The year in review

Some thoughts to end 2021:

1. The scientific impacts of covid have become more noticeable to me. Last year many theorists used the lockdowns to finish their ongoing projects. This year, the increased isolation and lack of in-person discussions has stymied creativity and new ideas. Last year in Singapore (and Korea) we were able to come to the office all the time without much disruption, the main limitation being that seminars were held online. This year we've had to work from home for about 4 months. The impact of this is worse for newer graduate students - for them this is the sad normal. I appreciate the in-person discussions since returning to the office last week.

2. Despite optimistic claims by conference organisers, in-person international conferences still seem to be a long way off. The killer is the need for pre-departure covid testing and with it the prospect of having your trip extended or delayed by weeks. Domestic conferences will need to fill the gap in the interim.

3. I applied for some grants but was not successful. This might be a blessing in disguise; with the covid restrictions it's hard to bring new hires into Singapore, and apart from conference travel research expenses for theorists are minimal. However, the lack of job security that comes with ongoing grants is a bummer. One big issue for senior postdocs in Singapore is that more permanent positions require a track record of successful grants, while to apply for most grants here you need a permanent position...

4. Science-wise, this year I've learnt a lot about (quantum) machine learning, quantum computing on the cloud, topological (Jackiw-Rossi) defect modes, applications of topological data analysis to physics (review article coming!), and classical shadows of quantum states. I have quite a few works in progress which will hopefully come to fruition next year.

5. Delegation is still a challenge, but I am slowly improving. Apologies to all my collaborators whose projects I've held up.

6. I started blogging. Writing posts was hard at first but has become a lot easier as the year progressed. Thanks to everyone who keeps reading and I hope the material is useful in some way. Comments on posts are always welcome.

Happy 2022!

Advances in quantum error correction

This month has seen a few different groups report implementation of quantum error correcting codes using superconducting quantum processors:

Logical-qubit operations in an error-detecting surface code

This article published in Nature Physics on 16th December by a Dutch team and collaborators implements a distance-2 surface code, encoding a single logical qubit in a 2D lattice of 7 physical qubits. They demonstrate state initialization and single-qubit gates on their logical qubit.

Realizing repeated quantum error correction in a distance-three surface code

This arXiv preprint posted on 7th December by a Swiss team and collaborators reports implementation of the surface code on a 17 qubit processor, yielding a single logical qubit protected against both bit flip and phase errors using a 1.1us error correction cycle.

Realizing an error-correcting surface code with superconducting qubits

This arXiv preprint by the USTC team was posted on 27th December. They similarly implement the distance 3 surface code using a 17 physical qubit grid selected from their 66-qubit superconducting quantum processor. Their error correction cycle is also on the order of microseconds, but seems a little longer than the Swiss team's because they use a slower readout scheme to reduce the error rate.

 

Points to note 

• Improvements in gate fidelity are still needed for the logical error rate for superconducting qubits to be less than the 2-qubit gate errors, such that the error correction algorithm beats the physical error rate. Ion trap quantum processors have on the other hand already reached this break-even point.
  
• At this stage the error correction is still done off-line, i.e. as a correction to the measured data. The ultimate goal is on-the-fly error correction, which will require integration of fast digital processing, feedback, and qubit resetting. Doing so without increasing the physical error rate will likely be challenging. Again, ion traps have the lead.
  
• Current experiments involve post-selection, with leakage states discarded. Leakage states are measurements not correctable via the error-correction scheme, e.g. due to too many or correlated errors, one source of which is cosmic rays. Without mitigation schemes, correlated errors may hinder large scale error correction, as highlighted by a recent paper by the Google team.
  

Real space topological invariants for metallic systems

A very nice paper was uploaded to arXiv last week: Local invariants identify topological metals. This paper presents a new way to compute the topology and identify robust edge states in gapless and metallic system. Here is my attempt at a summary of their approach:

Background

Introductions to topological phases typically define them in terms of the topological properties of Bloch Hamiltonians. For example, the Chern number is the integral of the Berry curvature over the Brillouin zone. These most familiar definitions assume your system is periodic with Bloch wave eigenstates.

Disorder breaks translation symmetry, such that the eigenstates are no longer Bloch waves. Nevertheless, topological phases remain robust as long as band gaps remain open. To rigorously explain this robustness, topological invariants can be recast in equivalent real space expressions, such as the Chern marker, which can be evaluated even when the system of interest is not periodic. 

The real space topological markers are typically based on the system's Wannier functions or ground state projection operator, which are only short-ranged when the system is gapped. For gapless or metallic systems these functions become long-ranged, leading to non-convergent integrals. But curiously, certain metallic or gapless systems still do exhibit robust edge modes. How can we explain their robustness?

