- Fabrication of well-aligned quantum registers by swift heavy ions (QURES)

David Weir and Kari Rummukainen

- Tensor networks with the Hila framework – hila-TV (‘hila-tensoriverkko’)

- Compact model theory and quantum logics

- Quantum optics, information and technology for teacher education, high schools and informal education: Societal impact through education

- Models of nuclear quantum effects for drug development
- Numerical atomic orbital basis sets for quantum chemistry on quantum computers

- Quantum algorithms to study emergent randomness in quantum many body systems beyond
- Advances in Multiparameter Quantum Estimation
- Quantum gate compilation and error mitigation schemes: from near-term to fault tolerant

quantum computers

- Graph-Theoretic Compiler for Quantum Computers
- Feasibility of Contemporary Quantum Machine Learning Models

- Quantum information in gauge theories

- Dark matter direct detection and quantum sensing

- Fundamental and operational limits on testing quantum fields in spacetime and the lab
- Quantum algorithms for simulating coherent quantum black holes

- Quantum Mechanics and Consciousness

- Mathematical Aspects of Tensor Network States

**David Weir**__Tensor networks with the Hila framework – hila-TV (‘hila-tensoriverkko’)__

The Hila framework [1] is a toolkit for performing very large-scale lattice field theory simulations.

Exploiting modern accelerated computing paradigms including parallelised GPU programming, it

supports lattices in arbitrary numbers of dimensions and performs well where the state at each site

in a configuration is represented by a large-dimensional matrix, such as in SU(N) lattice gauge

theories. Applications so far have been to Monte Carlo and real time simulations, but tensor

network states represent another fruitful area of study.

You will write a tensor network state layer for Hila that allows systems to be represented as matrix

product states and studied variationally using techniques such as the Density Matrix

Renormalisation Group (DMRG) [2]. Other GPU-accelerated frameworks for studying tensor

networks exist, such as iTensorGPU [3]; these will be used to validate the framework. We expect

that the multi-GPU parallelism made possible by Hila will provide a further speedup.

Given the focus of our group’s research we anticipate first investigating strongly coupled gauge

theories on the lattice [4,5]. As a starting point, you will study one-dimensional lattice QCD at finite

density [6], investigating the effect of the truncation of the gauge field state expansion on the

results, before going on to investigate the feasibility of simulating systems in higher spacetime

dimensions [7], or larger gauge groups. Your work will also enable large-scale numerical studies of

entanglement entropy in higher numbers of spatial dimensions.

The project will strengthen collaborative links between quantum information theorists and

theoretical particle physicists in Helsinki and beyond. It leverages Finland’s leadership in high

performance computing infrastructure at CSC, and represents a further step towards simulating

realistic lattice gauge theories on quantum computers.

**Anticipated results:**

- A new, portable, multi-GPU tensor network framework ‘hila-TV’, with validation, testing and

performance characterisation for (at least) ground state computations. - Studies of SU(2) and SU(3) QCD in one dimension at finite density, investigating the effects

of the implied cutoff in the gluon field coming from the state truncation.

**References:**

- https://cft-hy.github.io/HILA/index.html, accessed 11.3.2024.
- Steven R. White. Density matrix formulation for quantum renormalization groups, Phys.

Rev. Lett. 69 2863 (1992) [10.1103/PhysRevLett.69.2863]. - https://kshyatt.github.io/post/itensorsgpu/, accessed 11.3.2024.
- Pietro Silvi, Enrique Rico, Tommaso Calarco and Simone Montangero. Lattice gauge tensor

networks, New Journal of Physics 16 103015 (2014) [10.1088/1367-2630/16/10/103015]. - Erez Zohar and Michele Burrello. A Formulation of Lattice Gauge Theories for Quantum

Simulations, Phys. Rev. D 91 054506 (2015) [10.1103/PhysRevD.91.054506]. - Pietro Silvi, Yannick Sauer, Ferdinand Tschirsich, and Simone Montangero. Tensor network

simulation of an SU(3) lattice gauge theory in 1D, Phys. Rev. D 100 074512 (2019)

[10.1103/PhysRevD.100.074512]. - Giuseppe Magnifico, Timo Felser, Pietro Silvi and Simone Montangero. Lattice quantum

electrodynamics in (3+1)-dimensions at finite density with tensor networks, Nature

Communications 12 3600 (2021) [10.1038/s41467-021-23646-3].

**Ismo Koponen**__Quantum optics, information and technology for teacher education, high schools and____informal education: Societal impact through education__

Contemporary quantum optics, quantum information and quantum technologies have

recently been introduced as a part of teacher education and high school curricula in several

European countries, motivated by rapid increase and advancement of quantum-based

technologies. The project proposed here strengthens the already started research-based

development of teaching and learning of contemporary quantum optics, information and

quantum technology in school level and in teacher education. It produces new knowledge

about students’ conceptual and cognitive resources and abilities to learn the relevant

quantum concepts (e.g., quantum states, entanglement and transformation of states),

mathematical structures and concepts needed for such learning. The societal impacts of are

through improved and modernized teacher education and high school teaching and learning.

The research is carried out as part of physics education research in HU group of Didactic Physics.

The group has already started to renew the physics teacher education to include topics of quantum

optics, quantum information and technologies. Collaboration with local schools has been started.

