David Weir and Kari Rummukainen
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:
References:
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:
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.