More on quantum topological data analysis

 Two preprints on quantum topological data analysis (TDA) were posted to arXiv last week.

From the IBM team, Exponential advantage on noisy quantum computers. This is a follow-up to their proposal from last year, arXiv:2108.02811, implementing their linear depth NISQ-TDA algorithm (my earlier synopsis) using a trapped ion quantum processor. 

The introduction nicely frames the key ingredients required for demonstrating an end-to-end quantum advantage using near-term device, and then explains how NISQ-TDA meets all of the requirements, for example by having small input and output data sizes. Another advantage of NISQ-TDA is that the output observables, the Betti numbers, are known to be quantized topological invariants, leading to a robustness to shot noise and reducing the number of measurements required to obtain an accurate result. 

The article ends with the optimistic outlook that "a 96-qubit quantum computer with a two-qubit gate and measurement fidelity of ∼ 99.99% suffices to to achieve quantum advantage on the Betti number estimation problem." This really seems to me the strongest candidate for demonstrating a quantum advantage. Anyone interested in near-term quantum algorithms for machine learning applications should read this paper!

------

A second preprint was posted by researchers from Deloitte, Understanding the Mapping of Encode Data Through An Implementation of Quantum Topological Analysis. This work offers a more pessimistic viewpoint, stating that "the empirical results show the noise within the data is intensified with each encoding method as there is a clear change in the geometric structure of the original data, exhibiting information loss." However, their approach seems to be based on the original quantum TDA algorithm, based on Grover search and quantum phase estimation, which is not suited for near-term devices.

Fusion-based quantum computation

A brief summary of the great talks by Mercedes Gimeno-Segovia and Terry Rudolph at the 6th Quantum Africa Conference on PsiQ's approach for building a large scale photonic fault-tolerant quantum computer using entangling measurements: fusion-based quantum computation. See also an earlier perspective by Rudolph published in APL Photonics.

Fusion-based quantum computation can be seen as a middle ground between the gate model (employed in most other platforms for quantum computing) and measurement-based quantum computation, which replaced nonlinear operations (hard to do using quantum states of light) with a suitable sequence of single qubit measurements.

The first step in measurement-based quantum computation is to prepare a large scale entangled resource state that is big enough to perform the desired computation. This is hard.

Fusion-based on the other hand employs two-qubit (entangling) measurements as its basic building block. This allows the calculation to be performed using a steady stream of constant-size resource states. These resource states also require multiple photons to be entangled, which is hard, but at least their size is bounded. Creating constant size resource states with sufficient fidelity and speed is the challenge which PsiQ believes they can solve.

What distinguishes PsiQ from their competitors is that their platform is easily scalable to billions of logical qubits and gates using commercial silicon lithography employed to make all our conventional electronic computers. I think the only other platform which can make such a claim are the silicon qubits being pursued by a few groups, including the UNSW spin-off Silicon Quantum Computing. By contrast, the quantum processors currently available on the cloud (superconducting circuits and ions trap) are (relatively) large and clunky devices requiring painstaking optimisation and babysitting but nevertheless might only support a few logical qubits if quantum error correction can be implemented.

An interesting point raised in the talks was that error-corrected devices will be very different from any of the currently-available quantum processors; once you have working error correction many of the details of the physical qubits become unimportant. Thus, PsiQ's approach is to create billions of "good-enough" physical qubits rather than a lower number of perfect qubits.

Quantum Africa Conference (QA6)

Quantum Africa is a conference covering quantum information and quantum computing running next week (Monday 12th to Friday 16th of September 2022).

It will be held in hybrid mode with a mix of in-person and online talks.

The talks should be quite pedagogical and will be given by outstanding researchers from academia and industry, including Steve Girvin (Yale, USA), Francesco Petruccione (UKZN, South Africa), Pedram Roushan (Google Quantum), and Terry Rudolph (PsiQuantum).

Talks will be recorded for later on-demand viewing for registered participants. Registration is free for online attendance!

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.

Open access in physics

In the news last week: The US government will require federally-funded research to be immediately free to read upon publication. 

The Brief provides a detailed discussion of the planned changes. 

A perspective from physics publishers including the American Physical Society can be found in a recently prepared a white paper on open access publishing. The white paper was prepared in light of growing interest in open science, including open publishing.

In Europe, one model of open publishing being promoted by several funding agencies is Plan S (see coverage in Nature last year here). Plan S remains controversial and has attracted criticism for several reasons, including lack of academic freedom for researchers to choose the most appropriate publishing venue, penalising junior researchers who may not have the funds to pay the (large) open access publication fees, and rules that adversely impact non-profit scholarly societies.

