arXiv highlights

Here are some papers that caught my eye over the past month:

Germain Curvature: The Case for Naming the Mean Curvature of a Surface after Sophie Germain

This essay argues that the intrinsic curvature of a surface, aka the Gaussian curvature, should be named instead the Germain curvature, since Gauss was not the first to study it.

I remember attending a lecture by Sir Michael Berry (of Berry phase fame) where he made a compelling argument against naming new objects or effects after people, on account of the three "Laws of Discovery":

"1. Discoveries are rarely attributed to the correct person

2.Nothing is ever discovered for the first time

3. To come near to a true theory, and to grasp its precise application, are two very different things, as the history of science teaches us. Everything of importance has been said before by someone who did not discover it."

Indeed, versions of the Berry phase had been previously decades before Berry, by Pancharatnam, Rytov, and others. For this reason he prefers the name "geometric phase." Similarly, intrinsic curvature is perhaps a more suitable alternative to Gaussian curvature.

The problem with naming effects after people is that the nature of the effect becomes opaque unless one already knows what it means. The situation becomes even worse when different groups decide to name the same effect after different people. On the other hand, simple yet descriptive names including geometric phase and intrinsic curvature reveal some sense of what is meant to the outsider. The absence of a simple-sounding name may indicate that we don't really understand the effect.

An Aperiodic Monotile

The authors discover a family of shapes that can tile the 2D plane, but only aperiodically. The shapes are non-convex mirror-asymmetric polygons. Tiling the plane involves placing a mixture of the polygon and its reflection, but the two can never be arranged to form a regular pattern. Can this kind of aperiodic tiling lead to novel physical properties of some system or model? For example, tight binding lattices can be obtained from tilings by identifying corners as "sites", with coupling between sites linked by edges of the tiling shapes.

Spectral localizer for line-gapped non-Hermitian systems

The localizer theory I have discussed previously (here and here) is now generalized to non-Hermitian systems! This is relevant to understanding the properties and robustness of certain topological laser models.

A quantum spectral method for simulating stochastic processes, with applications to Monte Carlo

This preprint shows that the quantum Fourier transform can be used to efficiently simulate random processes such as Brownian motion. In contrast to previous "digital" quantum Monte-Carlo approaches, here the authors consider an encoding in which the value of the random variable is encoded in the amplitude of the quantum state, with different basis vectors corresponding to different time steps. Since Prakash's earlier work on quantum machine learning using subspace states was the inspiration of our recent quantum chemistry work I think this paper is well worth a closer read!

Photonic quantum computing with probabilistic single photon sources but
without coherent switches

 If you want to learn more about the photonic approach for building a fault tolerant quantum computer (being pursued by PsiQ), you should read Terry Rudolph's always-entertaining papers. Even though the approaches presented in this manuscript (first written in 2016-2018) are now obsolete this is still well worth a read as a resource on the key ingredients of potentially-scalable methods for linear optical quantum computing.

An Improved Classical Singular Value Transformation for Quantum Machine Learning

The field of quantum machine learning has seen two phases. The first phase was sparked by the discovery of the HHL algorithm. HHL and its descendants promised an exponential speedup for certain linear algebra operations appearing widely-used machine learning techniques, arguably triggering the current boom in quantum technologies. However, running these algorithms on any useful problem will require a full fault-tolerant quantum computer.

Consequently, novel quantum algorithms for machine learning have attracted interest as a possible setting for achieving useful quantum speedups before a large scale fault-tolerant quantum computer can be developed. The power of these newer algorithms is much less certain and still under intense debate. Nevertheless, researchers could find solace in the hope that, even if these NISQ-friendly algorithms do not end up being useful, eventually we will achieve a quantum advantage using HHL-based algorithms.

The dequantization techniques pioneered by Ewin Tang and collaborators are starting to suggest that even a quantum advantage based on fault-tolerant algorithms such as HHL may turn out to be a mirage. This paper presents a new efficient classical sampling-based algorithm that reduces the potential quantum speedup for singular value transformations from exponential to polynomial. This affects a variety of quantum machine learning algorithms, including those for topological data analysis, recommendation systems, and linear regression.

 

 

TDA Week 2023

TDA Week is a five-day conference on topics related to topological data analysis, held this year in person at Kyoto University from July 31 (Mon) to August 4 (Fri). It follows last year's conference, which was held online due to covid restrictions.

The abstract submission deadline for poster presentations is 14th April. Presenting authors may request partial support for travel expenses.

Predatory publishing and open access

I recently stumbled upon Predatory Reports, an anonymously-run website that lists journals and publishers with dubious practices and standards. This is a growing problem with the rise of open access publishing mandates; since authors only pay if their article is published, there is an incentive to lower standards and publish everything.

