Creative research takes time

Nowadays funding agencies prioritise research with immediate applications. Grants for early career researchers provide funding for only a few years, requiring funded projects to have a quick and clear path to fruition. However, in basic research the eventual applications are often not those that were first envisaged.

Perhaps my favourite research project was our study of topological effects in "leaky" optical systems, published earlier this year in Nature Physics. See here for a popular summary. I am proud of this work not merely because the results were eventually published in a glossy journal, but rather because it was a pure, curiosity-driven project involving short bursts of inspiration and progress separated by many months.

This project originated from a grant application we prepared in August 2018. The host institution had expertise in photonic crystal fibers, so we were interested in whether the photonic crystal fiber platform could be used to observe interesting topological phenomena. However, photonic crystal fibers are leaky wave systems which continuously radiate energy into their environment, so it was not clear whether our experience in designing topological states for bound modes would be useful in this setting.

We started working on the idea by implementing well-known approaches for numerically computing leaky modes with the help of a tutorial article, studying some simple one-dimensional examples to gain some intuition for the platform. 

By April 2019 we had developed a tight binding-like formalism allowing us to design and study topological wave effects in leaky wave systems, but we did not know what our formalism could be useful for apart from computing the decay rates of leaky topological edge states. 

After a few conferences and many discussions with other researchers, in October 2019 we finally stumbled upon the neat idea of using radiation losses to controllably fill energy bands and measure their bulk topological invariants. 

We finished a draft manuscript by the end of November 2019 and shared with some collaborators. Their feedback was that the idea was interesting, but it wasn't clear how easy it would be to experimentally test our theory. 

We spent a few more months carrying out numerical simulations of possible designs and polishing the manuscript, finally submitting it in May 2020. Our collaborators' impression was echoed by the referees, who requested more detailed and explicit simulations of our designs in a revised manuscript, which was finally accepted in December 2020.

Take home messages:

-Find inspiration for new lines of research in old reviews and tutorials, not the latest papers published in high impact journals.

-If you get stuck don't be afraid to put the project aside for a few months and work on other directions.

-Creative research takes time - 2.5 years between the initial idea and eventual publication in this case (a theory project). Experimental projects can take even longer.

Stronger quantum supremacy

 On arxiv today: Strong quantum computational advantage using a superconducting quantum processor, by the group of Jian-Wei Pan at USTC.

This preprint reports a large 66 superconducting transmon qubit quantum processor, with performance similar to Google's Sycamore processor.  The random circuit sampling protocol is used to demonstrate a quantum computational advantage with 56 qubits (c.f. the previous 53 qubit Google experiment). More measurements are taken per random circuit (19 million samples vs 3 million) to obtain a higher cross entropy benchmarking fidelity (9 sigma rejection of uniform sampling vs 5 sigma). Because the difficulty of classical simulation increases exponentially with the number of qubits, this small increase in the device size incurs a 2-3 orders of magnitude-increased cost of classically simulating the circuit.

This is a significant breakthrough - Google no longer has a monopoly on large scale programmable superconducting quantum circuits!

Edit: Today the USTC team released another preprint reporting an upgraded and programmable Gaussian boson sampling experiment!

CLEO covid conferencing

I attended (virtually) the CLEO/Europe conference last week. It's been said many times before by others, but networking and informal discussions which often lead to new creative lines of research do not occur to any significant extent at online conferences. The one silver lining is that when things return to normal, conferences will hopefully be run in a hybrid mode enabling those unable to attend in person to at least view talks remotely.

Some of the interesting talks I saw:

Fabio Sciarrino from Sapienza University of Rome gave an overview of Boson Sampling and discussed his group's recent work on using thermoelectric tuning of a laser-written waveguide array to create a semi-programmable Boson Sampling device. This aims to overcome the main limitation of the recent Chinese photonic quantum supremacy experiment (that their device is not programmable). The preprint is available here.

