We are researching the **application of quantum computing to different domains**. That includes aiming to understand the best ways to map large-scale use cases into mathematical and computational models that match the capabilities of (future) quantum computers. In particular, we are interested in **machine learning** use cases. We are researching how to leverage quantum annealing devices in classical machine learning tasks and how these quantum hardware solutions affect the training of these models.

A central characteristic of quantum computers is the ability to solve problems faster than classical computers. Celebrated examples are Shor’s algorithms for prime factorization and discrete logarithm computation, and Grover’s search algorithm, which both have a better quantum asymptotic time complexity than their classical counterparts. In this spirit, the **theoretical study and design of quantum algorithms** can make us understand for which problems quantum computing is superior to classical computing, and can give us a tool to measure this improvement.

Besides the theoretical performance, the **practical implementation-dependent performance** (as measured in speed, need for computational resources, electricity, etc.) of near-future quantum computing is essential. The performance of quantum computing is In order to run these algorithms on the available limited quantum hardware, we need to develop **compilation methods specific to quantum computers**. Due to the no-cloning theorem, we are unable to simply copy the state of one quantum register to another. Thus we are researching new creative techniques to map our quantum programs to the quantum hardware.

Additionally, we have developed “QuantMark,” a **benchmarking** system for quantum algorithms for solving electronic structure problems to find the ground state energy for molecules through simulation.

Quantum computing is maturing. The big question about what it is suitable for remains. How do we map a real-life use case to a form that is suitable for quantum computing? Which real-life use cases are most suitable for quantum computers? What kind of quantum computers are needed to solve some use cases? In our work we aim to help in finding answers to these questions.

Software is present in many levels of the quantum stack. Our prime focus is the upper layers – how problems are formulated to the quantum computers so that they (someday) are able to solve them efficiently.

Besides the application layer work, our interest is in transpiling and some other lower-level software that has an influence on the ability and efficiency to deal with computational tasks.

One key aspect is that instead of dealing with a single quantum computer, our focus is a computing system with quantum processors. For NISQ algorithm the efficient distribution of work between classical and quantum processors is essential.

**Quantum computing for databases** is a new and exciting field connecting quantum computing and databases. We are studying how the unique capabilities of quantum computation can be used to enhance existing database optimization techniques. Quantum computing can also provide an alternative way to model classical database optimization algorithms.

In quantum computing for database research, we study algorithms for universal quantum computers and quantum annealers. We aim to formulate, for example, join order optimization and prediction of database metrics in a way that can be solved on quantum computers. For instance, one of our projects develops a quantum computing framework which translates SQL queries into parametrized quantum circuits. The circuits can be optimized to make predictions about query metrics.

The most common question that a researcher in quantum computing and databases is asked must be: “What is a quantum database?” Unfortunately, this question is currently out of the scope of our research, and we have no answer. Anyway, we hope to find it out!

Coming soon...

Since 2020, the course called “**Introduction to the programming of quantum computers**” is available for Computer Science students. Details

HIIT Quantum Software Day 3.2.2023 in Kumpula campus for all quantum-curious computer scientists

Podcast discussion on quantum computing "Jakso 31: Mihin kaikkeen kvanttitietokone pystyy" (in Finnish)

FrameQ (2023-2024) (Prof. Nurminen) is a Business Finland -funded project for developing a framework for analyzing the feasibility of quantum computing use cases. The work is done together with VTT.

Post-quantum cryptography (2021-2022) (Prof. Niemi) is a Business Finland -funded project on post-quantum cryptography.

Professor Jukka K. Nurminen https://researchportal.helsinki.fi/en/persons/jukka-k-nurminen

Professor Valtteri Niemi https://researchportal.helsinki.fi/en/persons/valtteri-niemi

Professor Jiehen Lu https://researchportal.helsinki.fi/en/persons/jiaheng-lu

Postdoctoral Researcher Massimo Equi https://researchportal.helsinki.fi/en/persons/massimo-equi

Doctoral Resarcher Arianne Meijer https://researchportal.helsinki.fi/en/persons/arianne-meijer

Doctoral Resarcher Ilmo Salmenperä

Doctoral Researcher Valter Uotila https://researchportal.helsinki.fi/en/persons/valter-johan-edvard-uotila

MSc student Leo Becker