Highlights

Digital quantum simulation on quantum computers provides the potential to simulate the unitary evolution of any many-body Hamiltonian with bounded spectrum by discretizing the time evolution operator through a sequence of elementary quantum gates. A fundamental challenge in this context originates from experimental imperfections, which critically limits the number of attainable gates within a reasonable accuracy and therefore the achievable system sizes and simulation times. In this work, we introduce a reinforcement learning algorithm to systematically build optimized quantum circuits for digital quantum simulation upon imposing a strong constraint on the number of quantum gates. With this we consistently obtain quantum circuits that reproduce physical observables with as little as three entangling gates for long times and large system sizes up to 16 qubits. As concrete examples we apply our formalism to a long-range Ising chain and the lattice Schwinger model. Our method demonstrates that digital quantum simulation on noisy intermediate scale quantum devices can be pushed to much larger scale within the current experimental technology by a suitable engineering of quantum circuits using reinforcement learning.

A. Bolens et al., Phys. Rev. Lett. 127, 110502 (2021).

The one-body reduced density matrix $\gamma$ plays a fundamental role in describing and predicting quantum features of bosonic systems, such as Bose-Einstein condensation. The recently proposed reduced density matrix functional theory for bosonic ground states establishes the existence of a universal functional $F[\gamma]$ that recovers quantum correlations exactly. Based on a decomposition of $\gamma$, we have developed a method to design reliable approximations for such universal functionals: Our results suggest that for translational invariant systems the constrained search approach of functional theories can be transformed into an unconstrained problem through a parametrization of a Euclidian space. This simplification of the search approach allows us to use standard machine learning methods to perform a quite efficient computation of both $F[\gamma]$ and its functional derivative. For the Bose-Hubbard model, we present a comparison between our approach and the quantum Monte Carlo method.

J. Schmidt et al., Phys. Rev. Res. 3, L032063 (2021).

We combine quantum renormalization group approaches with deep artificial neural networks for the description of the real-time evolution in strongly disordered quantum matter. We find that this allows us to accurately compute the long-time coherent dynamics of large many-body localized systems in nonperturbative regimes including the effects of many-body resonances. Concretely, we use this approach to describe the spatiotemporal buildup of many-body localized spin-glass order in random Ising chains. We observe a fundamental difference to a noninteracting Anderson insulating Ising chain, where the order only develops over a finite spatial range. We further apply the approach to strongly disordered two-dimensional Ising models, highlighting that our method can be used also for the description of the real-time dynamics of nonergodic quantum matter in a general context.

H. Burau et al., Phys. Rev. Lett. 127, 050601 (2021)

Understanding how individual proteins work together to perform complex cellular processes such as transcription, DNA replication, and repair represents a crucial goal in cell biology. Transcription is a process in the nucleus where protein complexes work together to generate transcripts of RNA from genes. For proper transcriptional regulation, enhancers—short strips of DNA—must be brought into close proximity of the gene’s promoter. Given that enhancers and promoters are often located far apart within the genome, the question then arises: how do proteins bring these enhancers and promoters together in space and time? And what are the physics behind it?

Answering these questions would provide deep insights into the proper regulation of transcription in the cell nucleus. However, extracting such information is far from trivial. But recent work from the research group of Jan Brugués at the Max Planck Institute of Molecular Cell Biology and Genetics in collaboration with Frank Jülicher at the MPI for the Physics of Complex Systems has revealed an important clue: Forces. Jan’s lab is also located at the MPI for the Physics of Complex Systems and is affiliated with the Center for Systems Biology Dresden.

Interactions between liquids and solids have long been known to generate forces, such as those maintaining the tension of a spider web or those that allow insects to walk on water. However, whether such forces play a role inside the cell has remained unclear. With the development of precise biophysical methods and advanced imaging techniques, we are getting closer to not only observing such forces but also measuring them.

