Quantum Computing Summer School at Los Alamos National Laboratory

The Quantum Computing Summer School is an immersive 10-week curriculum that includes tutorials from world-leading experts in quantum computation as well as one-on-one mentoring from Los Alamos National Laboratory staff scientists who are conducting cutting-edge quantum computing research. Summer school fellowship recipients will be exposed to the theoretical foundations of quantum computation and will become skilled at programming commercial quantum computers, such as those developed by IBM, Quera, IonQ, Quantinuum, DWave. All students (undergraduate and graduate) are encouraged to apply.  

In the first 2 weeks, students will attend lectures given by world-leading experts – from academia, industry and national laboratories – in quantum computing research. Following the 2-week lecture period, each student will work on a research project in quantum computing for the remaining 8 weeks. For this research project, each student will be paired with a LANL mentor who will propose project topics and provide guidance. Each project will involve some hands-on programming of a quantum computer (IBM’s, Quantinuum’s, Quera, D-Wave’s, as available). If time permits, the students will begin preparing their results for publication.

This is an fantastic opportunity with so many of the student projects delivering important findings on various hot topics related to quantum computing. This is a testament to the quality of the mentorship provided by the staff scientists involved in the school.

More information including how to apply is available here. The application deadline is January 11th, 2026.

Quantinuum Technical Workshop

Yesterday I attended a workshop by Quantinuum, introducing their latest Helios chip to the Singapore quantum ecosystem. The programme included tutorials on hybrid quantum-classical computing workflows, including real-time measurement and conditional circuit operations, as well as applications to quantum error correction and quantum chemistry.

As someone who previously worked on NISQ processors and interested in trying out the latest generation of quantum processors, it was exciting to learn more about the new capabilities that are available:

• Real-time qubit measurements and reset combined with conditional operations open new opportunities for circuit design, such as the use of probabilistically generated magic states to reduce circuit depth.
• Gate fidelities are improved by an order of magnitude! 
• It seems like quantum error correction can actually work on real hardware!

 At the same time, some of the big challenges we struggled with before remain open problems:

• Trapped ion systems are slow. Current "error correction" capabilities are practically limited to error detection and post-selection - full-on error correction requires too big an overhead in terms of circuit depths. There is a need to carefully tailor the error correction code to the specific problem and hardware.
• Quantum chemistry use cases seem to have hit a wall in terms of the complexity of implementing the second-quantized Hamiltonians - circuit depths and required number of measurements become intractable well before one can use all of the available physical qubits. Switching from variational algorithms to subspace methods only partially addresses this.

And some other thorny issues mentioned during the discussion breaks:

• With superconducting quantum processors or other platforms with fixed qubit positions, one often has the luxury of choosing the best set of the qubits on the device and avoiding bad ones. This isn't supported on the Quantinuum processors due to the qubit shuttling - you have to use whatever you're given and can't keep track of which ions are the best to use. This might make the performance more unpredictable from day to day. One suggested approach was to instead perform a tomography on the different quantum logic regions of the device (where the gates are actually performed), to see if there is substantial variation in their fidelities.
• Because the gates are so slow, zero noise extrapolation (a simple and effective error mitigation scheme) have limited noise data to work with. Methods to generate more data (by probabilistically expanding only some of the two-qubit gates) need to execute many more circuits, giving a big overhead in terms of compilation time.
• Conditional circuit operations such as post-selection can substantially increase the number of shots required and expenses incurred by the end-user.

All in all, it was great to see the broad interest in the hardware and insightful technical questions from the audience. Looking forward to seeing what Singaporean researchers get up to with the new Helios processor once it is installed and operational in Singapore late next year!