Some thoughts on open publishing as a grant-starved researcher and part-time editor for the American Physical Society:

Academic freedom in where we choose to publish is important - any research article will have a particular audience in mind, and we should be free to (try to) publish in a journal with the best visibility to the intended audience. Many activists argue that publicly-funded research out to be free to read for any members of the public to read. This goal is already largely served by preprint servers and most existing publishing agreements, which allow author-prepared versions of the article to be made freely available on the arXiv, a repository provided by their institution, or even their personal website. Even in the case of publishers strictly enforcing an embargo, one is free to contact the authors directly via email if one really needs the journal-published version. Most authors would be more than happy to share their work.

Under open access plans the author is forced to pay to publish. Open access mandates severely curtail academic freedom - publication charges will restrict the choice of journal, potentially forcing authors to publish in a cheaper, low-visibility journal. This will adversely impact junior researchers, smaller and less well-funded institutions, and researchers from lower-income countries.

Why not just force open access journals to have lower publication fees? Aren't they simply charging to ask referees to reports for free and to upload a PDF on a web server? Why does this typically cost thousands of dollars?

In defense of seemingly-high open access article publication charges, one major contribution to the high costs is (and/or should) support the salaries of the journal editorial staff, who have an important role in selecting and vetting reviewers. In the case of many newly-established for-profit open access publishers, this important task is not handled by qualified scientists. However, unless one has a reasonable knowledge of the research subject, one will not have an idea on which referees are credible.

Another important difference between the subscription and open access models is that the open access publication charges need to also cover all manuscripts that are not published by the journal! The more selective the journal, the more articles will be considered and eventually rejected. The published articles need to cover the cost of processing the rejected articles. Under the subscription model the subscription fee can be tailored towards that institution's volume of manuscript submissions.

Since rejected articles generate no revenue, for-profit publishers have an incentive to publish everything and it quickly becomes a race to the bottom. So, why not just publish everything, and let researchers decide which works are most important? For a start, this is already handled (without the author paying) by preprint venues such as arXiv. We publish in journals to make our work visible. Visibility requires selectivity so that the most important research is highlighted. We don't have time to read everything that appears in our research area. If journals no longer enforce selectivity, we will end up focusing on reading works from authors we are familiar with - those from high profile, well-established groups. This will end up penalising junior researchers and those from institutions without a well-established brand.

It should be emphasized that open access is just one small part of the open science movement. Rather than penalising established scholarly societies that have a good track record of fostering excellent science, I think funding agencies should focus on broadening the support and dissemination of other styles of academic writing - the academic grey literature. For example, particularly in the life and medical sciences there is a bias towards publishing significant results, resulting in the replication crisis.

Another form of academic writing that is not widely made available for the public to read are white papers and grant proposals. I think this is one area where openness could be valuable not just for working researchers, but also for historians of science as a means of tracking the evolution of different ideas and research fields. 

Many funding agencies still do not even provide basic statistics on their grant programmes, such as the number of applications in a funding round and the success rate. It would be very interesting to see more detailed statistics (e.g. success rates versus research areas, perhaps aggregated over multiple years) as a way to track changes in the interests of the applicants and funding agencies.

It would also be valuable to see the full proposals funded by the grant agencies, most likely after am embargo period - perhaps the length of the project. This would be more beneficial to the public for getting an idea on the kind of research they are funding through their taxes - journal articles are aimed at a highly specialised audience, whereas grant proposals are usually aimed at a much broader audience. Moreover, early career researchers would be able to see what kinds of proposals are funded by a given agency, helping them to judge whether their applications will be competitive or a waste of time. Under the current system we need to ask professors directly for examples of successful applications.

The 2nd POSTECH MINDS Workshop on Topological Data Analysis and Machine Learning

Resuming (hopefully) semi-regular posting after a few weeks finishing revisions to a few manuscripts:

POSTECH in Korea is hosting another workshop on the intersection between topological data analysis (TDA) and machine learning at the end of September [Sep. 26 (Monday) ~ Sep. 29 (Thursday)]. From the conference website:

This workshop will bring together researchers and students working on TDA and machine learning and provide an opportunity where they present their recent research and share ideas. Further, this workshop will also provide tutorial sessions that will introduce various TDA computational tools and provide practical hands-on tutorials. This is a sequel to the workshop of the same name held in 2021 - ILJU POSTECH MINDS Workshop on Topological Data Analysis & Machine Learning, 2021.

I attended (virtually) last year's workshop and found it quite interesting. As a newcomer to the field it gave a good picture of some of the cutting-edge questions being pursued in TDA. There is no registration fee, but registration is required for access to the workshop live stream.

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.