• o.kyriienko@exeter.ac.uk

Differentiable quantum generative models (DQGM)


After some time in the making, we are ready to present new members of quantum machine learning toolbox - differentiable quantum generative models (or DQGM for short!) [arxiv]

Together with Vincent Elfving and Annie Paine we set a goal of advancing generative modelling by introducing quantum embeddings and model differentiation. Here is our strategy. We use feature maps for building models as functions of continuous parameters, and utilize projective measurements for fast sampling on quantum computers. The models we build can be automatically differentiated and benefit from differential constraints.

Why is it important? Recently, quantum computers have shown a promise in learning from data. But there are simply to many options when we choose (train) a model (circuit). What if we use an additional knowledge about typical processes happening in an underlying system, and constraint the model to satisfy corresponding differential equations?

We believe the power of data and differentiation can boost the process of building QML models, and enable efficient generative modelling. Huge thanks go to PASQAL for continuous support!


Announcing our conference on 2D Polaritonics



04-15 April, 2022. Stockholm, Sweden.

We are happy to announce that a NORDITA programme co-organized by Dr. Oleksandr Kyriienko will happen in person the coming spring! The main subject of the meeting is light-matter interaction in nonlinear two-dimensional materials. The conference will be held in Stockholm (Sweden), 04-15 April 2022. Due to Covid restrictions talks are confirmed for invited participants only, but we aim to offer virtual support and video streaming.

Please find the followinf link for more details: https://indico.fysik.su.se/event/7627/



Quantum Startups PASQAL and Qu&Co Announce Merger


Paris and Amsterdam, January 11, 2022 – PASQAL, a developer of neutral atom-based quantum technology, and Qu&Co, a quantum algorithm and software developer, today announced a merger to accelerate progress on achieving business advantage through quantum computing by leveraging their complementary solutions.

Continuing as PASQAL and headquartered in Paris, executives from the two firms say the combined company will deliver a 1000-qubit quantum solution in 2023, on pace with the announced roadmaps of the most advanced quantum platforms. The merged company will have operations in seven countries with employees from over 15 countries, supported by an academic advisory board with leading professors in quantum chemistry and quantum machine learning. Qu&Co’s pan-European activities will continue under the names Pasqal Netherlands, Pasqal Germany, Pasqal UK and Pasqal Spain.

Please find the detailed article here


Smart Nanomaterials (SNAIA) Conference



7-10 December, 2021. Paris, France.

Oleksandr Kyriienko was invited to give a talk at the STEMM Smart Nanomaterials (SNAIA) Conference. This edition will happen in Paris, 7-10 December, and collect the communities of 2D materials, optics, and related technologies. SNAIA series are unique, and serve as an stablished science-to-technology networking platform covering the most exciting emerging fields in smart technologies.

During the conference Oleksandr will present overview of trion polaritons as an emerging platform, and will share recent results on strong nonlinearities due to trion-trion repulsion.






23-25 November, 2021. Bilbao, Spain.

In person meetings are getting back, and QuDOS group is happy to join the community. This November Dr Oleksandr Kyriienko will present a talk on “Quantum simulation of the honeycomb Kitaev model” while visiting Quantum2021 conference in Bilbao, Basque country, Spain.

The 1st edition of the Quantum 2021 International Conference will be held on November 23-25, 2021. It aims for gathering the leading researchers in the community of near term quantum computing, simulation, and optics. We hope to see everyone there, generate new ideas and establish collaborations at the forefront of Quantum science.



Welcome Chukwudubem Umeano



We are welcoming Chukwudubem Umeano who is joining QUDOS group as a PhD student in quantum computing. Chiddy has been selected as Exeter Math DTP scholar, and will explore exciting directions in quantum machine learning. Before joining our team, Chiddy studied quantum algorithms developments at Imperial College London, and graduated as a physicist from Warwick university, doing the project on classical machine learning.

We expect the two subjects will join nicely in the future work, and definitely expect big results!




Generalized quantum circuit differentiation rules


Differentiation of quantum circuits is extremely important, being a backbone for variational methods and differential equation solvers. In the recently published work (in collaboration with Qu&Co) we have extended the tools of automatic differentiation for tackling generic unitaries. The rules are quite simple, and require a number of function evaluations at different points, which grows with the number of unique spectral gaps. The techniques are especially relevant when differentiation hardware-native, like those for Rydberg atoms and superconducting circuits.