Double-bracket quantum algorithms

Recently Marek Gluza visited SUTD to give a seminar on double-bracket quantum algorithms. This is an interesting family of quantum optimization algorithms based on Riemannian geometry, which diagonalize an operator (or minimize an energy) using gradient descent in the space of unitary operators. For example, minimization of energy via this gradient descent is realized as the flow,

$$ \partial_t \rho = [ [\rho (t), H], \rho(t) ], $$

where the first commutator $[\rho(t), H]$ is the energy gradient in the space of unitary operators - the direction that locally minimises the energy of the state $\rho(t)$ - and the second commutator evolves $\rho(t)$ in this direction. In other words, this is a nonlinear evolution governed by the effective time-dependent Hamiltonian $H_{\mathrm{eff}} = [\rho(t),H]$. Similar flows were introduced by R. W. Brockett in the 1990s as a way to use dynamical systems to diagonalize matrices. When implemented with a finite step size $s$, this flow recursively generates better approximations to the ground state as

$$ \rho_{k+1} =  e^{s [\rho, H]} \rho_k.$$

Because of the recursion (you need to first generate $\rho_k$ before applying the next set of gates to make $\rho_{k+1}$), the circuit depth grows exponentially with the number of steps. On the other hand, in contrast to variational quantum algorithms (where one has to measure gradients of all the classical control parameters of the circuit), to implement the double-bracket flow you only need specify the initial state $\rho_0$ and the step size $s$, avoiding big problems such as barren plateaux and choosing an appropriate variational ansatz. Double-bracket flow is guaranteed to converge, so it can pick up after other methods get stuck.

Marek noted that because of the circuit depth blow up, a warm start is essential to get the best performance. For example, one might optimize a shallow variational quantum circuit such as QAOA to obtain a low energy state, followed by a few steps of double-bracket flow to home in on the ground state.

This is a great example of how quantum computing can draw inspiration from classical algorithms and control theory, giving a fresh application of the humble idea of optimization via gradient descent! 

The slides are available here.

GenQ Hackathon: Quantum for Finance

Last weekend I had the pleasure to attend the GenQ Hackathon: Quantum for Finance, joining as a mentor for the teams. Events such as this are important as a means of building familiarity with quantum processors amongst the participants from diverse backgrounds, from physics to finance majors and from high school students to veteran software engineers. Applications of quantum processors will not just need PhD-level quantum algorithm specialists, but also people with a broader range of skills able to make sense of where quantum algorithms may be practically useful.

The overall winning team had the, in my opinion, crucial insight that whatever fancy new solution you come up with, be it AI or quantum-designed, it had better be interpretable. Particularly in the high-stakes world of finance, someone will ultimately be responsible for decisions made based on the quantitative model. End-users won't trust a black box model. A model that spits out a single number - such as an F-score or correlation coefficient - will never be as trustworthy as a model that can clearly show all the relevant variables. Because of this, the team incorporated Mapper into their solution for detecting anomalies in the form of fraudulent credit card transactions.

One thing I was surprised by was how few of the teams took into account the clear advice given in the opening statement from Hongbin Liu (from Microsoft Quantum): In future practical use-cases of quantum processors, the cross-over point at which a quantum processor is expected to out-perform existing (very powerful) classical algorithms and high performance computers will involve days to weeks of wall-clock runtime. One on the judging criteria specifically focused on the scalability of the proposed solution. Despite this, in their final pitches many of the (unsuccessful) teams focused on quantum circuits limited to several qubits with second-scale run-times, claiming apparent speedups compared to selected classical benchmarks. However, such small-scale quantum circuits are trivially classically simulable.

I observed almost all the teams using ChatGPT or some other favourite large language model, both for background research on the chosen problem as well as rapid code generation. It was also striking to see how much easier it is now to write, compile, and execute quantum circuits on a cloud quantum processor by making use of quantum middleware providers, who now sell this as a convenient service. 

 

International Conference on Quantum Science & Technology (6-9th October, 2025) - call for abstracts

The main aim of the conference, to be held in Quy Nhon, Vietnam, is to develop links between physicists in Vietnam and those in France and around the world who are contributing to the advances of quantum physics. The scientific programme features eminent invited speakers including Serge Haroche. The following themes are envisaged:

• quantum optics, quantum communication and quantum computation
• topics where condensed matter, atomic physics and chemical physics overlap
• high precision experiments involving spectroscopy and metrology
• cold atoms and simulation of materials
• theory and methods in quantum mechanics
• quantum high energy physics and cosmology
• quantum technologies and energy production

A focus on inter-generational exchanges will be planned between top level invited senior physicists and young students, opening new scientific horizons to them. Tutorials will be given (half a day before the colloquium) to provide the basis of the fields which will be covered by the speakers. Time will be given to young PhDs and postdocs to present their work. Round tables will allow informal discussions raised by the presentations and identify opportunities to develop scientific cooperative projects between Vietnamese and foreign laboratories. 

