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We offer our time and knowledge to assist you. Our business model is based on selling of the intellectual property (IP) rights to developed product, which covers knowledge, documentation and source-code. Our services would fall into one of the following categories.


We can research and develop novel solutions to your problems. We offer theoretical analysis as well as numerical simulations to back them up. We can also help you write a white paper describing them.


We are happy to connect and guide you through the research process. Even if you already have a project and encounter problems, you can count on us giving you a helping hand and provide directions according to our best knowledge and experience.


We have strong technical background and we can build prototype or even production ready solutions. We are happy to develop components, such as microservices, that could connect to the rest of your software stack.

We have a wide range of interests and we continue to expand them and learn more. We are also members of well conntected network of experts and we are willing to refer to them to serve your product needs. Our main focus covers the following areas of study.

Quantum Computing

Computing machines based on quantum mechanics could significantly speed-up solving particular kinds of problems. Quantum algorithms are meant to be run on those kind of quantum processors. We have experience working with quantum technologies and we have published our ideas in peer-reviewed journals.

Smart Contracts

Blockchain technologies bring technologies which can operate without central authority. A smart contract is a contract which is being enforced by the consesus of such a decentralized network. Such a contract can be interpreted as code run by the decentrlized network or a multi-party cryptographic protocol.

Zero-Knowledge Proofs

These are the cryptographic protocols that allow one to prove a certain statement is true without revealing the statement itself. Technologies based on zero-knowledge proofs could provide functionalities without violating users privacy as it is notoriously done under current paradigm.

AI / Optimization

Formally verified problems in which a set of contraints and/or a mathematical quantity has to be maximized or minimized. Those kind of problems often occur in the industry, logistics, but also artifical inteligence where computer has to take decision and thus solves an optimization problem that maximizes desired features of such a decision.


We are a microscopic and unreasonably ambitious research and development company founded by Marek Narozniak. Before we became sqrtxx.com we have been to Nantes, Shanghai, Hong Kong, New York, Shanghai again, Tokyo and now we are based in Warsaw, Poland. We love to connect the dots. We love challenges. We love to solve problems.

  • 13.8 billion years ago

    Observable Universe begins

    What we know as the observable universe is in its initial state of extremely high density and temperature. It expands and cools sufficiently to allow the formation of subatomic particles, and later atoms. These form molecules and become necessary ingredients to form building blocks of what we are used to refer to as the universe.

  • 2021-2022

    Our Humble Beginnings

    While conducting research in quantum computing at Tim Byrnes lab in Shanghai. After hours we did lots of projects from all sorts of areas. We falled in love with Mimblewimble and founded Grinventions to contribute to GRIN digital cash project. We also enjoyed learning about zero-knowledge proofs and interacted with O(1) Labs by helping to develop OCTA.

  • June 2022

    sqrtxx.com is born

    We decided to go beyond open-source contributions in the spare time and start doing research and development work on our own full time. We got the business registered, rented a basement and adapted to a tiny office space.

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This section contains most recent publications by members affiliated to sqrtxx.com. It includes peer-reviewed journals, conference proceedings and preprints. In the future we intend to author Bitcoin Improvement Standards (BIP), Ethereum Requests for Comments (ERC) and GRIN Requests for Comments (RFC) standards.

  1. Lazarev, I. D., Narozniak, M., Byrnes, T., & Pyrkov, A. N. (2022). Quantum assisted unsupervised data clustering on the basis of neural networks. In V. F. Lukichev & K. V. Rudenko (Eds.), International Conference on Micro- and Nano-Electronics 2021 (Vol. 12157, pp. 571–578). SPIE. 10.1117/12.2625092
  2. Mohseni, N., Narozniak, M., Pyrkov, A. N., Ivannikov, V., Dowling, J. P., & Byrnes, T. (2021). Error suppression in adiabatic quantum computing with qubit ensembles. npj Quantum Information, 7(1), 71. 10.1038/s41534-021-00405-2
  3. Huang, H.-L., Narozniak, M., Liang, F., Zhao, Y., Castellano, A. D., Gong, M., Wu, Y., et al. (2021). Emulating Quantum Teleportation of a Majorana Zero Mode Qubit. Phys. Rev. Lett., 126(9), 090502. 10.1103/PhysRevLett.126.090502
  4. Narozniak, M., Dartiailh, M. C., Dowling, J. P., Shabani, J., & Byrnes, T. (2021). Quantum gates for Majoranas zero modes in topological superconductors in one-dimensional geometry. Phys. Rev. B, 103(20), 205429. 10.1103/PhysRevB.103.205429
  5. Mohseni, N., Narozniak, M., Pyrkov, A. N., Ivannikov, V., Dowling, J. P., & Byrnes, T. (2020). Adiabatic quantum computation with spin ensembles. In Fifth International Conference on Quantum Technologies ICQT-2019. AIP Publishing. 10.1063/5.0011393
  6. Mandal, S., Narozniak, M., Radhakrishnan, C., Kondappan, M., Jiao, Z., Jin, X., & Byrnes, T. (2020). An observable based approach to evaluating quantum coherence. In Fifth International Conference on Quantum Technologies ICQT-2019. AIP Publishing. 10.1063/5.0011394
  7. Dodel, A., Pikovski, A., Ermakov, I., Narozniak, M., Ivannikov, V., Wu, H., & Byrnes, T. (2020). Cooper pair polaritons in cold fermionic atoms within a cavity. Phys. Rev. Research, 2(1), 013184. 10.1103/PhysRevResearch.2.013184
  8. Mandal, S., Narozniak, M., Radhakrishnan, C., Jiao, Z.-Q., Jin, X.-M., & Byrnes, T. (2020). Characterizing coherence with quantum observables. Phys. Rev. Research, 2(1), 013157. 10.1103/PhysRevResearch.2.013157


Occasionally, we are contacted by journalists and asked to comment on various problems. Mainly related to quantum computing or blockchain, especially if it involves an intersection of those two areas.

As Grinventions, we are often mentioned in the GRIN Post newsletters

Grinツ July 2022 by Grin POST
Grinツ July 2022 by Grin POST
Grin is DEAD? by Grin POST

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