I'm interested in theoretical computer science, especially quantum algorithms, their design, and upper and lower bounds. I'm also interested in restricted computation models and their applications.
I'm fascinated by category theory, formal methods, graphs, topology, and I would be happy to use their methods in my work.
You can download my CV (references are available upon request).
Shallow Quantum Fingerprinting
One of the useful techniques in quantum algorithms is fingerprinting. A quantum fingerprint captures essential properties of the input in a state of a small quantum register.
In my PhD thesis I explored how different abstract algebraic structures underlie fingerprinting, and which properties of these structures are important. However, quantum fingerprinting currently requires quantum circuits of a large (linear) depth, which is not feasible for today's quantum hardware.
Building upon my previous work, I plan to explore small-depth (sub-logarithmic) circuits for quantum fingerprinting. This would make it possible to use quantum fingerprinting in "near-term" quantum algorithms, such as quantum machine learning. I also plan to investigate possible applications of quantum fingerprinting as well as the its limitations.
If you are interested in discussing these ideas, please email me.
- «Quantum Information Transmission: Effective Cryptographical Protocols» (PDF in Russian)
- Institute of Computational Mathematics and Information Technology, Kazan Federal university, Kazan, Russia
- Scientific Advisor: Farid Ablayev.
In my PhD thesis I apply quantum fingerprinting to cryptography. Basically, a quantum fingerprint is a small quantum state with some information about a large classical input. You can use this fingerprint as a cryptographic hash of the input. By Holevo's theorem, an eavesdropper can't obtain much information about the input. However, fingerprinting properties allow legitimate parties to be sure that the message was not changed.
I generalised quantum fingerprinting to algebraic structures such as abelian groups and expander graphs, and showed how these generalised functions can be efficiently computed in the model of quantum branching programs. I also devised a quantum message authentication code and proved its security.
Another line of work in my PhD is the search for optimal sets of coefficients for quantum fingerprinting. I program and compare brute force, simulated annealing heuristics, and explicit algorithms for this task.
- Kazan Federal University, researcher (remote)
Full list on Google Scholar.