Quantum Quantile Mechanics: Solving Stochastic Differential Equations for Generating Time-Series



In this work with Qu&Co arxiv we propose a novel approach for generative modelling from SDE solutions. Stochastic differential equations are truly distinct from ordinary and partial differential equations. We approached their solution by using DQC-like structure, rewritten to find a quantile function. Based on quantile mechanics equations, the quantum solution may offer advantage in cases that are difficult to tackle with conventional methods.The applications are ubiquitous, many lying in the financial analysis.





Welcome Dr. Kok Wee Song



We are very happy to welcome Dr Kok Wee Song as a new member of the QuDOS team. Kok Wee will take a position of Postdoctoral Research fellow as a part of EPSRC funded project on 2D We. He has previously worked as a postdoc at Manchester centre for 2D materials, Argonne National Laboratory, and holds a PhD from UCLA. Expect excellent research in the field, as well as many team discussion, physics and beyond!






Hamiltonian operator approximation in PRX Quantum



Our paper with MSc student Ms Tatiana Bespalova is now published in PRX Quantum — new APS journal for top-tier quantum research. In the study, we have developed the strategy for representing a quantum system Hamiltonian through the derivative of the evolution operator. Using numerical differencing approach we approximate the Hamiltonian as sum of unitaries, and measuring quantum overlaps estimate the energy and prepare the ground state for complex material science models. The approach does not require variational procedure and is suitable for increasing system size, where we show it outperforms VQE for larger system sizes. When combined with analog quantum simulation of Fermi-Hubbard lattices, HOA can offer insight into unique physics that is classically inaccessible.



Congratulations, Tatiana Bespalova!

Tatiana Bespalova


Ms Tatiana Bespalova has successfully defended her Master Thesis, and we are happy to see her taking the PhD position at IBM Zürich doing quantum computing for chemistry. For the thesis she received highest honours and has been nominated by the committee for the best thesis award. Tatiana has asked to work on a quantum computing project with Dr Kyriienko two years ago, and fully embraced the challenges of moving between institutions, remote working, and working on several projects simultaneously. The hard work definitely paid-off with one paper to be published soon, and another draft being in the preparation. We expect great achievements from Tania during the PhD, and keep QuDOS connection as an alumni!



New preprint on single-polariton nonlinear effects

Single Polariton Shift


In the recently submitted study we describe the milestone achieved on the road to quantum polaritonic devices. Quantum polaritonics remains the holy grail for strong light-matter coupled systems with excitons in 2D samples. This relies on experimental observation of nonlinear response at the level of few polaritons, down to the single polariton level. In the recent study arXiv:2106.13650 we have teamed-up with experimental groups in Sheffield and Paris to reveal the phase shift induced by weak polariton probe. This offers the first demonstration of nonlinear effect that can be used for quantum information processing in the future. From the theory side we have described how polariton lattices offer the platform for high fidelity operation.



JuliaCon 2021 – annual event for Julia community



When: 28 Jul 2021 – 30 Jul 2021. Where: everywhere on Earth.

Every year JuliaCon connects professionals and enthusiasts who use Julia programming language for scientific computing, differential equations, machine learning, and many others. This year all QuDOS group members are joining the party! JuliaCon is an excellent event to see the overview of packages, learn about updates, and discuss advances in the field. Let's hope that the quantum community that uses Julia grows, and fast simulators are developed within the rich ecosystem that Julia offers.




Unsupervised machine learning of nonlinear optical lattices

Machine Learning


Our work on detecting phase transitions in polaritonic lattices is now out [arxiv]. Polaritons exhibit rich steady state structure as a function of controllable parameters, where qualitatively different polarization patterns are observed. We used the data-driven approach to separate polaritonic phases in the unsupervised way. Specifically, we employed t-SNE to sketch the boundaries of potential phases. From there the potential clusters of phases were conjectured. Next, we used agglomerative clustering to build the phase diagram. The boundaries between phases were tested by the neural network-based protocol with learnign by confusion. In the future we plan to extend the analysis to lattices of qubits, non-equlibrium patterns, and explore powerful convolutional neural nets for the analysis.



Talk at CQT, Singapore, by Dr. Oleksandr Kyriienko



22 April, 2021. Centre for Quantum Technologies, NUS, Singapore

Oleksandr has spent part of the PhD in Singapore. On Thursday 22 Apr he returned back, albeit virtually, to present latest research of QuDOS group at the Quantum Machine Learning seminar. In the talk Oleksandr covered dynamics-based protocols for ground state preration and energy estimation, and presented outlook for the development of NISQ software with analogue simulators. The video from the talk is now available at CQT's YouTube channel - link.