For more details and registration information, please visit the conference website. The abstract submission and registration deadline is September 7th, 2025. Registration is free, but participants must cover their own travel and accommodation expenses.

What's next for applied quantum computing?

NISQ (noisy intermediate-scale quantum) algorithms generated a lot of excitement and a lot of publications - the 2022 review has amassed almost 2000 citations! Nowadays the tone is more subdued, with many experts believing any useful practical applications of quantum processors will need quantum error correction. The new hot topics are understanding how to make useful error correction a reality, and what might be done with a few hundred logical qubits. 

What then should a new student interested in applied quantum computing focus on?

Ryan Babbush and collaborators already argued in 2021 that algorithms with quadratic speedups won't be useful in practice. So sorry, but we won't be able to solve complex industry optimization problems using Grover search. However, their analysis indicated that quartic speedups and beyond could be practically useful. Which quantum algorithms have this property?

Consulting the excellent review article Quantum algorithms: A survey of applications and end-to-end complexities, there are only a few examples of known or suspected quartic or beyond end-to-end quantum speedups! They are:

Tensor principal component analysis (PCA). Ordinary PCA is a data reduction step widely used in data analysis and machine learning. It's not yet clear what tensor PCA might be useful for, but if an application can be found quantum computers will probably give a useful speedup.

Topological data analysis (TDA). This is another promising direction where a useful speedup for certain problems is possible. Following an initial buzz of excitement in 2022, it's unclear whether there are practical applications for where such a speedup can be useful. Recently-developed quantum-inspired classical algorithms will be useful to identify potential use-cases for quantum TDA.

On the classical computing side, quantum-inspired tensor network methods are very promising for near-term applications.  

There are also other approaches (QAOA, quantum machine learning) which attracted a lot of interest since 2020 and are still being explored theoretically, but at least in their present formulations they seem unable to provide a useful speedup for classical problems, with their most promising applications related to directly studying or simulating certain quantum systems. Thus, interest has shifted from "beating" classical methods on carefully-selected problems to better understanding the foundations of quantum machine learning. While this is a fascinating topic, it is at this stage it is more theoretical than applied research.

Michael Berry on the next century of quantum mechanics

Prof. Michael Berry talked about his work and the future of quantum mechanics in an interview during his recent visit to ICTS-TIFR for the ‘A Hundred Years of Quantum Mechanics’ program. Some excerpts:

Q: What is the status of the foundational questions in quantum mechanics now?

A: I have no idea, I don’t work on them. [...] Transport the question back to classical mechanics. Two points. Is Newton’s equation more fundamental than Hamiltonian’s? Philosophers could argue about it. In fact, Newton’s equations are more general, that’s another matter. 

This refers to work by Berry and others on curl forces: position-dependent forces that cannot be written as the gradient of a potential. Curl forces have many peculiar properties - symmetries do not imply conservation laws, the dynamics are non-conservative yet non-dissipative, and in many cases they cannot be generated by a Hamiltonian. I first heard about this fascinating topic when Berry gave a colloquium at NTU in 2016. There has been quite a bit of work on this topic since then, including a recent generalization to quantum curl force dynamics.

Q: Do you have any advice for people who work in this field or who aspire to work in this field?

A: Yes. I have two contradictory pieces of advice for people who ask me for career advice.

The first piece of advice is: don’t take advice.

But, if pressed, I would say that if I were starting out, I would probably work on quantum information. Probably, though I can’t tell — this is what philosophers call counterfactual history. So I would say: work on quantum information. There are so many riches to be uncovered there to do with these big Hilbert spaces, even with a modest number of particles. So that’s what I would say.

For context, Berry's main contributions to physics relate to the "simple" case of linear wave equations and single particle quantum mechanics - well-established theories that nevertheless held numerous surprises and emergent behaviour in their singular limits and asymptotic phenomena. We've only scratched the surface when it comes to exploring these effects in complex many-body quantum systems.

The full text of the interview can be found here.