It is interesting to note the inclusion of MDPI and Frontiers Media in the Predatory Reports list. All of the justifying examples are, to the best of my knowledge, taken from life sciences journals, and it is not clear whether similar issues affect their physics journals. Personally, however, I have received occasional review requests from them for papers which I clearly have no expertise in reviewing. 

A bigger issue (particularly with MDPI) is their spamming of special issue invitations. Since the guest editors will nominally handle submissions, including selecting potential referees, this can lead large variations in quality and standards among the articles published in a particular journal. Paolo Crosetto has a blog post analysing of the business model of special issue publishing and how it has turned into a money-printing machine for MDPI.

In related news, Nature published a feature on the journal eLife's decision last year to switch to a "publish everything" model, in which all papers which are sent to peer review are published alongside the referee reports. Nature is itself experimenting with similar open review ideas and the potential for the role of journals to shift from selective publishing to obtaining credible peer review reports. This model is particularly attractive for for-profit publishers, since it offers an attractive and reliable new source of revenue - under the open access model a journal loses money on every paper it rejects.

What will probably limit uptake of the publish everything model is that authors are ultimately after visibility of their work. Visibility requires selectivity, and you cannot have selectivity without rejecting a lot of papers.

Speech-to-text with Whisper

Whisper is another neat productivity tool that has been translated to a high-performance model that can be run without specialized hardware, even on your phone!

The speed and accuracy is remarkable - it takes only a few minutes to create a transcript of an hour-long seminar. While these capabilities have been around for some time (e.g. subtitle options in Youtube and video conferencing programs), it is great there are now fast, open source tools that can be run locally, without an internet connection or the privacy risks of sending your data to some untrusted server on the cloud.

Some potential applications in research:

• Brainstorming - discussions can be transcribed to a text format that can be more easily reviewed later (e.g. searching for keywords).
  
• Paper drafting - often when writing or typing we fall into the habit of writing long convoluted sentences that need heavy editing to make them more readable and digestible. Dictating parts of a paper might be a better way to come up with clear and concise text.
• Converting recordings of conference / workshop talks into full-length paper drafts or conference proceedings. I am trying this one out on one of the online talks I gave during covid.

The ability to quickly and accurately convert research between different formats (text, audio, visual, different languages, etc.) will ultimately improve the accessibility of research, ensuring that it is open for all to use and build on. Further reading on this important initiative can be found on the arXiv blog.

 

How to run generative text models on your own computer or phone for free

It was only a matter of time - the resource-intensive, proprietary, pay-to-use ChatGPT now has a free-to-run and use competitor in the form of a tweaked version of Facebook's LLaMa model!

llama.cpp is an super-fast implementation of LLaMa in C++ obtained by reducing the numerical precision of the trained model weights. 

I installed it without any trouble, in contrast to other generative models where dealing with the python dependencies and incompatible library versions can be a massive pain.

Similar to ChatGPT, the raw generated output text might look convincing to a non-specialist even though it is spouting nonsense. Thus, careful editing of its output is essential if you want to use it for anything other than your own amusement. 

For example:

Prompt: Quantum neural networks and quantum kernel machines are two promising approaches for machine learning using emerging noisy intermediate-scale quantum computers [1].

Output: Quantum neural networks and quantum kernel machines are two promising approaches for machine learning using emerging noisy intermediate-scale quantum computers [1]. They exploit the inherent parallel nature of existing classical deep network architectures through encoding them into a series of unitary gates, which can then be applied to qubits. However in most cases their expressive power is severely limited by noise that quickly accumulates during gate execution and corrupts information encoded on quantum states [2]. Although methods have been developed for dealing with this issue (either by using error correcting codes or applying a particular type of operations, namely, magic state techniques), they are not fully successful in practice. In other words, current approaches to mitigate errors suffer from an excessive overhead that makes these methods impractical and therefore useless [3]. In this paper we describe novel quantum circuits for encoding NNs architectures onto qubits with a significantly reduced number of gates and without using magic states or error correcting codes. These new constructions are not only more efficient, but also less prone to errors since they employ fewer physical operations (and therefore have lower noise), which could lead them into practical use in future NISQ devices [4].

The pace of machine learning research is incredible.

Hype and anti-hype

Claims of high temperature superconductivity were yesterday published in Nature and presented at the APS March Meeting. Given the history of the group, discussed in detail during a workshop on reproducibility in condensed matter physics, no doubt this should be taken with a pinch of salt.

On arXiv yesterday: Russians tear down claims of QAOA-accelerated factorization algorithms which hit news headlines last December. The comments on Scott Aaronson's blog on the original paper have some amusing (or depressing) background on the group behind this work.

Similarly, a few weeks ago claims of quantum simulation of wormhole dynamics using superconducting processors were heavily criticized.

These examples are all high profile works which have been (and will be) carefully scrutinized. The vast majority of preprints and publications do not attract as much interest. If you're having trouble reproducing a result in a paper, keep in mind that the paper may have errors that went undetected through peer review. The real peer review begins after the paper is published.