2025 in review

I was sad to hear that my former workplace, the Center for Theoretical Physics of Complex Systems, is winding down. It was such a great academic environment with time to think and ample opportunities to learn from colleagues and the regular seminars and international workshops. From the Center's last Scientific Report:

Outlook: The center counts 492 publications, a total of 12813 citations, and an h-index h = 56 on Google Scholar. Despite its tremendous success, a continuation with a new division headed by a new director could not be realized by IBS, which is a pity and raises other IBS related questions which are not part of the current report. As a result of the foreseeable retirement of the current director, the PCS is winding down by the end of 2025. Practically all members of the PCS quickly found or are successfully securing new positions in research institutes and universities worldwide. The successful concept of the PCS will continue to exist through its alumni who carry the message into the world. These include twenty three (23!) faculties worldwide, including eight (8!) in Korea, six (6!) in China, and five (5!) in India, but also in Singapore, Vietnam, Brazil, USA, and the Philippines.

It's a real shame, especially since support for similar theory-focused research centers is so limited. Short term grants promote "safe" topics rather than giving researchers the time and freedom to follow their curiosity and try new ideas.

Looking back, memorable moments at PCS include:

• A visit and seminar in 2018 by J. Michael Kosterlitz in which he recounted his unusual journey to his Nobel Prize-winning work, including the important role played by job rejections and rock climbing. We didn't record his talk, but what seems to be a similar version can be found here.
• Workshop weeks, particularly the ability to sit in on workshops beyond one's own areas of expertise and get a first-hand glimpse of how informal interactions differ between different fields. Sometimes the welcome reception and evening activities would wind down within an hour or so, other times they would continue into the early morning, prime time for forging new collaborations and hearing important gossip. This is also why online conferences are a poor substitute for in-person events. 
• We went through a period where we were required (as a government institute) to have personal identifying information in all job applications be anonymised, to eliminate bias in their evaluation. Whoever came up with this didn't understand you cannot anonymise academic CVs - the publication list will inevitably give the name away!

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Physical Review A saw a significant increase in submissions, including some LLM-written papers. When used properly, LLMs can be a great productivity enhancer, particularly for non-native English speakers. On the other hand, if one uses the LLM to "cheat" and write the paper entirely, it is really easy to spot. Some dead giveaways: formatting, em-dashes, fake references, overly wordy text that doesn't say much (or makes no sense at all). 

For similar reasons it is easy to spot when a referee report (or student homework assignment) has been prepared using an LLM instead of real intelligence! During one of my classes this year, I was sad to see some students completing their hand-written humanities assignment by directly copying the output from ChatGPT. At the end of the day, tedious "homework" like unpaid reviews are not just a box to tick off, they are exercise for your mind. By looking carefully for flaws and inconsistencies in someone else's work, you are also developing the critical thinking skills that will improve your own writing and research. Don't short-change yourself by delegating to an LLM!

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My own research is going at a slower pace. A lot of thinking time has been replaced with grant-writing. I hope to see some payoff for this substantial effort in 2026! 

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!

Tenure-Track Assistant Professor Opening at Singapore University of Technology and Design

My department is looking for a new tenure track faculty member with expertise in high performance computing applied to many-body quantum systems! Here is the job posting. Interested potential candidates are welcome to contact me with any questions about working at SUTD or the application process.

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The Singapore University of Technology and Design (SUTD) is a young and growing university with a unique structure and mission in the vibrant nation of Singapore. SUTD features a focus on design from an engineering and technological perspective, an intimate student to faculty ratio, an innovative active-based learning pedagogy, an interdisciplinary pillar organization, a stellar faculty, and a beautiful new campus. SUTD was established in 2009, in collaboration with MIT and Zhejiang University, as the fourth publicly funded university in Singapore. SUTD is also considered by international experts as an emerging leader in engineering education:  http://news.mit.edu/2018/reimagining-and-rethinking-engineering-education-0327

 

The Science, Mathematics and Technology (SMT) cluster has an open position to hire a tenure-track Assistant Professor with a strong record of scholarly research in high performance computing applied to many-body quantum systems such as condensed matter, quantum chemistry, quantum simulation or others. We are particularly interested in candidates with a background in tensor networks and/or neural quantum states. Postdoctoral experience is desired. We seek candidates with an open mind towards multidisciplinary research and whose research area, methods and/or tools can impact multiple fields and society. We can consider more senior candidates too, e.g. Assoc. Prof. and Prof.