The Localizer

The novel approach taken by Cerjan and Loring in their preprint is based on an operator termed "the localizer" L(x, E). Loosely speaking, the eigenvalues of the localizer measure the strength of perturbation that must be applied to the system's Hamiltonian H in order to shift one of its eigenstates to position x and energy E.

 

In contrast to more conventional measures such as the local density of states, the localizer treats space and energy on the same footing. This allows it to distinguish trivial edge states from topological edge states even in the absence of a bulk energy gap.

For example, the signature of the localizer (difference between the number of its positive and negative eigenvalues) corresponds to the Chern number. The localizer can also be used to detect other kinds of topological states, including corner states of higher order topological insulators.

Outlook

The localizer enables the identification and study of new classes of metallic and gapless topological systems. The authors have suggested that generalizing this approach to higher dimensional topological phases and the full set of symmetry classes is a natural next step. It might also be interesting to consider how one might experimentally measure properties of the localizer. One useful application will be the identification of robust modes in low index contrast photonic systems lacking complete band gaps

The best of both worlds

A wealth of photonic devices including precision sensors and quantum light sources depend on strong light-matter interactions.

Two leading platforms for enhancing (usually weak) light-matter interactions are photonic crystal waveguides and whispering gallery resonators.

In photonic crystal waveguides light is scattered back and forth by a periodic wavelength-scale modulation of the dielectric constant. This multiple scattering reduces the speed at which light pulses propagate, resulting in slow light that has more time to interact with matter. While photonic crystals can be used to slow or even stop light, the enhanced interaction strength is accompanied by increased sensitivity to scattering losses due to imperfections and roughness in the periodic modulation, which limits their performance in practical applications.

On the other hand, whispering gallery resonators guide light along the boundary large (many wavelengths in size) dielectric particles. These boundaries can be exceptionally smooth, resulting in ultralow scattering losses, allowing light to circulate millions of times before being lost from the cavity. However, one is limited to cavity sizes somewhat larger than the operating wavelength and cannot confine light to the nanoscale volumes achievable using photonic crystals.

Published yesterday in Nature Photonics, a collaboration between researchers at NIST and the University of Massachusetts report a novel hybrid whispering gallery microring resonator. The outer edge of the microring is smooth, leading to whispering gallery modes with high quality factors. The inner edge of the microring is periodically modulated, forming a one-dimensional photonic crystal that reduces the group velocity of the whispering gallery modes by a factor of 10. Moreover, defects in the inner edge photonic crystal can be used to confine the whispering gallery modes to a small part of the ring, enhancing their interaction with localized emitters such as quantum dots.

The exceptional lifetimes of whispering gallery modes combined with the ability to tailor modal properties using periodic modulations of the inner edge makes this a highly promising platform for a variety of nonlinear optics applications.

 

Optics in 2022 & Beyond

Posting is a bit less often than usual since I'm on holiday.

My thoughts on what will be big in topological photonics next year have been published in the December issue of Optics & Photonics News. Previously I posted some initial thoughts on hot emerging topics. In the end I chose topological lasers and photonic crystal waveguides as directions likely to see increased attention in the coming year, and indeed interesting preprints on topological photonic crystal waveguides and polariton lasing have appeared since I submitted my paragraph.

In a broad sense, all of the predictions this year highlight advances in light sources and their potential applications in imaging and communication systems.

Optics in 2021

Every December Optics and Photonics News creates a list of the most exciting optics research published over the past year, based on article summaries submitted by hopeful authors. Some highlights from this year's list:

Silica Fiber Lasers and Amplifiers That Run Cold: Generation of excess heat limits the performance of optically pumped lasers. By detuning the optical pump beam such that its energy is slightly less than that of the laser transition, phonons (heat) are used to cover the energy difference, meaning that the laser cools itself below the ambient temperature while it operates!

More optics applications of artificial neural networks: Label-free identification of cancer cells using images obtained via coherent anti-Stokes Raman scattering microscopy, and characterization of the nonlinear dynamics of ultrashort pulses.

The 100-mode Gaussian boson sampling experiment that made headlines earlier this year. This is an important milestone despite recent theoretical advances in the classical simulation of the output photon distributions.

Chaotic dynamics as an alternative to quantum key distribution for encrypted communications. The chaotic approach is based on a pair of near-identical lasers (transmitted and receiver) anti-synchronized using optical feedback. The individual outputs are chaotic and seemingly random, with the message hidden in the sum of the two outputs.

Enhancing mode quality factors using levitating resonators. Edges and surfaces of resonators are messy and lead to unwanted scattering losses. Employing resonators formed by the whispering gallery modes of oil droplets, optical tweezers can be used to levitate droplets and create highly spherical resonators with enhanced quality factors.