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!

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.

Quantum computing debated in The Financial Times

Criticism of quantum computing hype and a rebuttal recently appeared in The Financial Times. The first article argues that even "well-established" applications of future quantum computers - breaking encryption and efficient quantum chemistry calculations - may not be useful in practice. The second article notes that even though there is tremendous hype, there is also slow but steady progress in scaling up quantum processors and understanding which quantum algorithms might provide value and which will not.

It is worth emphasizing that quantum technologies are much broader than quantum computing. For example, quantum research in Singapore are also encompasses quantum communications and quantum sensing. While these areas a seen as being closer to useful commercial applications, there are still some important caveats:

Quantum communication technologies are often marketed as the solution to the problem of future quantum computers being able to break widely-used public key cryptography schemes, with quantum key distribution providing unbreakable encryption protected by the laws of physics. The reality is that sharing of encryption keys is just one part of a secure communications network; a far bigger problem is authentication - how can you prove the other party is who they claim to be? Indeed, the vast majority of data breaches or online scams are not due to encryption protocols being broken or passwords being hacked, but rather are a result of phishing attacks where the victim is tricked into believing the attacker is someone else. The UK's National Cyber Security Centre's position on quantum communication technologies is:

"Given the specialised hardware requirements of QKD over classical cryptographic key agreement mechanisms and the requirement for authentication in all use cases, the NCSC does not endorse the use of QKD for any government or military applications, and cautions against sole reliance on QKD for business-critical networks, especially in Critical National Infrastructure sectors.

In addition, we advise that any other organisations considering the use of QKD as a key agreement mechanism ensure that robust quantum-safe cryptographic mechanisms for authentication are implemented alongside them."

Quantum sensing promises the ability to perform measurements with precision unattainable using classical devices. This encompasses many well-established approaches based on quantum coherence, including SQUIDs, atomic clocks, atomic gravimeters, and squeezed light interferometers, and more speculative ideas based on large-scale quantum entanglement. The latter entanglement-based approaches have however attracted criticism (see for example this preprint).

In all these examples - quantum computing, quantum communications, and quantum sensing - useful technologies will not emerge from quantum researchers working in isolation. Collaboration with researchers working in other disciplines and industry is essential to keep quantum "solutions" honest and ensure that we are solving problems that need to be solved, and to establish that quantum techniques provide a better solution than well-established classical methods.

More on quantum error correction

Hot on the heels of the Google team's recent demonstration of quantum error correction, last week Quantinuum released a heavily-promoted preprint: Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code. This work studies the performance of quantum error correcting codes using trapped ion quantum processors.

The authors compare the performance of logical gates implemented using two different error-correcting codes (5 qubit code and the colour code), without running error correction cycles. Logical CNOT gates were performed with higher fidelity compared to physical CNOT gates, however "the inclusion of QEC cycles along with more careful measurements will be crucial components in a “fair” comparison between the performance of physical and logical qubits."

Error rates are still too high for the 5 qubit code to be useful; even with a 1000-fold reduction in the physical two-qubit gate errors, simulations indicate the error correction using the 5 qubit code will not give an improvement compared to non error-corrected circuits! The authors speculate that this code might still be useful as a quantum memory.

On the other hand, "the color code CNOT with an added FT QEC cycle should eventually outperform the standalone gate, but requires somewhat lower error rates than we currently achieve. In contrast, adding a non-FT QEC to the end of the gate operation causes the simulated logical gate to always perform worse than the physical operation in the error regimes we probed." 

One challenge with the ion trap architecture is that adding additional qubits (ions) generally reduces the gate fidelities due to effects such as cross-talk. 

Another challenge identified in this work is that different error correction codes can have different performance depending on the quantum computing platform used and relative strengths of different noise sources. "It is currently difficult to predict which codes and implementations of those codes may perform the best in general scenarios, and when considering anything but the simplest error models, one is usually forced to resort to numerical studies. Additionally, the exploration space is vast."

Useful error-corrected quantum circuits are still a long way off, requiring difficult improvements to the performance of physical gates.

Pushing the limits of nonlinear optics

 Another entertaining and insightful perspective by Jacob Khurgin was uploaded to arXiv this week: Nonlinear optics: a look from the interaction time viewpoint and what it portends. It is similar in tone to his earlier article on high refractive index materials.

 This is real old-school physics - using simple intuitive models to understand fundamental limits to nonlinear optical response and "the universal principle of unavailability of free lunch."

On the one hand, the take-home message is somber: no huge magic enhancement of nonlinearity is possible due to fundamental physical constraints; hype regarding various wondrous materials does not stand up to scrutiny. On the other hand, finding new "boring" materials exhibiting modest enhancements to properties such as optical damage threshold or propagation loss is still a worthy goal as a means of improving the performance of existing nonlinear optical devices including light sources based on harmonic generation, optical frequency combs, and parametric amplifiers.

 

Recently in glossy journals

Engineering topological states in atom-based semiconductor quantum dots

Very nice work implementing the SSH / Hubbard model using quantum dots, forming a platform for studying the interplay between band topology and quantum interactions. The accompanying press release from the spin-off company (Silicon Quantum Computing) is unfortunately pure hype, however. This is not a molecular simulation - it is an implementation of a model. A neat example of analogue quantum simulation, but this is not a general-purpose reprogrammable integrated quantum circuit. 

Quantum advantage in learning from experiments

 

An exponential quantum advantage for quantum machine learning! The fine print is that the advantage is for learning from quantum data.

An on-chip photonic deep neural network for image classification

 

A photonic neural network that uses optoelectronics to implement nonlinear activation functions. "Direct, clock-less processing of optical data eliminates analogue-to-digital conversion and the requirement for a large memory module, allowing faster and more energy efficient neural networks for the next generations of deep learning systems."

Quantum computing's hype problem

Prof. Sankar Das Sarma provides a lucid perspective on much-hyped near-term applications of quantum computing.

I think a lot of this hype can be blamed on commercial interests or non-specialist science journalists who hide the nuances of the field in search of clickbait.

From what I've seen in talks by researchers from hardware companies such as Google, Xanadu, etc., they do try to focus on the interesting physics of the current generation of quantum processors, rather than trying to overhype unlikely or far-off commercial applications.

I think the same is true for academic researchers working on quantum computing. Unfortunately funding for basic science at universities is scarce, and many governments are keen to promote partnerships with industry even when the science may be at a far too early stage.

The quest for high refractive index materials

Expanding the Photonic Palette: Exploring High Index Materials

An entertaining and provocative article on why we should care about broadening the palette of high refractive index materials and where we might find them.

 

While graphene is singled out as the "king" of exotic materials with limited practical applications in optics and photonics, it is worth emphasizing that the huge interest in graphene has been a source of funding, techniques, and inspiration for studies of related quasi-2D materials. Among these, transition metal dichalcogenides seem quite promising for photonics applications including high index metasurfaces.

Thanks to nanoscale views for making me aware of this article.

Has topological photonics plateaued?

Not yet.

Data taken from Web of Science. I compare the publication rate of papers on topological photonics with some other hot topics in photonics during my graduate studies. Of course, the number of publications measures interest in a topic and does not necessarily correlate with real progress.

Whether topological photonics was close to reaching a plateau was a topic of discussion during a workshop I attended in 2019. Close to half of all papers on topological photonics have been published since 2019! During this period the main emerging research directions have been nonlinear effects, non-Hermitian topological structures (i.e. with gain and/or loss), higher order topological phases, and bulk topological defects. Ongoing experimental efforts in all of these directions is likely to sustain interest for the next few years, at least. Will the peak be followed by a sustained plateau or an immediate decline?