Haldane on the second quantum revolution

This week I attended a great public lecture by Duncan Haldane: "Quantum Mechanics After One Hundred Years, and the 'Second Quantum Revolution' Today"

Starting from the discovery of quantum mechanics, he explained how the concept of quantum entanglement is fueling today's second quantum revolution and its connection to his Nobel Prize-winning work.

Haldane remarked that his work on quantum spin chains was controversial. He had theorists accosting him at conferences arguing he was wrong. These kinds of disputes among theorists are best settled by experiment. Undoubtedly, Haldane would not have received his Nobel Prize if his predictions had not been validated by experiments. How can you motivate some experimental group to be interested in your theory? If it generates controversy!

Similarly, experiments often are the drive for fresh theoretical advances. For example, the experimental discovery of the quantum Hall and fractional quantum Hall effects came before the theoretical predictions or understanding. 

A good example of this is a second important work by Haldane also cited in his prize: quantum Hall effects in absence of Landau levels. This now-seminal work went largely unnoticed for a decade, because the model based on a two-dimensional honeycomb lattice seemed unfeasible to realize in an experiment. Later, the unanticipated work experimental isolation of graphene drove theorists to this fresh area. Haldane's early theory work was recognised as the foundation for the discovery of time reversal-symmetric topological insulators and the whole "zoo" of topological materials that followed.

Haldane also emphasized the importance of luck in making ground-breaking discoveries. von Klitzing was not the first person to attempt quantum Hall measurements, but previous attempts had used a different experimental setup: varying current with a fixed magnetic field. Imperfections in the current source led to fluctuations in the measured resistivity, which seemed to be consistent with previous approximate theoretical calculations based on perturbation theory. von Klitzing's approach of measuring resistivity as a function of magnetic field strength, with current kept fixed, led to unexpectedly precise quantization which needed new theory to explain. 

Haldane's take-home message was thus: anyone can win a Nobel Prize, but you need luck and the perseverance to defend your work if it is challenged.

An earlier iteration of this talk is available here. A more detailed write-up is available here. 

   

Quantinuum Technical Workshop

Yesterday I attended a workshop by Quantinuum, introducing their latest Helios chip to the Singapore quantum ecosystem. The programme included tutorials on hybrid quantum-classical computing workflows, including real-time measurement and conditional circuit operations, as well as applications to quantum error correction and quantum chemistry.

As someone who previously worked on NISQ processors and interested in trying out the latest generation of quantum processors, it was exciting to learn more about the new capabilities that are available:

• Real-time qubit measurements and reset combined with conditional operations open new opportunities for circuit design, such as the use of probabilistically generated magic states to reduce circuit depth.
• Gate fidelities are improved by an order of magnitude! 
• It seems like quantum error correction can actually work on real hardware!

 At the same time, some of the big challenges we struggled with before remain open problems:

• Trapped ion systems are slow. Current "error correction" capabilities are practically limited to error detection and post-selection - full-on error correction requires too big an overhead in terms of circuit depths. There is a need to carefully tailor the error correction code to the specific problem and hardware.
• Quantum chemistry use cases seem to have hit a wall in terms of the complexity of implementing the second-quantized Hamiltonians - circuit depths and required number of measurements become intractable well before one can use all of the available physical qubits. Switching from variational algorithms to subspace methods only partially addresses this.

And some other thorny issues mentioned during the discussion breaks:

• With superconducting quantum processors or other platforms with fixed qubit positions, one often has the luxury of choosing the best set of the qubits on the device and avoiding bad ones. This isn't supported on the Quantinuum processors due to the qubit shuttling - you have to use whatever you're given and can't keep track of which ions are the best to use. This might make the performance more unpredictable from day to day. One suggested approach was to instead perform a tomography on the different quantum logic regions of the device (where the gates are actually performed), to see if there is substantial variation in their fidelities.
• Because the gates are so slow, zero noise extrapolation (a simple and effective error mitigation scheme) have limited noise data to work with. Methods to generate more data (by probabilistically expanding only some of the two-qubit gates) need to execute many more circuits, giving a big overhead in terms of compilation time.
• Conditional circuit operations such as post-selection can substantially increase the number of shots required and expenses incurred by the end-user.