 

 

 

From classical to quantum HodgeRank

This is a rather late summary of a cool preprint I saw a few months ago: Quantum HodgeRank: Topology-Based Rank Aggregation on Quantum Computers 

This work is inspired by and builds on quantum subroutines developed for efficiently solving high-dimensional topological data analysis problems, offering superpolynomial speedups for ranking higher-order network data by developing a quantum version of the classical HodgeRank algorithm.

What is HodgeRank? It was originally proposed in 2011 as a better way of ranking incomplete or skewed datasets, for example based on user ratings or scores.

The basic idea is to apply an analogue of the Helmholtz decomposition (used routinely in electromagnetics) to graph data, enabling one to assign a ranking based on incomplete pairwise preferences. Importantly, HodgeRank outputs not just a raw ranking, but also an estimate of the quality of the ranking via the construction of local and global cycles present in the optimal ranking. To be specific, the returned optimal ranking is unique and fully consistent if the preference matrix can be written as the gradient of some scalar ranking function. If it cannot, then there are inevitable ambiguities present in the preference data due to the existence of global or local cycles. 

An example of a local ranking cycle is the following: B is preferred over A, C is preferred over B, and yet A is preferred over C. This leads to the ranking A < C < B < A, thus forming a cycle. It is better to identify cycles such as these and acknowledge that a traditional ranking does not make sense for these items. This is what HodgeRank does! User preference data is rarely consistent, so cycles such as these routinely occur in the wild, for example in user rankings of movies on online platforms such as Netflix. 

As a generalization of HodgeRank, Quantum HodgeRank promises the ability to perform ranking tasks on preference data forming higher-order networks, avoiding the exponential scaling with network dimension faced by classical algorithms. Moreover, the authors of the preprint argue that HodgeRank cannot be dequantized (i.e. implemented efficiently using a randomized classical algorithm) in the same manner as quantum TDA algorithms for the Betti number problem. Moreover, while applications of high-dimensional Betti numbers (and even their occurrence in real datasets) remain unclear, HodgeRank represents a ranking problem with more likely concrete applications. Thus, this looks like an exciting area to keep an eye on. 

It is also interesting to speculate on whether (classical) HodgeRank or HodgeRank-inspired methods can be useful for understanding the behaviour of interacting many-body quantum systems, where it is typically intractable to sample all of the pairwise interaction elements of Hamiltonians as the system size increases, but incomplete or skewed sampling is readily available. Watch this space!

Part-time Associate Editor position in quantum science at Physical Review A

Physical Review A (PRA) is looking for a new part-time Associate Editor in the area of quantum science to join our team.

For more than 50 years, PRA has been publishing important developments in the rapidly evolving areas of AMO physics, quantum science, and related fundamental concepts. The journal is growing, and we are looking for someone working in the area of quantum science to join our team of editors on a part-time basis. The candidate would be expected to maintain their current academic position while serving as an editor for PRA.

The advertisement for the position can be found here, including further details about the expectations for this role, time commitment, how to apply, etc. We look forward to applications from qualified candidates. The deadline to apply is August 10th, 2024.

 

A few notes about the selection criteria:

 

(1) Current active involvement and stature in the relevant field of research. 

 

You should be publishing, and in good journals. Invited talks at or involvement in organisation of reputable conferences or awards can also serve as evidence of active involvement and stature in the field. Within quantum science there is an enormous breadth of sub-topics ranging from fundations to applications, so someone with experience in a wider variety of topics is likely to be preferred over someone with more narrow expertise. This is another reason why you should work on something a bit different after your PhD.

 

(2) An outstanding record as a referee and a demonstrated commitment to peer review. 

 

Serve as a good referee on papers when asked, obviously. If you haven't reviewed for APS, you can express your interest here. Write useful, constructive reports including suggestions on how the manuscript can be improved (even if you don't think it meets the standards of the journal). Return reports quickly and/or within the timeframe you promise. It's OK to decline if a paper is outside your expertise or you are too busy - we really appreciate fast responses. We don't have access to your referee record at other journals, so it is better to concentrate your refereeing service at a few publishers that you submit your own manuscripts too, rather than spreading your efforts across dozens of different publishers. Particularly for the case of for-profit publishers - if you don't publish with them why should you volunteer your time for their benefit?

