More papers, less progress?

Slowed canonical progress in large fields of science

This thought-provoking article was published in PNAS a few months ago. The authors analyze the Web of Science dataset containing ~ 90 million papers and ~1.8 billion citations to quantify how the size of a discipline correlates with its rate of innovation and disruptive advances.

One measure of innovation is the rate at which new papers accumulate citations. Larger fields exhibit a rich get richer effect, with highly-cited papers disproportionally accumulating new citations. Thus, established ideas become entrenched, while potentially disruptive new ideas may get lost in the crowd of less-read and less-cited papers and forgotten.

The growth of physics has been easy to see even during my short career. The size of the daily arXiv postings has doubled since the time I was a PhD student. It is impossible to carefully read all of the new papers relevant to one's field - there is not enough time! We need to work together to not just promote our own work, but also spread the word to colleagues and collaborators whenever some exciting new idea appears in the daily posting.

The authors list some potential remedies to reduce the quantity of publications, but admit there is no perfect solution. For example, proscribing a limit to the number of annual publications incentives safer, follow the leader-type research that is more likely to attract a healthy number of citations. 

Senior researchers are not publishing more frequently to advance their own careers, but to ensure their students and postdocs have a chance on the hyper-competitive academic job market. This will continue as long as hiring committees and funding agencies base decisions off simple metrics such as citation counts.

More sophisticated metrics such as the "disruption measure" mentioned in the paper may be a better way to quantify the impact of publications. Unfortunately truly disruptive ideas may not be recognised quickly enough; fixed-term academic contracts rarely last more than a few years.

On the other hand, perhaps the use of bibliometrics is too narrow a way of quantifying scientific progress. Growing publication rates is also indicative of a growing, highly-skilled workforce capable of innovation in other areas.  A PhD does not lock you into an academic career forever.

What do you think?

US Blacklists Chinese Quantum Computing Companies

In the news this morning was a report that USA has added 12 Chinese-affiliated companies to its export blacklist, including one based in Singapore, with the headline in the Financial Times being "US Blacklists Chinese Quantum Computing Companies".

I was curious as to which quantum computing company based in Singapore may have been blacklisted. However, the headline was misleading; only a few of the newly-blacklisted companies deal with quantum computing (Hefei National Laboratory for Physical Sciences at Microscale, QuantumCTek Co., and Shanghai QuantumCTeck Co., Ltd.). The one Singaporean company blacklisted, Corad Technology Pte Ltd., seems to only design and manufacture printed circuit boards. Here is the original document outlining the additions to the blacklist.

Regardless, as quantum computers become more powerful and start to develop useful capabilities more technology restrictions and export controls will likely be introduced. Today's news highlights the importance of building up a domestic quantum industry even in small countries such as Singapore and Australia; we cannot rely simply on buying the final product from the big players based in the USA and China.

arXiv highlights

Some arXiv preprints that caught my attention over the past week:

Fock lasers based on deep-strong coupling of light and matter

Researchers at MIT predict that the deep strong coupling regime achievable in state-of-the-art superconducting quantum circuits can be used to design novel light sources of N photon Fock states with N ~100. The mechanism is a suppression of stimulated emission via a many-body photon blockade. Large N Fock states are a key ingredient in certain quantum sensing and superresolution schemes, but are extremely hard to make using conventional quantum light sources. This proposal focuses on the generation of microwave photons. A related preprint considers the extension to optical frequencies.

Eigenvalue topology of non-Hermitian band structures in two and three dimensions.

This is a theory follow-up to the authors recent publication demonstrating knotting and braiding of non-Hermitian energy bands. In 2D systems the braid group describes non-contractible loops in the Brillouin zone which can either encircle non-Hermitian degeneracy points or wrap around the whole Brillouin zone. In 3D it is the non-Hermitian degeneracies themselves that form curves that can be knotted or braided. The group theory used to classify general N-band non-Hermitian systems seems rather heavy at first glance.

Anderson localization of a Rydberg electron.