All in all, it was great to see the broad interest in the hardware and insightful technical questions from the audience. Looking forward to seeing what Singaporean researchers get up to with the new Helios processor once it is installed and operational in Singapore late next year!

Double-bracket quantum algorithms

Recently Marek Gluza visited SUTD to give a seminar on double-bracket quantum algorithms. This is an interesting family of quantum optimization algorithms based on Riemannian geometry, which diagonalize an operator (or minimize an energy) using gradient descent in the space of unitary operators. For example, minimization of energy via this gradient descent is realized as the flow,

$$ \partial_t \rho = [ [\rho (t), H], \rho(t) ], $$

where the first commutator $[\rho(t), H]$ is the energy gradient in the space of unitary operators - the direction that locally minimises the energy of the state $\rho(t)$ - and the second commutator evolves $\rho(t)$ in this direction. In other words, this is a nonlinear evolution governed by the effective time-dependent Hamiltonian $H_{\mathrm{eff}} = [\rho(t),H]$. Similar flows were introduced by R. W. Brockett in the 1990s as a way to use dynamical systems to diagonalize matrices. When implemented with a finite step size $s$, this flow recursively generates better approximations to the ground state as

$$ \rho_{k+1} =  e^{s [\rho, H]} \rho_k.$$

Because of the recursion (you need to first generate $\rho_k$ before applying the next set of gates to make $\rho_{k+1}$), the circuit depth grows exponentially with the number of steps. On the other hand, in contrast to variational quantum algorithms (where one has to measure gradients of all the classical control parameters of the circuit), to implement the double-bracket flow you only need specify the initial state $\rho_0$ and the step size $s$, avoiding big problems such as barren plateaux and choosing an appropriate variational ansatz. Double-bracket flow is guaranteed to converge, so it can pick up after other methods get stuck.

Marek noted that because of the circuit depth blow up, a warm start is essential to get the best performance. For example, one might optimize a shallow variational quantum circuit such as QAOA to obtain a low energy state, followed by a few steps of double-bracket flow to home in on the ground state.

This is a great example of how quantum computing can draw inspiration from classical algorithms and control theory, giving a fresh application of the humble idea of optimization via gradient descent! 

The slides are available here.

IIT Bombay visit

Last month I had the pleasure of visiting the Department of Physics at IIT Bombay. The huge campus is a (relatively) quiet green bubble insulated from the traffic and noise of the city outside. My host was new faculty member Subhaskar Mandal, whom I first met last year towards the end of his postdoc at Nanyang Technological University.

I gave a talk on "Conical intersections and angular momentum" (slides available here). This is a long-running story which I started working on at the very beginning of my PhD studies, taking another look at it in the context of borophene lattices a few years ago. Interesting questions related to the origin and applications of  the "microscopic" orbital angular remain unanswered and worth revisiting with the current surging interest in quantum geometric effects.

I really enjoyed the other presentations on plasmonic nanocavities, bound states in the continuum, and axion topological photonic crystals, as well as interactions with the students and local faculty members. The full workshop programme is available here.

Asian Network Mini-School on Quantum Materials 2024

Last week I visited the University of Indonesia to present two lectures on topological photonics at the Asian Network Mini-School on Quantum Materials 2024. This is one of a series of events held in South East Asian countries held by the ICTP Asian Network. The school attracted 95 participants from Indonesian universities, the majority being advanced undergraduates or graduate students. Meetings such as these provide valuable opportunities for early career scientists to learn about cutting-edge research areas and build collaborations with others in the region. I was impressed by the level of engagement from the audience - even though I ended my first lecture 20 minutes early, the remaining time was fully occupied by questions! Many thanks to the local organizers for putting together such an enjoyable meeting! Two more schools will be held this year, both in Thailand, on complex condensed matter systems and magnetism and spectroscopy, with more planned for next year.

CQT Colloquium on strongly interacting photons in superconducting qubit arrays

 Yesterday at CQT Jonathan Simon from Stanford University gave a wonderful colloquium talk on "Many-body Ramsey Spectroscopy in the Bose Hubbard Model," covering experimental studies of strongly interacting quantum fluids of photons in arrays of superconducting qubits, spanning work from 2019 on the preparation of photonic Mott insulating states to ongoing studies of entangled many-body states of light.