Vera Neef from Rostock University discussed the generation of non-Abelian geometric phases using two photon quantum states propagating through an adiabatically-modulated array of four coupled waveguides. The approach can be extended to photonic simulation of quantum chromodynamics.

Christophe Galland from EPFL gave an overview of his group's recent work on molecular optomechanics and nanocavities. The former is an interesting platform for observing quantum coherent effects at room temperature, by using a laser beam to excite a high frequency vibrational resonance of a molecule; Raman scattering can then be used to probe the resulting vibrational quantum states.

Nathan Goldman from Universite libre de Bruxelles presented a scheme to detect fractional quantum Hall states of bosons. The idea is to prepare a few-body ground state of bosons in a topological (Chern) band trapped by a confining potential, turn off the confining potential, and then apply a uniform acceleration. The resulting transverse Hall shift exhibits quantized plateaus which can be used to measure the many-body Chern number. For larger numbers of bosons, density measurements can be used to obtain the Chern number. The study was published in PRA last year. These effects could be probed using superconducting qubits using an approach similar to this paper, but with a larger lattice and more photons.

Christina Jörg from Pennsylvania State University discussed the creation of bound states in the continuum in photonic crystals using tailored environmental coupling. By embedding a photonic crystal in a suitably-designed thin photonic crystal cladding, one can create bound states in the continuum above the diffraction limit (i.e. with a volume larger than the operating wavelength). The preprint is available here.

Dynamical versus spectral localization in dissipative systems

A short summary of this paper which was published in Nature Photonics last week.

Waves in random or disordered media can exhibit Anderson localization. In Anderson localization, interference between different wave scattering paths (and in particular, constructive interference of backscattering) results in a complete suppression of wave propagation; waves remain localized around their sources indefinitely, with an amplitude (or intensity) decaying exponentially with the distance from the source.

Anderson localization is a universal phenomenon. It was originally predicted in a 1958 publication analyzing electrons in disordered crystalline materials, and has since been observed for a wide variety of waves including matter waves (Bose-Einstein condenstates), optics, and acoustics.

Historically, a thorny issue complicating the observation of Anderson localization in classical wave systems such as optics and acoustics has been the question of how to distinguish Anderson localization from absorption-induced localization; both lead to a similar exponential decay of the wave amplitude.

The present work concerns the generalization of Anderson localization to disordered dissipative optical wave systems with random distributions of gain and/or loss, and the subtle distinction between spectral localization and dynamical localization.

Spectral localization refers to localization of the modes of the medium. Each mode has a specific energy (frequency). The mode may be excited by placing a source (e.g. a speaker in the case of acoustic waves) in the medium tuned to that frequency, in which case the amplitude profile of the generated wave will match the profile of the correspond mode.

Dynamical localization refers to the time evolution behaviour of wavepackets comprising a range of frequencies, excited by switching the source on for a short time.

In wave systems that are Hermitian (conservative, i.e. no gain or loss of energy), spectral and dynamical localization coincide because the time evolution of any wavepacket can be obtained by expanding it as a sum of the medium's modes. The paper shows that this is not the case for wave systems with dissipative disorder; dynamical delocalization can occur despite spectral localization. In other words, waves generated by a monochromatic source will have an exponentially localized amplitude profile, whereas waves emitted by a broadband source will spread to distant parts of the system.

To demonstrate this dynamical delocalization, the authors had to carefully distinguish between energy transport and energy loss due to absorption. In particular, for lossy media the wave amplitudes are always decaying exponentially in time. At any moment in time we can consider the shape of the wave's amplitude distribution (e.g. by increasing the sensitivity of the camera or microphone used to detect the waves) and how it decays with separation from the source. 

In dissipative wave media the modal expansion is still valid, but different modes will have different loss rates. Therefore, the relative amplitudes of the different modes in the expansion will change in time, leading to large changes and in particular spreading in the normalized wave amplitude profile - dynamical delocalization. This is the main result of the study, which observes the phenomenon using a cleverly-designed system of coupled optical fibres.

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?