Rydberg atoms host highly excited electrons residing in orbitals with large principal quantum numbers n. Thanks to spherical symmetry, each n corresponds to n^2 degenerate orbital angular momentum modes, forming a large set of available modes. Using now-sophisticated optical tweezer technology it the authors propose placing strong scatterers in the vicinity of the Rydberg orbitals, inducing coupling between them. By controlling the effective inter-orbital coupling and energies by the scatterer positions' the authors propose the realization of the Anderson tight binding model describing localization of electrons in disordered systems. This is a neat idea as it means a single Rydberg atom may be used as a toolbox for exploring various fundamental models from condensed matter physics.

Superconducting optomechanics in topological lattices.

Topological lattice designs are now attracting growing experimental interest in optomechanics, following seminal theoretical proposals several years ago. Here 1D Su-Schrieffer-Heeger lattices and 2D honeycomb lattices are implemented. Optomechanics is a promising setting for exploring both nonlinear and quantum topological phenomena in lattices.

Finally, some self-promotion:

Nonlinear signatures of Floquet band topology.

We finally finished the follow-up to our PRL published earlier this year on measuring Chern numbers using nonlinear modulational instability. The approach also works for periodically-driven Floquet systems, at least for identifying Chern insulator phases. The detection of anomalous Floquet phases is a little more tricky.

 

Classical shadows of quantum states

Reconstructing quantum states is hard. Full tomography of an n-qubit quantum system requires a number of measurements, computing power, and memory that grows exponentially with n.

There are a variety of more efficient (e.g. polynomial scaling) methods for reconstructing classes of quantum states under simplifying assumptions such as sparsity or short-ranged entanglement.

Quantum shadow tomography is a new efficient technique applicable to arbitrary quantum states.

The key idea is that in most situations we don't need to reconstruct the full density matrix of the quantum state; what we are interested in is expectation values of certain observables of that state. By performing measurements of the state in a set of randomly-chosen bases, one can predict O(M) low weight observables using only O(log M) measurements.

This is important because many important potential applications of quantum computers including quantum chemistry scale poorly with the problem size, e.g. requiring O(n^8) observables to be measured with high precision to obtain molecular energies. Existing methods for more efficiently obtaining these observables (e.g. by grouping commuting observables) are challenging to scale, since finding the optimal grouping is an NP-hard problem.

Last year an efficient protocol for quantum shadow tomography was proposed.

A PRL paper published last week has now experimentally demonstrated quantum shadow tomography using a 4-qubit system.

Related work using spatial modes of photons and re-analysis of existing experimental data.

Orthogonality catastrophe on quantum devices

I recently read Walter Kohn's Nobel Lecture on density functional theory. It's an accessible introduction to a method that is hugely important for materials science. Sec. IIC makes some remarks on the orthogonality catastrophe, arguing that many-body wave functions are not meaningful for more than ~1000 particles because the exponential growth of the Hilbert space makes any approximation to a desired state have an exponentially-vanishing overlap with that state.

Quantum computational chemistry is promoted as one of the most promising potential applications of quantum computers, offering an exponential speed-up compared to classical algorithms. But there is a big caveat hidden behind these claims: Algorithms exhibiting rigorous speed-ups such as quantum phase estimation require as an input an approximation to the ground state wavefunction. The overlap with the ground state determines the success probability of the algorithm. Thus, computing the ground state energy of a large many body system will require an exponentially good approximation to the corresponding wavefunction, potentially killing the quantum speed-up.

Some experts in quantum chemistry considered this issue in an arXiv preprint a few years ago: Postponing the orthogonality catastrophe: efficient state preparation for electronic structure simulations on quantum devices. There the authors estimated that efficiently-computable approximations such as Hartee-Fock wavefunctions may provide a sufficiently good overlap for moderate system sizes of up to 40 electrons that are already beyond the reach of classical computations. But it seems quantum computers won't be a magic bullet for larger systems involving hundreds of electrons; it will still be necessary to use physical insight to decompose large systems into smaller tractable subsystems. 

 

It is curious that this study has only received 18 citations to date and was not published in a journal - there must be a story behind that...

