**A**s it rarely happens with Nature, I just read an article that directly relates to my research interests, about a secure physical random number generator (RNG). By Peter Bierhost and co-authors, mostly physicists apparently. Security here means that the outcome of the RNG is unpredictable. This very peculiar RNG is based on two correlated photons sent to two measuring stations, separated by at least 187m, which have to display unpredictable outcomes in order to respect the impossibility of faster-than-light communications, otherwise known as Bell inequalities. This is hardly practical though, especially when mentioning that the authors managed to produce 2¹⁰ random bits over 10 minutes, post processing “the measurement of 55 million photon pairs”. (I however fail to see why the two-arm apparatus would be needed for regular random generation as it seems relevant solely for the demonstration of randomness.) I also checked the associated supplementary material, which is mostly about proving some total variation bound, and constructing a Bell function. What is most puzzling in this paper (and the associated supplementary material) is the (apparent) lack of guarantee of uniformity of the RNG. For instance, a sentence (Supplementary Material, p.11) about a distribution being “within TV distance of uniform” hints at the method being not provably uniform, which makes the whole exercise incomprehensible…

## Archive for quantum computers

## certified randomness, 187m away…

Posted in Statistics with tags Bell inequality, Nature, quantum computers, random number generation, randomness, RNG, total variation, uniformity test on May 3, 2018 by xi'an## Nature snapshots [and snide shots]

Posted in Books, pictures, Statistics, Travel, University life with tags Bayesian inference, Boltzmann machines, corrigendum, machine learning, Nature, neural network, principal components, quantum computers, quantum comuting, statues, typewriter, Vienna on October 12, 2017 by xi'an**A** very rich issue of Nature I received [late] just before leaving for Warwick with a series of reviews on quantum computing, presenting machine learning as the most like immediate application of this new type of computing. Also including irate letters and an embarassed correction of an editorial published the week before reflecting on the need (or lack thereof) to remove or augment statues of scientists whose methods were unethical, even when eventually producing long lasting advances. (Like the 19th Century gynecologist J. Marion Sims experimenting on female slaves.) And a review of a book on the fascinating topic of Chinese typewriters. And this picture above of a flooded playground that looks like a piece of abstract art thanks to the muddy background.

“Quantum mechanics is well known to produce atypical patterns in data. Classical machine learning methods such as deep neural networks frequently have the feature that they can both recognize statistical patterns in data and produce data that possess the same statistical patterns: they recognize the patterns that they produce. This observation suggests the following hope. If small quantum information processors can produce statistical patterns that are computationally difficult for a classical computer to produce, then perhaps they can also recognize patterns that are equally difficult to recognize classically.”Jacob Biamonte et al., Nature, 14 Sept 2017

One of the review papers on quantum computing is about quantum machine learning. Although like Jon Snow I know nothing about this, I find it rather dull as it spends most of its space on explaining existing methods like PCA and support vector machines. Rather than exploring potential paradigm shifts offered by the exotic nature of quantum computing. Like moving to Bayesian logic that mimics a whole posterior rather than produces estimates or model probabilities. And away from linear representations. (The paper mentions a O(√N) speedup for Bayesian inference in a table, but does not tell more, which may thus be only about MAP estimators for all I know.) I also disagree with the brave new World tone of the above quote or misunderstand its meaning. Since atypical and statistical cannot but clash, “universal deep quantum learners may recognize and classify patterns that classical computers cannot” does not have a proper meaning. The paper contains a vignette about quantum Boltzman machines that finds a minimum entropy approximation to a four state distribution, with comments that seem to indicate an ability to simulate from this system.