The proposed research project should integrate well to already ongoing research projects and would

significantly support them. The responsibility of the new PhD student will be:

- to reinforce and consolidate already ongoing research and help to augment it.
- to carry out a systematic literature study to locate the key conceptual and cognitive requirements

for successful learning of contemporary quantum optic and technology. - to participate in empirical research and in designing empirical approaches and settings, carrying

out data analysis. - to participate in reporting and to report the research results.

Dissertation is assumed to be article based including at least 3 publications + summary. Defense is

assumed to take place in the end of the third year.

**Susi Lehtola**__Models of nuclear quantum effects for drug development__

Chemical processes that involve the movement of protons (e.g. keto-enol tautomerism) exhibit

strong nuclear quantum effects: the balance of the process can be significantly affected by changing

some of the affected protons to deuterons. Recently, there is arising interest in the pharmaceutical

industry to use these nuclear quantum effects to tailor the potency, safety, and stability of drug

molecules, but existing computational methods are not sufficiently reliable for these effects.

This project pursues improved modeling of nuclear quantum effects on both classical and quantum

computers to enable efficient in silico design of deuterated drug molecules. The aim is to develop

fully reusable open source software components [J. Chem. Phys. 159 , 180901 (2023) ] for

performing computationally efficient many-body quantum chemical calculations, following the

established ladder of quantum chemical methods (Hartree-Fock, density functional theory, MÃller-

Plesset perturbation theory, configuration interaction theory, and coupled-cluster theory). Previous

experience with many-body methods is highly beneficial to this project.

In addition to participating to method development, you are expected to apply the newly developed

programs to performing calculations of proton transfer in pharmaceutical and atmospheric chemical

applications in collaboration with partners at the University of Helsinki and elsewhere.

**Susi Lehtola**__Numerical atomic orbital basis sets for quantum chemistry on quantum computers__

The structure and properties of matter can be modeled on a computer by solving the Schrödinger

equation for the electrons. To allow a solution on a computer, the equations must first be

discretized. The traditional way to discretize the electronic one-particle states also known as orbitals

in quantum chemistry is to use a linear combination of atom-centered Gaussian functions. However,

they are a poor choice for heavy atoms, leading to increased computational cost and large

discretization errors.

This project explores the alternative avenue of a linear combination of numerical atomic orbitals

(NAOs), which are obtained as the numerically exact solution to the Schrödinger equation of the

noninteracting atom, or a model of an interacting atom. NAOs afford a lower level of truncation

error than Gaussians, even with a lower computational cost, and they are a promising avenue for

quantum chemistry applications on both classical and quantum computers: smaller orbital spaces

will suffice than those required in the presently-used alternatives [ Int. J. Quantum Chem. 119 ,

e25968 (2019)].

The project begins by determining reliable reference energies with state-of-the-art fully numerical

methods. Fully numerical methods have recently become tractable for reasonably sized systems,

and you will start out by collecting databases of highly accurate wave functions that can also be

used to determine NAO basis sets [Electron. Struct. 6, 015015 (2024) ].

At a later stage, you will participate in the generation and benchmarking of accurate numerical

NAO basis sets, following established methodologies for NAO and Gaussian basis sets. These

techniques will be included in new modular software based on fully reusable software components

[J. Chem. Phys. 159 , 180901 (2023) ].

**Jukka K Nurminen**__Graph-Theoretic Compiler for Quantum Computers__

With the recent advances in quantum computing comes a need for efficient compilers that

translate quantum software to the hardware. If quantum software is not efficiently compiled

to the target quantum hardware, quantum advantage may be unobtainable due to poor

communication within the quantum stack. Conversely, an efficient translation layer from

sotware to hardware enables quantum advantage.

Recently, quantum compilation algorithms have seen a shift from swapping qubits

(swapbased compilation), to regenerating a new quantum circuit (synthesis-based

compilation).

These algorithms show that quantum programs designed for near-term quantum computers

should be generated for a target machine directly, instead of generated for all-to-all

connectivity and subsequently routed using SWAP gates. The goal of this project is to build

up these compilation algorithms into a full-fledged open-source compiler.

**Jukka K Nurminen**__Feasibility of Contemporary Quantum Machine Learning Models__

Quantum Machine learning (QML) is a novel outlook on how to use quantum computing in the

widely successful field of machine learning. Many of these contemporary QML models are mostly

tested on various existing classical datasets in “toy example” – scenarios, which causes many of

these results to be incomparable with each other. There also exist many theoretical results that seem

to indicate that there exist specific contexts where the usage of QML can make more sense. The aim

of the project is to investigate quantum machine learning challenges, especially in the large-scale,

realistic use case perspective, and develop solutions to key steps.

**Jani Lukkarinen**__Mathematical Aspects of Tensor Network States__

A central challenge in quantum many body physics is to

find effective compressed representations of systems whose degrees of freedom grow exponentially

with the number of constituents. Tensor network states provide a tool to economically describe

physically relevant states of many body systems. The present project addresses mathematical open

problems related to the construction and characterization of tensor network states. We will study

how to generalize matrix product states (MPS) based methods for systems with infinite number of

degrees of freedom using MPS of infinite bond dimension. One of the main objectives is to

construct a mathematical framework for using MPS and matrix product operators (MPO) in infinite

dimensional Hilbert spaces. This includes studying the generalizations of the canonical forms of

MPS to the infinite-dimensional case, their connections to Hilbert-Schmidt operators and the

existence of the MPO decomposition for several classes of operators on infinite-dimensional Hilbert

spaces.