A good colloquium talk should understandable to a broad audience (ideally, including undergraduates) while still going into enough depth to keep specialists in the topic interested. If you cannot frame your research in terms of some simplified model, chances are you do not yet fully understand it.

Simon did this using the neat example of emergence in 2D point clouds: observing non-trivial emergent properties requires three key ingredients: many particles, interactions between the particles, and dissipation (in this case, friction) to allow the system to relax to some ordered state. When all three are included, the cloud self-organizes into a triangular lattice with properties qualitatively different from those of the individual constituent particles, supporting low energy vibrational modes (phonons).

Typically, a colloquium talk will cover research spanning several years. It is important to have some clear common motivation. In this case, the question of how to make quantum states of light exhibit similar emergent properties? Three ingredients are required: give photons an effective mass, achieve strong photon-photon interactions, and introduce a suitable form of dissipation that allows the system to relax to some interesting equilibrium state while preserving non-trivial many-particle effects.

After this framing, the talk went deep into how these ingredients can be realized using arrays of superconducting qubits, and how the relevant dimensionless quantities (interaction strength vs hopping strength vs photon lifetime) compare to other platforms, such as cold atoms (handy, given the mix of expertise in the audience).

The talk finished with a vision for the future - to connect this "photonic quantum simulator" to a small-scale quantum processor to test NISQ-friendly algorithms, such as shadow tomography of many-body quantum states.

A recording will probably be uploaded to the CQT Youtube page later. In the meantime, related talks given at JQI and Munich are already available online!

Talks-to-papers with Whisper

Last year I wrote about a neat and lightweight implementation of the Whisper speech-to-text model. One of the potential applications I mentioned was converting recorded presentations (seminars, lectures, etc.) into written notes. A few weeks ago a review article I wrote using this approach was published in AAPPS Bulletin. Here's how I did it:

 1. Identify source material. In this case, I had an online conference talk that had been recorded and uploaded to Youtube.

2. Download the raw audio using a tool such as yt-dlp

3. Convert audio to a text transcript. I used whisper.cpp (can run on CPU). The base and small models sizes already do pretty well in terms of accuracy and run quickly.

4. Transcript editing. Whisper won't have perfect accuracy, especially when attempting to transcribe scientific jargon. So it's necessary to carefully review the generated text.

5. Figure conversion. In this case since it was my own talk, I had access to high resolution version of the figures I wanted to include in the paper. Minor reformatting required.

6. Add references. While I cited papers in the slides, the citations need to be converted to a .bib file or other reference manager format. It would be helpful to have an AI assistant that could do this automatically.

And with that I had a first draft completed! Very nice, since the first draft is usually the hardest to write. I did spend some more time polishing the text, adding some details that didn't make it into the original talk, and making the language more formal in parts, but it ended up being a lot easier than writing the whole text from scratch!

Looking back on 2023

The end of the year is good time to reflect on what went well and what didn't over the past twelve months, and what changes we hope to make in the year to come. Here's my list:

1. Presentations. I gave 11 talks this year to a variety of audiences (conferences, workshops, internal presentations, external seminars). Some went better than others. The main culprits for my bad talks are (still) trying to say too much in the time allotted, and failing to pitch well to the specific audience. It is particularly challenging to convey the broad strokes of the research to everyone present at a level that interests them while still going into enough depth to satisfy the few experts in the audience. The best presentations I gave involved audience participation using QR code polls - even including one or two over the course of an hour-long talk is a great way to get the audience to stop, think, and start paying attention again. The best talks I attended spent most of the time explaining the problem set up and broader context and very little time on the speaker's own contribution.

2. Publications. Midway through the year it seemed like I was going to put out fewer papers than usual. Then in November and December I ended up being swamped with finalising several manuscripts all at once (hence a reduced blogging frequency). The final tally is nine original manuscripts completed this year. Is this too many? Many decry the publish or perish culture, the endlessly increasing rate at which papers are being published, courtesy coauthorships, salami publishing, and whatnot. At least in my case, I think I have made a meaningful contribution to every paper I have coauthored this year, but I need to strike a better balance between deep work on new research directions and easier (but still time-consuming) work on existing areas of expertise.

