Speaker
Description
Artificial nanostructures built from magnetic atoms, molecules, or quantum dots coupled to superconducting substrates offer a tunable platform for realizing correlated quantum states and, eventually, designer quantum materials. Extending such few-site structures toward larger artificial quantum materials quickly leads to strongly correlated many-fermion problems that challenge established classical methods. Building on a canonical transformation that maps these superconducting cluster problems onto particle-number-conserving fermionic Hamiltonians, this project investigates which quantum-circuit representations can efficiently capture the resulting correlated physics in one-dimensional clusters, in regimes related to the Hubbard and Heisenberg models.
Our current work focuses on one-dimensional systems using matrix-product-state-based quantum circuits (qMPS). In this representation, each site of the classical MPS is mapped onto a small quantum register whose qubits are split into physical and auxiliary groups, with the auxiliary qubits encoding the bond dimension logarithmically rather than polynomially, as in classical tensor networks. Sites are prepared and optimized through variational routines, including quantum singular value decomposition and reshape operations, that bring each site into canonical form, allowing a variational qMPS (vqMPS) scheme closely analogous to the classical density matrix renormalization group algorithm (DMRG), updating one site at a time via sweeps rather than optimizing the full system simultaneously. Preliminary implementations of this approach have already been tested on quantum simulators with promising accuracy.
We aim to extend this approach to larger and more strongly correlated 1D clusters, characterizing how circuit depth, gate count, and accuracy scale with system size, bond dimension, and correlation strength. Looking further ahead, this framework could in principle be extended toward more complex two-dimensional geometries, where correlations and entanglement structure become substantially richer.
Computational resources were provided by IT4Innovations National Supercomputing Center, the MetaCentrum, and CERIT-SC under the Project e-INFRA CZ (ID:90254) supported by the Ministry of Education, Youth and Sports of the Czech Republic. Access to CESNET storage facilities provided by the project e‑INFRA CZ under the program Projects of Large Research, Development, and Innovations Infrastructures (LM2023054) is appreciated. Financial support from the Czech Academy of Sciences via the Praemium Academiae awarded to Martin Friák, from the Institute of Physics of Materials, Czech Academy of Sciences, Brno, Czech Republic, is gratefully acknowledged.