## oxwasp@amazon.de

Posted in Books, Kids, pictures, Running, Statistics, Travel, University life with tags Amazon, Berlin, bier, Brauhaus Lemke, doubly intractable problems, Germany, Google, Ising model, machine learning, normalising constant, optimisation, OxWaSP, quantum computers, Spree, Stadtmitte, University of Oxford, University of Warwick, workshop on April 12, 2017 by xi'an**T**he reason for my short visit to Berlin last week was an OxWaSP (Oxford and Warwick Statistics Program) workshop hosted by Amazon Berlin with talks between statistics and machine learning, plus posters from our second year students. While the workshop was quite intense, I enjoyed very much the atmosphere and the variety of talks there. (Just sorry that I left too early to enjoy the social programme at a local brewery, Brauhaus Lemke, and the natural history museum. But still managed nice runs east and west!) One thing I found most interesting (if obvious in retrospect) was the different focus of academic and production talks, where the later do not aim at a full generality or at a guaranteed improvement over the existing, provided the new methodology provides a gain in efficiency over the existing.

This connected nicely with me reading several Nature articles on quantum computing during that trip, where researchers from Google predict commercial products appearing in the coming five years, even though the technology is far from perfect and the outcome qubit error prone. Among the examples they provided, quantum simulation (not meaning what I consider to be *simulation*!), quantum optimisation (as a way to overcome multimodality), and quantum sampling (targeting given probability distributions). I find the inclusion of the latest puzzling in that simulation (in that sense) shows very little tolerance for errors, especially systematic bias. It may be that specific quantum architectures can be designed for specific probability distributions, just like some are already conceived for optimisation. (It may even be the case that quantum solutions are (just next to) available for intractable constants as in Ising or Potts models!)

## Nature snapshot

Posted in Statistics with tags @ScientistTrump, algorithmic policing, D-wave, Elsevier, Nature, quantum computers, R, scientific computing on March 5, 2017 by xi'an** T**he recent issue of Nature, as of Jan 26, 2017!, contained a cartload of interesting review and coverage articles, from the latest version of the quantum computer D-Wave, with a paragraph on quantum annealing that reminded me of a recent arXiv paper I could not understand, seemingly turning the mathematical problem of multivariate optimisation into a truly physical process, to the continuing (Nature-wise) debate on how to oppose Trump, to the biases and shortcomings of policing software, with a mention of Lum and Isaac I discussed here a few months ago, to the unsuspected difficulty to publish a referee’s report when the publisher is Elsevier (unsuspected and unsurprising!)—although I know of colleagues and authors disapproving my publishing referee’s reports identified as such—, to an amazing picture of a bundle of neurons monitored simultaneously, to an entry in the career section on scientific computing and the importance of coding for young investigators, with R at the forefront!

## quantic random generators

Posted in Books, Statistics with tags Bell inequality, hardware random generator, Nature, quantum computers, quantum physics, random number generator on January 5, 2017 by xi'an

“…the random numbers should be unpredictable by any physical observer, that is, any observer whose actions are constrained by the laws of physics.”

**A** review paper in Nature by Acin and Masanes is the first paper I ever read there about random number generation! The central debate in the paper is about the notion of randomness, which the authors qualify as above. This seems to exclude the use of “our” traditional random number generators, although I do not see why they could not be used with an unpredictable initialisation, which does not have to be done according to a specific probability distribution. The only thing that matters is unpredictability.

“…the standard method for certifying randomness consists of running statistical tests^{1}on sequences generated by the device. However, it is unclear what passing these tests means and, in fact, it is impossible to certify with finite computational power that a given sequence is random.”

The paper supports instead physical and quantum devices. Justified or certified by [violations of] the Bell inequality, which separates classic from quantum. Not that I know anything about this. Or that I can make sense of the notations in the paper, like

which is supposed to translate that the bits are iid Uniform and independent of the environment. Actually, I understood very little of the entire review paper, which is quite frustrating since this may well be the only paper ever published in Nature about random number generation!

“…a generation rate of 42 random bits after approximately one month of measurements, was performed using two entangled ions in two traps at 1-m distance.”

It is also hard to tell whether or not this approach to quantum random number generation has foreseeable practical consequences. There already exist QRNGs, as shown by this example from ANU. And this much more readable review.