associated with AS (odds ratio, 1.59; 95% confidence interval, 1.13 -2.23; p = 0.008). Men also exhibited a trend for higher frequency of AS-related hospitalization (p = 0.054). CONCLUSION: Men are more likely to have high cumulative AS-associated healthcare utilization than women. Further investigation of the causal factors is warranted

Local minima in quantum systems

Finding ground states of quantum many-body systems is known to be hard for both classical and quantum computers. As a result, when Nature cools a quantum system in a low-temperature thermal bath, the ground state cannot always be found efficiently. Instead, Nature finds a local minimum of the energy. In this work, we study the problem of finding local minima in quantum systems under thermal perturbations. While local minima are much easier to find than ground states, we show that finding a local minimum is computationally hard for classical computers, even when the task is to output a single-qubit observable at any local minimum. In contrast, we prove that a quantum computer can always find a local minimum efficiently using a thermal gradient descent algorithm that mimics the cooling process in Nature. To establish the classical hardness of finding local minima, we consider a family of two-dimensional Hamiltonians such that any problem solvable by polynomial-time quantum algorithms can be reduced to finding ground states of these Hamiltonians. We prove that for such Hamiltonians, all local minima are global minima. Therefore, assuming quantum computation is more powerful than classical computation, finding local minima is classically hard and quantumly easy.Comment: 9+80 pages, 4 figure