A central development of the ongoing second quantum revolution is the ability to control and observe the individual quantum degrees of freedom (e.g., in neutral atoms, ions, superconducting circuits, lattice defects, etc.) and their interactions with the highest precision. This discloses several directions for fundamental research as well as for technological applications. Quantum Simulators are experimental platforms that realize specific models of matter in a tailored way and give direct access to relevant observables: They therefore embody Feynman’s original vision to circumvent the curse of dimensionality by performing the simulation itself in a quantum setup. Ultimately, the goal is to develop QS for increasingly complex models of matter, in- and out-of-equilibrium, in order to tackle pivotal problems in quantum many-body physics and quantum chemistry, e.g., high-temperature superconductivity or chemical reaction dynamics. The availability of early-stage QS, together with sophisticated numerical techniques that keep pushing the classical computational capabilities, puts us today in the exciting situation that both rely on each other for mutual certification while entering otherwise uncharted terrain. Recent examples of ours include:

• “Quantum simulation of the tricritical Ising model in tunable Josephson junction ladders”, link to the paper.

• “Cold Atoms meet Lattice Gauge Theory”, link to the paper.

Many-body systems are plagued by the curse of dimensionality: a priori, the quantum wavefunction is indeed an element of a Hilbert space whose dimension grows exponentially with the number of system constituents. Tensor Networks consist of a convenient decomposition of the system wave-function into smaller tensors, whose interconnection bonds carry the entanglement structure at the heart of quantum effects. Such a quantum-information inspired rewriting brings along an increased efficiency (from exponential to polynomial, typically) in dealing with ground-state searches and extraction of many relevant quantities (e.g., local observables, long-range and edge-to-edge correlations, entanglement spectra, etc.). Moreover, TN-based simulations of the non-equilibrium dynamics of quantum systems are also attainable, at least on moderate time scales, after which one has indeed necessarily to resort to quantum computation platforms. We conduct methodological developments as well as employ TNs to investigate phenomena of interest. Recent examples of ours include:

• “Charge and statistics of lattice quasiholes from density measurements: a Tree Tensor Network study”, link to the paper.

• “variPEPS -- a versatile tensor network library for variational ground state simulations in two spatial dimensions”, link to the paper.

• “Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model”, link to the paper.

Interesting questions arise when the quantum systems are open, especially in terms of being subjected to measurements and resets of ancillas. Building upon our recent results, we are pushing investigations in two directions: i) to enhance noise-robust state preparation protocols – useful for fiducial states of quantum computers – by making active use of (i.e., learning) the measurement outcomes; ii) to study measurement-induced phase transitions beyond the realm of free fermionic quantum dynamics, where they have been found, via inserting interactions that preserve or break integrability and/or via active feedback. A recent example is:

• “Quantum state preparation via engineered ancilla resetting”, link to the paper.
• "Learning Feedback Mechanisms for Measurement-Based Variational Quantum State Preparation", link to the paper.

The cross-link between machine-learning related topics and the quantum world is of growing importance. On one hand, we initially made use of generative adversarial networks directed onto the entanglement spectrum, and then came up with a much simpler approach based on the scrutiny of an experimentally more accessible quantity, namely the particle number probability distribution. On the other hand, we are exploring the construction of an effective low-dimensional representation of quantum operators based on snapshot ground states at particular parameter values: Greedy algorithms to guide such parameter choice and TN-based numerical solutions can be powerfully combined to produce high-resolution scans of quantities of interest at a much cheaper price than via traditional parameter scans, thus contributing to green computing. Examples include:

• “Phase Diagram Detection via Gaussian Fitting of Number Probability Distribution”, link to the paper.

• “Reduced basis surrogates for quantum spin systems based on tensor networks”, link to the paper.

Preprint

Roughening dynamics of interfaces in two-dimensional quantum matter
W. Krinitsin, N. Tausendpfund, M. Rizzi, M. Heyl, M. Schmitt
arXiv:2412.10145

Learning Feedback Mechanisms for Measurement-Based Variational Quantum State Preparation
D. Alcalde Puente, M. Rizzi
arXiv:2411.19914

Deconfined quantum critical points in fermionic systems with spin-charge separation
N. Baldelli, A. Montorsi, S. Julià-Farré, M. Lewenstein, M. Rizzi, L. Barbiero
arXiv:2407.04073

Bisognano-Wichmann Hamiltonian for the entanglement spectroscopy of fractional quantum Hall states
A. Nardin, R. Lopes, M. Rizzi, L. Mazza, S. Nascimbene
arXiv:2312.07604

Publications

Quantum nonlinear optics on the edge of a few-particle fractional quantum Hall fluid in a small lattice
A. Nardin, D. De Bernardis, R. O. Umucalilar, L. Mazza, M. Rizzi, I. Carusotto
Phys. Rev. Lett. 133, 183401 (2024) (Editor's suggestion)

Quantum Simulation of the Tricritical Ising Model in Tunable Josephson Junction Ladders
L. Maffi, N. Tausendpfung, M.Rizzi, M. Burrello
Phys. Rev. Lett. 132, 226502 (2024)

Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
E. L. Weerda, M. Rizzi
Phys. Rev. B 109, L241117 (2024)

Phase diagram detection via Gaussian fitting of number probability distribution
D. Contessi, A. Recati, M. Rizzi
Phys. Rev. B 107, L121403 (2023)

Collisionless drag for a one-dimensional two-component Bose-Hubbard model
D. Contessi, D. Romito, M. Rizzi, A. Recati
Phys. Rev. Research 3, L022017 (2021)

Cold atoms meet lattice gauge theory
M. Aidelsburger, L. Barbiero, A. Bermudez, T. Chanda, A. Dauphin, D. González-Cuadra, P.R. Grzybowski, S. Hands, F. Jendrzejewski, J. Jünemann, G. Juzeliunas, V. Kasper, A. Piga, Shi-Ju Ran, M. Rizzi, G. Sierra, L. Tagliacozzo, E. Tirrito, T.V. Zache, J. Zakrzewski, E. Zohar, M. Lewenstein
Phil. Trans. R. Soc. A 380, 20210064 (2021)

Tensor Network Annealing Algorithm for Two-Dimensional Thermal States
A. Kshetrimayum, M. Rizzi, J. Eisert, R. Orús
Phys. Rev. Lett. 122, 070502 (2019)

• Homepage of the group at the Institute for Theoretical Physics at the University of Cologne, https://www.thp.uni-koeln.de/rizzi/index.html
• Joint software development activity with the Jülich Supercomputing Center (JSC) via the CASA/SDL “Quantum Materials” towards a truly HPC-ready suite for tensor manipulation (add link as soon as a page exists there)