 

(3) The ability to work within the editorial team and the desire to maintain the quality and reputation of the journal. 

 

Evidence of desire to maintain the quality and reputation of the journal can include service as a good referee and submitting your own good papers to the journal.

 

From NISQ to small logical quantum circuits

After six years of huge interest in NISQ (noisy intermediate-scale quantum) circuits there are still no practical applications where a noisy quantum device can outperform the best classical methods. Noise is too detrimental, and classical methods are too powerful. Experts continue to argue that now is not the time for commercial applications: quantum error correction, hundreds of logical qubits, and millions of error-corrected gates are needed.

Then what's next? Circuits of a moderate size with some limited error correction capabilities. LISQ (logical intermediate-scale quantum) or something else, for short.

What can we expect from these up and coming small scale logical circuits?

First, a lot of the tools developed for the NISQ era will become obsolete. For example, variational quantum circuits involving continuously-parameterised quantum gates cannot be easily implemented in a fault-tolerant manner. Instead, post-variational hybrid quantum-classical algorithms for this era will need to offload the continuously-parameterised part of the algorithm to a classical computer, with the quantum circuit used to measure a set of (hopefully classically-intractable) observables that are used as inputs to the classical tunable model.

Second, the hardware, algorithms, and the error correcting code cannot be considered in isolation. Choosing the right error correcting code will be essential to get the most out of the current hardware. Examples of this can be seen in QuEra's logical circuit demonstration from late last year, where the use of a 3D quantum error correction code allowed them to perform random IQP circuit sampling with error detection, and Quantinuum's recent demonstration of repeated error correction. Similar to the NISQ era, different hardware platforms will have different strengths and limitations in what kinds of circuits they will be able to run.

Finally, the most valuable software tools in the NISQ era were for quantum control and state tomography, essential to get the most out of the noisy hardware. These tools will remain important, since fidelities at the physical qubit level directly affect the amount of quantum error correction overhead required. As we move to logical circuits, the new valuable quantum software will be in the form of compilers that will take all the hassle out of hardware and error code selection out of the end-user and translate a given logical circuit into simple, understandable hardware requirements.

A busy January

There's been a lot going on here...

Machine Learning & Physics

Unsupervised learning of quantum many-body scars using intrinsic dimension - Now available on arXiv! We applied manifold learning techniques to identify scar states in the PXP model The take-home message: manifold learning techniques are a powerful alternative to more popular deep learning methods, especially in physics problems where you might not have access to enough training data for deep learning to work well.

Identifying topology of leaky photonic lattices with machine learning - Just published in Nanophotonics! We apply various machine learning methods to distinguish different topological phases in a photonic lattice, assuming one only has access to intensity measurements. This can serve as an alternative to full state tomography or phase retrieval methods, but one needs to be careful when training the models on ideal / pristine systems and then applying them to disordered systems. The journal also published a press release on WeChat!

Quantum Computing

Computing electronic correlation energies using linear depth quantum circuits - Finally published in Quantum Science & Technology, after more than a year and a half working through the peer review system. We use perturbation theory to determine electronic correlation energies in small molecular systems (hydrogen, lithium hydride, etc.) using a large set of shallow circuits, giving an alternative to existing methods which require deeper circuits infeasible for current quantum processors. We also tested the algorithm on cloud quantum processors, observing the detrimental impacts of noise. It would be interesting to run this again now to see how much (or how little) the performance from the different cloud providers has improved!

Landscape approximation of low-energy solutions to binary optimization problems - Published in Physical Review A. We present a method to obtain approximate solutions to binary optimization problems using the localization landscape, a function which is able to place bounds on the regions of Anderson localized eigenstates in disordered media without solving the underlying eigenvalue problem. We lay out the conditions required for these bounds to hold, outline how a quadratic unconstrained binary optimization problem can be transformed to fit these conditions, and provide details on how the quantum state representing the landscape function can be produced and sampled using techniques developed for near-term quantum devices.

 

On a related note, I was interested to see this month a new arXiv preprint in which the localization landscape was used to engineer multifractal resonances in SiN membranes!