Developing industrial use-cases for the DQC algorithm



We are happy to see how our quantum algorithms are entering pipelines of multisimulation industry. The DQC protocol for solving nonlinear differential equations has laid the foundation for the partnership between LG corporation and Qu&Co (covered in the press release here and discussed in the recent quantumcomputingreport).

We developed DQC as a part of Qu&Co-sponsored research, and are thrilled that it will be applied to relevant use-cases. DQC serves as bulding block for other algorithms that use expressible quantum circuits and automatic differentiation for solving complex differential equations in the near term. We are also working to extend it to new scenarios. More to come!



Participation in ICTP's "Conference on Time Crystals"


8 - 10 March 2021, The Abdul Salam International Center for Theoretical Physicis, Trieste, Italy.

The field is continuing to grow fed with new theoretical ideas and experimental works. Main goal of the conference is to bring together the most active groups in the field to exchange their latest results. Topics that werecovered in the activity devoted to discrete time-crystals, continuous time-translation symmetry breaking, dissipative time crystals, time-crystals in classical systems, condensed matter physics in time crystals.

Dr. Kyriienko was invited to describe the field of quantum time crystals to the wide audience of reserchers in this emergent area. He has presented the results on Hamiltonian simulation of continuous time crystals dynamics, and offered the vision on the link between fault-tolerant quantum computing and time crystalline phase of matter.

The talk is now availble at the ICTP's YouTube channel - link.


Workshop “Useful Quantum Computation For Quantum Chemistry


22 - 26 February 2021. Lorentz Center, The Netherlands

The aims of the workshop was to bring together fields of quantum computing and quantum chemistry. Determine which classes of problems in chemistry are most promising for quantum-assisted solutions. Estimate the gap between current state-of-the-art quantum hardware performance and requirements for useful quantum simulations of molecular systems. Further the integration of quantum computers in quantum chemistry codes, either as embedded subroutines or hybrid quantum-classical schemes. The workshop lasted for 5 days in total. Together with usual talks, the organisers set up breakout rooms for important discussion we ought to have (thanks Tom O'Brien, Lucas Visscher and Lorentz Center!). Moderated by Nicholas C. Rubin and Jarrod McClean, the questions were far way from trivial. We expect more conferences of similar format will happen and consolidate the quantum community.



New technique to study molecules and materials on quantum simulator discovered

Inverse Iteration

The ground-breaking new technique, by physicist Oleksandr Kyriienko from the University of Exeter, could pioneer a new pathway towards the next generation of quantum computing.

We propose a quantum inverse iteration algorithm, which can be used to estimate ground state properties of a programmable quantum device. The method relies on the inverse power iteration technique, where the sequential application of the Hamiltonian inverse to an initial state prepares the approximate ground state. To apply the inverse Hamiltonian operation, we write it as a sum of unitary evolution operators using the Fourier approximation approach. This allows to reformulate the protocol as separate measurements for the overlap of initial and propagated wavefunction. The algorithm thus crucially depends on the ability to run Hamiltonian dynamics with an available quantum device, and can be used for analog quantum simulators. We benchmark the performance using paradigmatic examples of quantum chemistry, corresponding to molecular hydrogen and beryllium hydride. Finally, we show its use for studying the ground state properties of relevant material science models, which can be simulated with existing devices, considering an example of the Bose-Hubbard atomic simulator. More information you can find in our [paper] published in npj Quantum Information.

Here you can read an excellent summary written by Duncan Sandes at Phys. Org.


Quantum Time Crystals from Hamiltonians with Long-Range Interactions

Time Crystals

Time crystals correspond to a phase of matter where time-translational symmetry (TTS) is broken. Up to date, they are well studied in open quantum systems, where an external drive allows us to break discrete TTS, ultimately leading to Floquet time crystals. At the same time, genuine time crystals for closed quantum systems are believed to be impossible. In this study we propose a form of a Hamiltonian for which the unitary dynamics exhibits the time crystalline behavior and breaks continuous TTS. Find more details in our paper published in Physical Review Letters[paper] and APS Physics synopsis

We have shown that a genuine quantum time crystal behaviour appears for the system with infinite range interactions. The question I've got multiple times: How do we realize this complex system? As time goes, Dr. Kyriienko is confident that to have time crystallization in a perfectly quantum environment we need a fault-tolerant quantum computer. The goal is set, now just need to implement it!