01
Quantum algorithms
Algorithms for quantum simulation, Gibbs sampling, and complexity-theoretic questions relevant to near-term and long-term quantum technologies.
Research
Quantum algorithms and tensor networks
02
Tensor networks
Efficient classical representations for high-dimensional systems, with emphasis on matrix product states, functional tensor methods, and quantum-inspired numerical algorithms.
03
Applied computation
Methods targeted at physical modeling, machine learning, finance, and engineering problems where structure, uncertainty, and scale matter.
People
Current members
Michael James Kastoryano
Associate Professor
Works on quantum algorithms and tensor networks with applications in physics, machine learning, finance, and engineering, with earlier work on quantum Markov chain mixing and dissipative state preparation.
Lasse Bjorn Kristensen
Postdoc
Works on theoretical and computational methods spanning physics, chemistry, and tensor-network based modeling.
Quantum simulation
Many-body physics
Sebastian Bugge Loeschcke
PhD Student
Works on efficient training of deep learning models, focusing on low-rank methods and quantization.
Machine learning
Low-rank methods
Quantization
Jonas Vinther
PhD Student
Works on continuous-variable quantum computation and tensor-network simulation methods.
Continuous-variable QC
Tensor networks
Lucas Silva Arenstein
PhD Student
Focuses on quantum-inspired PDE solvers and high-dimensional numerical methods built from tensor decompositions.
PDE solvers
Quantum-inspired algorithms
Martin Mikkelsen
PhD Student
Develops tensor-network methods for computational physics and scientific machine learning.
Scientific ML
Tensor methods
Giacomo Fregona
PhD Student
Works on theoretical aspects of quantum computation and related algorithmic questions.
Quantum theory
Algorithms
Publications
Recent papers
TensorGRaD: Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training
arXiv preprint, 2025.
TensorGRaD factorizes gradient tensors into complementary low-rank and sparse components, reducing optimizer-state memory by up to 75% while matching the accuracy of Adam, even on turbulent Navier-Stokes at Re = 10^5.
Fast and Flexible Quantum-Inspired PDE Solvers with Data Integration
Quantum-inspired quantized tensor train methods for solving high-dimensional PDEs with logarithmic memory scaling and data-driven extensions.
Functional Matrix Product State Simulation of Continuous Variable Quantum Circuits
A functional matrix product state framework for simulating non-Gaussian continuous-variable quantum circuits in real space.
Variational Tensor Network Simulation of Gaussian Boson Sampling and Beyond
Reformulates sampling problems as tensor-network variational tasks, enabling classical simulation of Gaussian Boson Sampling and related models.
LoQT: Low-Rank Adapters for Quantized Pre-Training
NeurIPS 2024. Equal contribution with Mads Toftrup. Best Paper Award at WANT@ICML.
LoQT enables efficient quantized pre-training of LLMs with results close to full-rank non-quantized models, including a 13B model on a 24GB GPU without model parallelism, checkpointing, or offloading.
Coarse-To-Fine Tensor Trains for Compact Visual Representations
ICML 2024.
PuTT learns a coarse-to-fine tensor train representation of visual data for 2D and 3D fitting and novel view synthesis, even with noisy or incomplete data.
An Efficient and Exact Noncommutative Quantum Gibbs Sampler
Presents an exactly detailed-balanced and efficiently implementable Lindbladian approach to quantum Gibbs sampling for noncommutative Hamiltonians.
Presentations
Slide decks, PDFs, and videos
2025
Low-Rank Adapters for Quantized Pre-Training
Slides for the best paper presentation at the WANT@ICML workshop on LoQT and low-rank adapters for quantized pre-training.
2026
Structured Learning Under Memory Constraints
Research talk at the Pioneer Centre for AI covering Sebastian Loeschcke's work on machine learning, low-rank methods, and quantization.
2026
TensorGRaD - Tensor Gradient Robust Decomposition for Memory-Efficient Neural Operator Training
Presentation at the SAINTS Lab Workshop 2026 on TensorGRaD and memory-efficient training of neural operators using tensor gradient decomposition.
Repositories
Code and project repositories
TensorTrainNumerics.jl
Julia pacakage for numerical computations with quantics tensor trains
Tensor networks
Quantics tensor trains
Numerical linear algebra
Alumni
Previous group members
Nikita Gourianov
Former Postdoc
Now at
Aarhus Energy A/S
Andreas Bock Michelsen
Former Postdoc
Now at
NQCP Programme Manager
Contact
Collaborations, students, and visitors
The group is interested in collaborations across theory, algorithms, and application domains. The Department of Computer Science is part of the Faculty of Science at the University of Copenhagen, and the group is based in the Machine Learning section. Students interested in joining or learning more about the group's work are encouraged to reach out to Michael, PhD students, or postdocs depending on their research interests.
mkastoryano@gmail.com
Universitetsparken 1, 2100 København, Department of Computer Science, University of Copenhagen