3. Upskilling. I played around with using AI tools like StableDiffusion (text to image), LLama (text generation), whisper (speech to text), and a few different web-based academic paper summarisation / recommendation tools. Given the tendency of large language models to hallucinate and spit out falsehoods, it's hard to trust them when seeking new knowledge (e.g. summarising or suggesting new papers to read), but I've found them quite useful for rephrasing ideas in an amusing way or making cool images for talks (see below).

Happy 2024!

Doing literature reviews the smart way

Despite literature surveys being a key component of research, strategies for reviewing the scientific literature and identifying promising avenues of research are rarely included in graduate student coursework. This means that students may be unaware of more powerful tools that are available.

It is useful to have a tiered search strategy, starting with resources aimed at a broad audience, for example technical magazines such as Optics & Photonics News, to identify interesting or promising directions to study in more detail. While wikipedia is a popular first choice, peer-reviewed alternatives such as Scholarpedia provide more reliable and trustworthy articles written by known experts.

Google Scholar is perhaps the most popular scholarly search engine, but its limitations mean it is most useful for exploring papers on highly specific lines of research, mainly by following citation trains and highly-cited papers. Subscription-based search engines such as Web of Science are usually available under university subscriptions and give much more powerful tools for exploring a research area and seeing the bigger picture, such as the ability to filter search results by journal or author affiliations and visualise how publication trends are evolving over time using citation reports

Thanks to covid, many academic talks can now be viewed online. These are a great alternative to reading the papers themselves, particularly because the speaker may reveal insights that didn't end up in the journal article. One should keep in mind differences between workshops and larger conferences - target audience, breadth and depth of individual talks and the programme as a whole, and sometimes the candour of the speakers, particularly if the talk will be made available online. This means that in-person conference attendance is still highly valuable, because speakers may be more willing to share unpublished work and future research ideas during smaller more informal discussions. Talking to the right person can save hours of time figuring out what the key references are!

The volume of publications in an area may shape your research strategy. If a given keyword has hundreds or thousands of articles coming out each year, it's usually a sign that you need to narrow your focus to find a niche in which you can shine. Publications often follow a hype cycle, that is, an initial surge of interest leading to a transient peak in activity, followed by a more stable plateau as the field matures. Sometimes a line ends up being infeasible, leading to interest dying off before such a plateau can form.

It is important to emphasize the number of publications in an area should not be used to judge whether a field is worthwhile to study. For example, one researcher might see a booming field and be put off, desiring to work in a smaller area with a better potential for growth. A short peak of activity followed by little interest may suggest a research line has a difficult problem that nobody knows how to solve, offering an opportunity for you to make your mark.

Does artificial intelligence have a place in reviewing the literature and deciding on promising lines of research? Yes and no. Artificial intelligence is more than just large language models and chatbots, encompassing a variety of other machine learning-based tools for enhancing productivity, for example by helping to analyse and visualise citation networks. Some experimental examples of these network analysis tools are available on arXiv through arXivlabs and are worth a try - even if their capabilities are limited or inaccessible today (e.g. requiring a subscription), in the coming years the best ones will become more widely available via university-wide subscriptions, similar to the growth of collaborative paper-writing tools such as Overleaf.

And what about large language models? In my opinion, it's best to avoid them when carrying out literature reviews. Language models are trained to favour fluency over accuracy, so rather than generating new knowledge they are better used for performing tasks where the end-user can verify the output. Even when asked to analyze specific papers, you can't be sure that the model missed or misunderstood an important point, for example when jargon used within a research area differs from the commonly-understood meaning of a word. And even if (or when) these issues are solved by new and improved models, at the end of the day large language models are designed to spit out probable-sounding sequence of tokens. On the other hand, scientific breakthroughs often come about through the pursuit of unlikely or unexpected avenues of investigation.

Finally, one should not read too much. Too much time spent reading what other people have done not only takes time away from your own research, but it can also sap your creativity and ability to pursue directions away from the groupthink. Richard Hamming explained this eloquently in famous lecture "You and Your Research" he gave at Bell Labs, available both as a text transcript and a video recording. I highly recommend reading or watching!

In summary:

1. You should use a variety of sources, search engines, and media types
2. Remember every source and search engine has a bias
3. Aggregated statistics are just as important as individual papers
4. Try emerging AI-powered search & visualization tools
5. Don't read too much!