Photonic Flatband Resonances

Photonic Flatband Resonances in Multiple Light Scattering - Published in Physical Review Letters. We reveal that flatbands can emerge as collective resonances in fine-tuned arrays of Mie-resonant nanoparticles, leading to giant values of the Purcell factor for dipolar emitters. The article was also highlighted with a Synopsis in Physics Magazine!

Quantum Jobs

PRX Quantum seeks an Associate Editor, Quantum Information. Physical Review is home to the most Nobel Prize-winning physics papers in the world. This is an opportunity to be at the forefront of the most exciting breakthroughs in quantum science!

Many postdoctoral openings at the Centre for Quantum Technologies, Singapore, ranging from experimental integrated photonics to applying quantum-inspired algorithms to bioinformatics!

Coming soon: ARC Centre of Excellence in Quantum Biotechnology. This newly-funded centre aims to pioneer paradigm-shifting quantum technologies to observe biological processes and transform our understanding of life. Stay tuned for openings in this exciting new field...

Towards fault-tolerant quantum computing with Rydberg atoms

 I'm a bit late to the party, but finally managed to get a chance to read the paper "Logical quantum processor based on reconfigurable atom arrays" by Harvard, QuEra, and collaborators, which hit the headlines a few weeks ago. My thoughts:

• Sadly many articles covering the paper gloss over the important distinction between error detection and error correction: QuEra's press release, The Harvard Gazette, EurekaAlert, and others. Optics & Photonics News provides more balanced coverage. The impressively high (above break-even) fidelities demonstrated in the paper require post-selection, discarding experimental runs where errors were detected. The post-selection probability is as low as 0.04% for the largest system sizes studied, and will get exponentially smaller for bigger circuits. The bottom line: scaling up to a useful size needs integration of error correction.
• How to integrate error correction? One needs to process the error detection measurements in real-time and then apply correcting gates to the qubits while the circuit is being run. Figure 4 of the paper does demonstrate implementation of measurement-dependent feedforward operations, but not yet integrated with error decoding and correction operations. This seems to be in principle an engineering challenge that can be solved with more hard work.
• Scaling up to more qubits and deeper circuits will require continuous pumping and replenishment of Rydberg atoms. Otherwise, the circuit width will be limited by the finite success probability for trapping each atom, and the depth by the ~10s trapping lifetime.
• The quantum processor architecture, involving separate storage, processing, and readout zones, as well as the ability to execute gates with arbitrary connectivity and in parallel using just a few structured laser beams, looks much more promising for scalability compared to superconducting quantum processors.

There is more discussion over at Shtetl-Optimized.

Updates

Infrequent posting due to other commitments. Here are a few brief items of note from the past month:

• Beng Yee uploaded his second paper from his PhD research to arXiv: A Unified Framework for Trace-induced Quantum Kernels. This project tackled the problem of how to choose the best quantum kernel for a given learning task using tools from classical multiple kernel learning theory. The bottom line: the optimal problem formulation (e.g. as a kernel model, projected kernel model, or quantum neural network) depends on the relative amount of training and test data, whether one wants to impose constraints to the trained model, and whether one has many qubits with low-fidelity gates or a fewer qubits with high fidelity gates. Read to find out more!
• The December issue of Optics & Photonics News highlights some of the most exciting peer-reviewed research in optics and photonics published over the past year. There is also an accompanying perspective on areas to watch in 2024 and beyond by selected summary authors.
• Two papers recently published in PRL caught my eye: Universal Sampling Lower Bounds for Quantum Error Mitigation suggests the quantum error mitigation being pushed by IBM and others as a means of getting useful applications out of current noisy quantum processors may be foiled by an exponentially growing measurement overhead, and Classifying Topology in Photonic Heterostructures with Gapless Environments shows how a recently-developed real space formulation of topological invariants may be a more useful tool for quantifying the robustness of topological states in photonic systems, particularly those exhibiting radiation losses of optical nonlinearities.
• The 7th International Conference on Optical Angular Momentum will be held 24 - 28 June 2024 in South Africa. The abstract submission deadline is 7 January 2024.
• The next edition of the Quantum Techniques in Machine Learning conference will be held in Melbourne, 25-29 November 2024. The abstract submission deadline is 5 July 2024. 
• In the news headlines: Alibaba shuts quantum computing lab. Seems to be part of a wider trend of industry funding shifting from quantum to generative AI - see also Zapata and Normal Computing.
  

