arXiv subjects

Gesa Dünnweber

Publications and source records attributed to Gesa Dünnweber.

4 recordsLinked to original sources

arXiv2026

Quantum Memory and Autonomous Computation in Two Dimensions

Quantum error correction (QEC) normally requires active maintenance using measurements, classical processing and externally controlled correction schedules. Passive QEC, by contrast, was previously established only in unphysical spatial dimensions. Here, we give an explicit scheme for autonomous quantum error correction and computation in two dimensions, formulated as a dissipative quantum cellular automaton with a fixed, local and translation-invariant update rule. The construction uses hierarchical, self-simulating control elements based on ideas from the seminal classical results of Gács (1986, 1989) together with a measurement-free concatenated quantum code. We prove the existence of a nonzero noise threshold under a local noise model. Below this threshold, logical errors on encoded initial states are suppressed exponentially with increasing system size and the memory lifetime diverges in the thermodynamic limit. As an extension, we outline how this mechanism can also be implemented in continuous time by a time-independent, translation-invariant local Lindbladian. Quantum circuits can moreover be encoded in the automaton's initial state and executed fault-tolerantly with polylogarithmic overhead under the same circuit-independent rule. Our scheme thus realizes a self-correcting quantum computer capable of universal computation.

quant-ph↗

arXiv2026

Effective theory of the hidden-order pseudogap phase in a doped antiferromagnet

The microscopic origin of the pseudogap phase constitutes a longstanding puzzle related to the emergence of high-temperature superconductivity in cuprate materials. In this work, we develop an effective model for doped antiferromagnets in terms of fluctuating stripes, or string-like domain walls, which obscure the antiferromagnetic order of the spin background. The open ends of such domain walls of the N'eel order are treated as vortices in the resulting lattice gauge theory. We numerically evaluate the phase diagram by classical Monte Carlo simulations, using percolation-based geometric order parameters to diagnose hidden N'eel order. At high temperatures, we identify a BKT-type crossover in which the domain wall ends become deconfined. We interpret this as the $T^*$ crossover from the hidden order regime to the paramagnetic metal above. At low temperatures, we identify stripe instabilities. Predictions of our effective model can be tested in ultracold fermion quantum simulators.

cond-mat.str-el↗

arXiv2024

Percolation renormalization group analysis of confinement in $\mathbb{Z}_2$ lattice gauge theories

The analytical study of confinement in lattice gauge theories (LGTs) remains a difficult task to this day. Taking a geometric perspective on confinement, we develop a real-space renormalization group (RG) formalism for $\mathbb{Z}_2$ LGTs using percolation probability as a confinement order parameter. The RG flow we analyze is constituted by both the percolation probability and the coupling parameters. We consider a classical $\mathbb{Z}_2$ LGT in two dimensions, with matter and thermal fluctuations, and analytically derive the confinement phase diagram. We find good agreement with numerical and exact benchmark results and confirm that a finite matter density enforces confinement at $T<\infty$ in the model we consider. Our RG scheme enables future analytical studies of $\mathbb{Z}_2$ LGTs with matter and quantum fluctuations and beyond.

cond-mat.stat-mech↗

arXiv2023

Physical Entanglement Between Localized Orbitals

In [arXiv:2207.03377] the first closed formula of a faithful entanglement measure applicable to realistic electron systems has been derived. In the present work, we build on this key achievement with the ultimate goal of guiding the development of quantum technologies. For this, we first elucidate the process of entanglement swapping in electron systems such as atoms, molecules or solid bodies. This clearly demonstrates the necessity of both the reference to localized few-orbital subsystems and the implementation of the number-parity superselection rule. Accordingly, in virtue of Wick's theorem, we then provide a fully analytical study of the true physical entanglement between sites in free electron chains. In that sense, we break the common paradigm of restricting such analytical analyses to unitarily invariant settings, i.e. bipartitions of the chain into rather impractical, macroscopically large subsystems. We then upgrade this model to a hydrogen ring of interacting electrons and construct the sought-after localized orbitals. For both systems, we confirm the presence of long-distance entanglement, provided the filling fractions are sufficiently low/high.

quant-ph↗