Lasing in a Mobius strip microcavity

 

A neat paper was just published in Physical Review Letters and highlighted as an Editor's Suggestion: Möbius Strip Microlasers: A Testbed for Non-Euclidean Photonics

 

In conventional microring lasers based on whispering gallery modes each lasing mode can be described semiclassically as a light ray that is reflected off the boundary between the outer edge of the high refractive index ring and the ambient medium. The ray returns to the same position after completing one cycle of the ring, forming a periodic orbit. Rays with a large angle of incidence with the outer edge will undergo total internal reflection and thus have extremely low losses. Thus, the rays follow the outer edge closely.

What happens if we add a twist to the ring to form a Mobius strip? Do the whispering gallery lasing modes survive?

 

No. The boundary of a Mobius strip forms a single closed curve; following the (concave) outer edge for one cycle you will end up at the (convex) inner edge, which cannot support whispering gallery modes.

 

The simplest periodic orbits supported by the Mobius strip involve alternating reflections off the inner and outer edges. The low angle of incidence makes these orbits highly lossy and unlikely to lase.

 

The authors fabricated Mobius strip cavities and measured their lasing spectra. The spacing between the peaks was used to obtain the optical path length of the lasing modes, revealing that they are neither whispering gallery modes nor the alternating reflection periodic orbits. Instead, they reveal a novel class of periodic orbit unique to three-dimensional Mobius strips, in which the ray only reflects off the outer edge (ensuring low losses), but also crosses the interior of the strip to avoid ending up on the inner edge.

The experimental observations are corroborated with numerical solutions of the Helmholtz equation and semiclassical computation of the periodic orbits. Future work will consider the full vectorial Maxwell's equations to unveil the role of polarization in this peculiar class of twisted cavities.

What's new in topological photonics

Quite a few significant pre-prints relevant to different aspects of topological photonics appeared on arXiv this week:

Nonlinear topological photonics

Combining strong single photon interactions with topological bands is being hotly pursued as a means of creating fractional quantum Hall states of light. In contrast to their electronic counterparts, photons can be lost due to absorption or scattering. Researchers from Yale University ask whether photonic fractional quantum Hall states stable against losses. It turns out the simplest way to protect against losses (by injecting more photons) doesn't work for these exotic topological states due to their nonlocality: photon loss can generate "fractional" holes in the state, whereby half a photon is lost from one part of the system, and half a photon from another part. Due to this nonlocality, adding a single photon to one part of the system is insufficient to restore the ideal fractional quantum Hall state.

In the weak mean field interaction regime, a collaboration between Russia, Germany, and Portugal has developed theory for edge solitons supported by quadratic nonlinear media. Such solitons comprise a bound state between some fundamental frequency and its second harmonic. Because of the need to take two very different propagation frequencies into account, modelling must be based on the full continuum paraxial equation, rather than simpler tight binding models.

Performance of topological photonic crystal waveguides

As I mentioned a few weeks ago, an exciting trend is that research groups not specifically focused on topological photonics are starting to become interested in topological designs. Researchers from the Niels Bohr Institute report full wave simulations of photonic crystal waveguides for quantum photonics, comparing the performance of their non-topological glide-plane waveguide against topological valley Hall waveguides. The valley Hall waveguides can exhibit stronger coupling between quantum emitters and the optical modes, and with lower scattering losses due to fabrication imperfections. The authors emphasise that the lower losses are not due to the topological protection, but rather due to the differing modal profile, which is less strongly localized to the air-dielectric interfaces responsible for the losses.

Topological phases using orbital hybridization

Most designs for topological photonic systems are based on suitably-designed coupling between identical "atoms" formed by modes of a fixed symmetry bound to waveguides or resonators. This is because modes with different symmetries typically have very different energies or propagation constants, making the interaction (or hybridization) between them weak. But by suitable fine-tuning it is possible to engineer near-degeneracies between modes with different symmetries, opening up new possibilities for controlling photonic band structures. A proof of concept demonstration using one-dimensional optical waveguides was published in PRL a few months ago. Now a team from ITMO University have predicted that hybridization between s- and d-type orbital modes of two-dimensional lattices can give rise to higher order topological phases. Since this approach does require fine-tuning to ensure the degeneracy between the different orbitals, microwave implementations will be a lot easier than optical frequency ones.