What I've been reading lately

Continuity Equation for the Flow of Fisher Information in Wave Scattering

We can get an intuitive understanding of a wide variety of wave systems ranging including photonics, acoustics, and electronic condensed matter by visualizing the flow of intensity, energy, or probability density through them. These flows are useful for understanding the behaviour of conserved quantities, since they can be decomposed into sources, sinks, and solenoidal components. This paper shows that the Fisher information, a measure which bounds the precision with which parameters of interest can be measured, similarly obeys a conservation law enabling its visualization in terms of information flow. Remarkably, the Fisher information flow gives distinct insights into wave propagation in complex media and is complementary to more standard analysis methods based on the energy flow. This work raises many interesting questions and opens new possibilities!

Energy and Power requirements for alteration of the refractive index

This is another paper in a series of perspectives on estimating the capabilities and potential limits to the performance of photonic devices using relatively simple classical oscillator models and sharp physical insights. The take home message is that the power required to achieve a given level of optical modulation depends primarily on the interaction time, which depends on the device geometry (e.g. resonator vs travelling wave), without substantial variation among different materials. This suggests that improvements in power efficiency are more likely to come from improvements in fabrication methods and device design, rather than the discovery of some new material with substantially better physical properties.

Quantum Algorithm for Computing Distances Between Subspaces

There's growing evidence that the best place to look for a quantum advantage for classical machine learning will be geometrical or topological problems that have a natural connection to quantum systems. One example is the Betti number problem, which maps to computing the ground state of supersymmetric many-body Hamiltonians. This work shows that computing distances between k-dimensional subspaces of an n-dimensional space can be done exponentially faster using a fault-tolerant quantum computer. The algorithm exploits the ability to efficiently encode subspaces into quantum states combined with quantum signal processing. Subspace distances have to large scale machine learning and computer vision problems, suggesting the asymptotic exponential advantage promised by a fault-tolerant quantum computer could lead to practical speedups.

Quantum chemistry with subspace states: the conclusion

 Just over a year ago I wrote about a paper on quantum machine learning using subspace states, which inspired a project we undertook on applications of similar quantum states to variational quantum circuits for quantum chemistry and condensed matter physics. Over the weekend our manuscript was published in Physical Review A!

We were fortunate to have three knowledgeable referees who gave constructive and insightful comments on the original manuscript. We heavily revised the manuscript compared to the original arXiv preprint to not only improve the presentation, but also emphasize the broader applicability of the subspace space approach, specifically the ability to prepare correlated fermionic ansatz states beyond pairwise correlations. Our approach can yield substantially shallower quantum circuits for solving problems where the electron density (number of electrons d / number of orbitals used N) is small, for example when trying to extrapolate finite basis set calculations to the complete basis set limit. This is illustrated in the figure below, taken from the paper:

Estimated two-qubit gate depth per occupied mode d to prepare an N-mode Slater determinant and pairwise-correlated ansatz states using subspace states, compared to existing d-independent and linear in N approaches.

Will there be a useful quantum advantage for topological data analysis?

 

We don't know yet. 

Prominent applications of topological data analysis (TDA) including Mapper-based visualisation are based on fast and interpretable heuristics. While quantum TDA may speed up the calculation of high-dimensional Betti numbers, it doesn't help with understanding when and why high-dimensional topological features might be important, and whether they need to be computed to high precision or classical Monte Carlo methods can give a sufficient accuracy in practice. What high-dimensional Betti numbers might be good for needs to be determined empirically using machine learning benchmark datasets and the best classical algorithms.

Beyond the Betti number problem, for which quantum algorithms have already been proposed, it will be interesting to explore what other TDA methods could be sped up using quantum subroutines. For example, the nonzero eigenvalues of the persistent Laplacian also seem to be useful as features for machine learning algorithms, in contrast to traditional persistent homology methods that focus only on the zero or near-zero eigenvalues of the persistent Laplacian. The speedup for quantum persistent homology comes from being able to construct the persistent Laplacian exponentially faster the best-known classical methods. If there is useful information that can be extracted from the persistent Laplacian without requiring the quantum singular value transformation or rejection sampling, the resource requirements for a quantum advantage would be reduced enormously.