 

The candidate will join a young and growing department including other experts in many-body quantum systems working in areas such as quantum simulation and quantum computation, quantum error correction, quantum-inspired computing, quantum open systems, quantum transport, quantum thermodynamics, photonics etc. Furthermore, Singapore offers a stimulating and well-funded research environment with many experts in town.

 

Candidates must be committed to excellence in teaching at the undergraduate and graduate levels and to developing and maintaining an active research program. Candidates should be able to teach undergraduate courses in mathematics, physics or chemistry. We are particularly interested in individuals with a strong and genuine interest in promoting STEM education at all levels. The successful candidate can look forward to internationally competitive remuneration, attractive research startup packages and grant opportunities, and assistance for relocation to Singapore.

 

Additional information about the university and the SMT cluster and SUTD can be found at www.sutd.edu.sg and https://smt.sutd.edu.sg/.

 

Application Requirements

 

Applications will be accepted online at https://careers.sutd.edu.sg/ and the review of applications will close on 4 January 2026.

 

Candidates should submit their full application packages, which should include:
 
•    Complete resume with full publication list (Including Statement of interest / Cover letter)
•    Research statement/plans
•    Teaching statement/plans
•    3 Research papers
•    Contact information of 3 referees

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.

Topological Photonics: Limitations and Possibilities

Last week our Perspective article "Limitations and possibilities of topological photonics" was published in Nature Reviews Physics. As the title suggests, we address some overblown claims of topological robustness frequently made in the literature and clarify in which areas topological protection can play a useful role for applications in photonics.

We first thought of writing such an article in July 2023, in response to several papers somehow being published in high impact journals despite their central claims being based on a misunderstanding of the nature of topological protection and robustness in the systems they studied. For example, claims of "topologically enhanced" or "topologically protected" localization are generally unfounded, given that the localization length is generally determined by the width of the band gap, a non-topological quantity.

Another common problem we wanted to address was the frequent use of comparisons between trivial and non-trivial structures to claim various forms of topological "enhancement". Sadly, such claims also frequently appear in top journals. As we discuss in the article, such a comparison ends up being meaningless because trivial and non-trivial structures host modes with differing dimensionality. For example, in 2D structures the edge modes (localized along the 1D boundary of the system) will naturally give a stronger light localization than a trivial 2D structure without any edge states. However, there are many ways to create edge states that do not require complicated topologically non-trivial designs. What matters is whether unidirectional chiral edge states (which are unique to topologically non-trivial systems) offer some advantage compared to non-chiral states, appearing either as trivial edge states or, more simply, as bulk states of a one-dimensional system. This kind of fair comparison is surprisingly rare in the literature - the most prominent example I know of is the 2014 paper "Topologically Robust Transport of Photons in a Synthetic Gauge Field". 

Unfortunately, this methodology was not widely adopted, and there was little progress on the hard problem of demonstrating quantitative performance enhancements of topological designs compared to state-of-the-art non-topological designs; for example, we had to wait until 2023 to see a rigorous comparison between scattering in valley Hall and non-topological photonic crystal waveguides. In this work, the non-topological W1 photonic crystal waveguide had lower scattering losses in the slow light regime.

Promoters of topological photonics may argue that such a comparison is also unfair, given that the W1 photonic crystal waveguide design is the result of years of testing, experimentation, and optimization, whereas the valley Hall design is much newer, with the potential for further optimization. This point brings me to the "possibilities" of topological photonics we discuss in our article: a topologically non-trivial band structure should not be the end of the design process. Rather, topological bands provide a unique starting point for further optimization, for example by guaranteeing the creation of localized modes near the middle of a band gap. Before the advent of topological band theory we did not have a systematic way to do this!

In the next phase of research in topological photonics, the focus will not be on demonstrating ever more exotic topological phenomena in increasingly more complicated setups. Rather, we should be aiming to integrate this new design tool with other approaches such as fine-tuning or inverse design to move from proofs of concept to genuinely better devices. Photonic crystal waveguides and fibers, integrated lasers, and frequency combs are three areas ripe for further breakthroughs, in my opinion. Watch this space for more on these topics!

GenQ Hackathon: Quantum for Finance

Last weekend I had the pleasure to attend the GenQ Hackathon: Quantum for Finance, joining as a mentor for the teams. Events such as this are important as a means of building familiarity with quantum processors amongst the participants from diverse backgrounds, from physics to finance majors and from high school students to veteran software engineers. Applications of quantum processors will not just need PhD-level quantum algorithm specialists, but also people with a broader range of skills able to make sense of where quantum algorithms may be practically useful.