Non-Hermitian topology without gain and loss

A pet peeve of mine regarding many studies of non-Hermitian topology is that they consider Hamiltonians that are intrinsically unstable due to the presence of amplifying modes. To determine the fate of these amplifying modes, higher-order corrections such as gain saturation should be taken into account. The simplest solution - add some overall loss to make the system stable - tends to make any topological modes strongly lossy, which is undesirable for applications. 

 

An alternate solution is to come up with conservative systems that can somehow support non-Hermitian topological phenomena. One example we found was simply Maxwell's equations, where non-Hermiticity emerges because the inner product depends on the local constitutive parameters of the medium. 

 

This week, researchers from IFW Dresden report that the reflection matrix describing scattering of waves from insulating (gapped) systems could be a simple setting for observing non-Hermitian topological effects. In another study, researchers from NTU Singapore show how non-reciprocal coupling can be designed to achieve non-Hermitian topological phases with purely real spectra.

Squeezed Spin States

Today I read the classic paper Spin Squeezed States, which was highlighted as a Milestone paper by Physical Review A last year.

In this paper the authors generalize squeezing transformations (usually considered in the context of bosonic modes) to spin S systems. Squeezing allows one to reduce the fluctuations along one spin axis, at the expense of increased fluctuations along another axis, enabling precision measurements with noise below the standard quantum limit.

The ability to use squeezing to reduce quantum noise is particularly important for near-term quantum processors, potentially enabling calculations to be carried out using fewer measurements. Writing in PRX: Quantum, Pezze and Smerzi last month proposed an improved quantum phase estimation algorithm employing spin squeezed states. The key advantage of spin squeezed states compared to an earlier algorithm employing GHZ states is their enhanced robustness to noise and losses.

It is interesting to consider how spin squeezing might be useful for improving the robustness to noise and performance of noisy intermediate-scale quantum algorithms...

More on nonlinear Thouless pumping

A follow-up to my earlier summary on the experimental observation of quantized nonlinear Thouless pumping.

A few theoretical groups have now posted preprints to arXiv proposing explanations for this effect:

The Chern Number Governs Soliton Motion in Nonlinear Thouless Pumps, by two of the authors of the original experimental study, focuses on the weakly nonlinear limit. By rewriting the governing discrete nonlinear Schrodiner equation in the basis formed by the lattice's Wannier functions, the weakly nonlinear dynamics in the complex topological lattices reduces to that of a simple 1D lattice, in which the nonlinear modes are peaked at the centre of the Wannier functions. Thus, the pumping of the solitons follows from the pumping of the linear Wannier functions, which is protected and quantized by the Chern number. Using their theory, the authors design and simulate a soliton pump in a two-dimensional lattice.

Quantized transport of solitons in nonlinear Thouless pumps: From Wannier drags to topological polarons also uses the Wannier function picture to explain the quantization of nonlinear pumping for weak mean-field nonlinearities. In addition, the authors analyze the underlying quantum model (from which the nonlinear Schrodinger equation is obtained by taking the mean field limit) of a Bose gas strongly interacting with massive impurities. Strong coupling between the Bose-gas results in formation of a quasi-particle (Bose polaron), which also exhibits stable quantized pumping.

Nonlinear Thouless pumping: solitons and transport breakdown, submitted before publication of the Nature paper, uses the Wannier function representation to understand the strongly nonlinear limit. In the Wannier basis high power solitons are a superposition of Wannier functions from multiple bands. In this case, the energy difference between the constituent bands leads to a rapid oscillatory motion of the wavepacket during the pumping cycle, superimposed with a slower (average) drift. The average drift speed is quantized by the sum of the bands' Chern numbers. The transition between the low and high power pumping is sharp, occurring as a nonlinear bifurcation (also reported in the experimental paper).