Thanks to the the team at QCWare for inviting me to give a seminar on this topic and the thought-provoking discussions afterwards!

arXiv highlights

Quantum-noise-limited optical neural networks operating at a few quanta per activation

Suitably-trained optical neural networks can still perform classification tasks accurately using low intensity light with a low signal to noise ratio. This suggests that specialized light-based analogue hardware for machine learning may offer a route towards reducing the enormous energy consumption of neural networks!

Dissipative mean-field theory of IBM utility experiment

Another approach towards reproducing the results of IBM's kicked Ising model quantum simulation experiment, this time using mean field theory. The Appendix gives a simple rule of thumb for estimating the quantum volume of specific devices based on their two-qubit gate and readout fidelities and compares some different hardware providers.

Maximally-Localized Exciton Wannier Functions for Solids

Wannier functions - localized states constructed as a superposition of Bloch waves from an energy band of interest - are an important tool of the condensed matter physicists' trade. This work presents a method for constructing maximally-localized Wannier functions for multi-particle states, focusing on applications to excitons (electron-hole pairs).

Tensorized orbitals for computational chemistry

This work presents a tensor network-based compression of the matrix elements that need to be computed and stored when performing quantum chemistry calculations, based on Tensor Cross Interpolation. This is yet another example of how tools from quantum many-body physics can be used to speed up time-consuming computational tasks - no working quantum computer needed!

Seeking quantum speedups using supersymmetric systems

There is a neat correspondence between the question of whether a simplicial complex has a k-dimensional hole and whether the ground state of a related supersymmetric (SUSY) quantum many-body Hamiltonian is at zero energy:

Complexity of Supersymmetric Systems and the Cohomology Problem

Clique Homology is QMA1-hard

A less technical presentation of the latter paper at QIP2023 and can be viewed here.

Both problems are QMA1-hard, meaning that the correctness of a trial solution can be efficiently checked by a quantum computer (but finding the correct solution remains hard even for the quantum computer). In contrast, recently-proposed quantum algorithms for TDA consider relaxations of the homology problem that can be solved efficiently using quantum algorithms, such as estimating the normalized number of k-cycles to some finite precision.

What other seemingly classical or purely mathematical problems can be naturally framed in the language of supersymmetric quantum mechanics? This promises to be fertile ground for exponential quantum speedups, and you don't need to be an expert in quantum algorithms to join the hunt!

Tensor network simulations challenge claims of quantum advantage...again!

Hot off the arXiv today: Efficient tensor network simulation of IBM's kicked Ising experiment

The authors report efficient classical simulations of the experiments by the IBM quantum computing team reported in Nature last week: Evidence for the utility of quantum computing before fault tolerance

What's going on here?

Tensor network methods are proving to be extremely powerful for computations related to quantum systems and large-scale neural networks. They work best for simulations of 1-dimensional or tree-like quantum systems (corresponding to the special case of matrix product states). Higher-dimensional systems or those with long range coupling containing looped paths, however, incur increasing overheads.

The Eagle quantum processor used in IBM's recent experiments is based on a two-dimensional network of qubits on a "heavy hexagon" grid. Thus, even though it is two-dimensional (harder for tensor network methods), its loops are longer than that of a more compact square lattice. The time required to traverse a single loop is comparable to the circuit depths probed in the experiment, meaning that by applying some clever factorization tricks the dynamics can be reproduced by efficiently-simulable tree-like tensor networks!

 

This is not the first time tensor networks have challenged claims of supremacy - they have also been used to simulate Google's original quantum supremacy experiments. What is particularly striking here is that the time between the publication of the quantum experiment and publication of the classical reproduction has dropped from years to weeks!

Here are some libraries for trying out tensor network simulations of quantum systems:

tensorcircuit: Python library developed by Tencent Quantum Lab - can handle shallow circuits involving hundreds of qubits.

ITensorNetworks: Julia library developed by the Flatiron Institute, which was used to reproduce the IBM experiments.

For theorists, getting familiar with these simulation tools that can also be applied to other important areas (such as large-scale machine learning or numerical simulations) seems to be a better use of time than getting to grips with the intricacies of ever-changing device-specific error models and quantum error mitigation schemes!