Quantum machine learning with large data sets

Today I came across this interesting paper by Aram Harrow, which presents a lucid discussion and possible solution to one of the big problems with quantum machine learning: how to obtain useful quantum speedups when dealing with big data sets that are slow to feed into and read out of the quantum processor.

The main point is that real world classical data sets are likely to lack special structure to enable them to be efficiently encoded into quantum states (a prerequisite for quantum algorithms with a proven speedup). Input and output of large data sets will thus overwhelm any possible near-term quantum advantage. Therefore, an essential step of any practical quantum machine learning algorithm will be to first preprocess the data to obtain a smaller but representative subset.

How then can the quantum computer help us? We should look for quantum speed ups in searching the space of machine learning models used to describe the reduced data set. Most machine learning models have some form of structure. That is, they can be specified in terms of relatively simple functions such as matrix multiplications or minimizing quadratic loss functions. The quantum computer can exploit this structure to place the available models in a quantum superposition and then achieve a speedup using rigorously-proven algorithms, such as Grover search to find the best model.

However, Grover search is impractical to run on near-term devices, which are largely limited to variational quantum algorithms which lack proven speedups. This paper has tested how well classical data preprocessing works in combination with the quantum approximate optimization algorithm (QAOA), focusing on k-means clustering. In the small scale examples considered, QAOA did not work well with the reduced data set. The authors conjecture that the poor performance may either be limitation of QAOA (requiring the exploration of other NISQ-friendly algorithms), or due to the rather small sizes of the reduced data sets (up to 20 points are used to summarize the full sets containing thousands of points). 

It will be interesting to explore these ideas further.

Cloud quantum computing on AWS

Some thoughts on Amazon's quantum computing offerings available via AWS, based on a quantum computing workshop I recently attended:

The AWS-Braket library conveniently provides access to three different hardware backends (DWave, Rigetti, IonQ), which each has its own strengths and limitations. 

You can also run two different cloud quantum simulators (SV1 and TN1). SV1 is a state vector simulator (so it runs circuits without any approximation), and can apparently handle up to 24 qubits, which is about double what can be easily done on a standard personal computer. TN1 uses tensor networks to more efficiently simulate certain larger circuits, but it doesn't always work.

Presently the AWS-Braket library only handles circuits defined using the gate model of quantum computation, so there is no ability to control the individual pulses used to implement the gates on the hardware, which are required to perform analog quantum simulation or implement specialised pulse sequences in order to improve the performance of specific circuits. Amazon plans to include this functionality in a later release.

The hardware: the DWave devices have 5760 and 2000 "qubits" (however with limited connectivity, and restricted to quantum annealing), the Rigetti chip has 32 qubits arranged in a quasi-1D geometry, while the IonQ device currently supports 11 qubits, with plans to extend to 32 qubits later this year. This means that one can run circuits that are in principle a real pain to simulate using the best classical computers. However, it's still unclear whether the current levels of device noise and limited qubit connectivity (in the case of the DWave and Rigetti devices) rule out a quantum advantage using these devices.

The catch: running these state-of-the-art devices is expensive! The schedule of prices can be found here: $0.30 per circuit run, plus an additional charge per measurement repetition. How much will this cost the end user? Let's take as a representative example solving the MaxCut problem using the quantum approximate optimization algorithm, taking parameters from a recent proof-of-concept experiment by the Google group. For the simplest implementation of the algorithm, optimization of the two variational parameters to find the optimal solution required ~10 iterations, each comprising 6 energy evaluations with 25,000 shots per energy. Using Rigetti's superconducting chip's fee of $0.00035 per shot, this translates to a total cost of 60*(0.03 + 25000*0.00035) = $527! Larger real world problems will likely require many more iterations in order to converge to good solutions, pushing the price up further. 

Therefore the priority for users of these noisy intermediate-scale quantum computers should be to not merely to use them to solve problems faster existing classical algorithms; it would be more cost-effective to simply throw more classical computing power at them. Instead, focus on problems that will remain too hard to solve even as classical computers continue to improve.