The overall winning team had the, in my opinion, crucial insight that whatever fancy new solution you come up with, be it AI or quantum-designed, it had better be interpretable. Particularly in the high-stakes world of finance, someone will ultimately be responsible for decisions made based on the quantitative model. End-users won't trust a black box model. A model that spits out a single number - such as an F-score or correlation coefficient - will never be as trustworthy as a model that can clearly show all the relevant variables. Because of this, the team incorporated Mapper into their solution for detecting anomalies in the form of fraudulent credit card transactions.

One thing I was surprised by was how few of the teams took into account the clear advice given in the opening statement from Hongbin Liu (from Microsoft Quantum): In future practical use-cases of quantum processors, the cross-over point at which a quantum processor is expected to out-perform existing (very powerful) classical algorithms and high performance computers will involve days to weeks of wall-clock runtime. One on the judging criteria specifically focused on the scalability of the proposed solution. Despite this, in their final pitches many of the (unsuccessful) teams focused on quantum circuits limited to several qubits with second-scale run-times, claiming apparent speedups compared to selected classical benchmarks. However, such small-scale quantum circuits are trivially classically simulable.

I observed almost all the teams using ChatGPT or some other favourite large language model, both for background research on the chosen problem as well as rapid code generation. It was also striking to see how much easier it is now to write, compile, and execute quantum circuits on a cloud quantum processor by making use of quantum middleware providers, who now sell this as a convenient service. 

 

Cusp solitons mediated by a topological nonlinearity

Harvey just finished what should be the last paper of his PhD studies: Cusp solitons mediated by a topological nonlinearity

Harvey's PhD project studied the intersection between topological data analysis (TDA) techniques and nonlinear and many-body quantum dynamics. His first paper devised a TDA-based pipeline for detecting the emergence of quantum chaos in a periodically-driven nonlinear Kerr cavity. He followed this up with a demonstration of many-body quantum scar detection using topology-based dimensional reduction.

These works, while very nice, were ultimately using TDA to recover known physics. We really want to find examples where TDA can unveil new physics. This is a hard problem. Where to look? And what counts as "new"?

The easier solution for us was to insert TDA "by hand" into a nonlinear model, and see what came out of it.

For our testbed we took the nonlinear Schrodinger equation, frequently used to model nonlinear waves in various platforms. In the usual nonlinear Schrodinger equation, the conserved energy is the Hamiltonian,

$$ H = \int dx \left[ \frac{1}{2} |\partial_x \psi |^2 - \frac{g}{2} |\psi|^4 \right] $$

The second term, responsible for the nonlinear dynamics, can be interpreted as an intensity-dependent potential of depth $\frac{g}{2}|\psi|^2$. We looked at what would happen if we replaced this term with a quantity obtained using TDA. When dealing with one-dimensional functions, such as intensity profiles $|\psi(x)|^2$, TDA frequently uses sublevel set persistent homology, characterizing shape in terms of the persistence of local maxima and minima. We used the total persistence of these features as an energy penalty term, leading to

$$ H^{\prime} = \int dx \left[ \frac{1}{2} |\partial_x \psi|^2 - \alpha \mathrm{sgn}( \partial_x |\psi|^2 ) (\partial_x |\psi|^2) \right]  $$

Deriving the equations of motion, we found that this topological energy penalty gives rise to effective $\delta$ function potentials at the local maxima and minima of intensity, which act to enhance or suppress local maxima, depending on the sign of the nonlinear coefficient $\alpha$. We then studied the resulting nonlinear dynamics, including the focusing of Gaussian and flat-top beams.

The dynamics are very different from the regular nonlinear Schrodinger equation with focusing nonlinearity, where such a flat top beam would quickly break up into a collection of tightly-focused bright solitons. In this case, since the nonlinearity is proportional to the intensity gradient, its influence is mainly limited to the edges of the flat-top beam. 

We also uncovered some interesting connections to the physics of nonlocal nonlinear systems. Specifically, our "topological nonlinearity", when regularized, resembles a weakly nonlocal nonlinearity with a vanishing local part. Such nonlinearity leads to cusp solitons, as was previously studied in the context of plasma physics!

We hope to follow up this study with investigations of similar "topological" nonlinearities and potential experimental realizations. In the present work we speculated that similar nonlinearities may arise in the context of fluid-mediated nonlinearities and lattices undergoing Floquet modulation, but demonstrating such implementations explicitly remains an open problem for us.