The Brugués lab imaged the interactions between single molecules of DNA and the transcription factor FoxA1, a protein responsible for determining cell fate in many species. They discovered that FoxA1 molecules brought distant regions of DNA together, generating forces that condensed the DNA. When the single molecule of DNA was stretched tightly — like a tightened elastic band — FoxA1 molecules could not bring DNA together. However, when the DNA molecule was floppy, FoxA1 molecules worked together to condense the DNA, overcoming the DNA’s intrinsic tension. This new information helps paint a clearer picture of the interactions between transcriptional regulators and the surface of the DNA.

Remarkably, the physics underlying these FoxA1-DNA interactions are reminiscent of the forces that maintain the tension of a spider web. Similar to how liquid droplets on a spider web generate forces that reel in broken strands of silk, FoxA1 acts as the liquid phase that condenses DNA and brings it together.

This study demonstrated how proteins work together to generate forces in the cell nucleus. Such a result opens an exciting research direction to understanding other complex processes in the cell. Thomas Quail, post-doctoral researcher in the Brugués lab says: “Our findings set forth a novel mechanism that the cell nucleus may use to organize its chromatin and DNA. It’s possible that these condensation forces generated between solid and liquid surfaces could also be relevant for other cellular bodies such as the mitotic spindle and membranes.”

T. Quail et al., Nature Physics (2021)

In many species including humans, the cells responsible for reproduction, the germ cells, are often highly interconnected and share their cytoplasm. In the hermaphrodite nematode Caenorhabditis elegans, up to 500 germ cells are connected to each other in the gonad, the tissue that produces eggs and sperm. These cells are arranged around a central cytoplasmic “corridor” and exchange cytoplasmic material fostering cell growth, and ultimately produce oocytes ready to be fertilized.

In past studies, researchers have found that C. elegans gonads generate more germ cells than needed. Only half of them grow to become oocytes, while the rest shrinks and die by physiological apoptosis, a programmed cell death that occurs in multicellular organisms. Now, scientists from the Biotechnology Center of the TU Dresden (BIOTEC), the Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG), the Cluster of Excellence Physics of Life (PoL) at the TU Dresden, the Max Planck Institute for the Physics of Complex Systems (MPI-PKS), the Flatiron Institute, NY, and the University of California, Berkeley, found evidence to answer the question of what triggers this cell fate decision between life and death in the germline. Prior studies revealed the genetic basis and biochemical signals that drive physiological cell death, but the mechanisms that select and initiate apoptosis in individual germ cells remained unclear. As germ cells mature along the gonad of the nematode, they first collectively grow in size and in volume homogenously. In the study just published in Nature Physics, the scientists show that this homogenous growth suddenly shifts to a heterogenous growth where some cells become bigger and some cells become smaller.

The researcher Nicolas Chartier in the group of Stephan Grill, and co-first author of the study, explains: “By precisely analyzing germ cell volumes and cytoplasmic material fluxes in living worms and by developing theoretical modeling, we have identified a hydraulic instability that amplifies small initial random volume differences, which causes some germ cells to increase in volume at the expense of the others that shrink. It is a phenomenon, which can be compared to the two-balloon instability, well known of physicists. Such an instability arises when simultaneously blowing into two rubber balloons attempting to inflate them both. Only the larger balloon will inflate, because it has a lower internal pressure than the smaller one, and is therefore easier to inflate.” This is what is at play in the selection of germ cells: such pressure differences tend to destabilize the symmetric configuration with equal germ cell volumes, so-called hydraulic instabilities, leading to the growth of the larger germ cell at the expense of the smaller one. By artificially reducing germ cell volumes via thermoviscous pumping (FLUCS method: focused-light-induced cytoplasmic streaming), the team demonstrated that the reduction in cell volumes leads to their extrusion and cell death, indicating that once a cell is below a critical size, apoptosis is induced and the cell dies. By using confocal imaging, the researchers could image the full organism of the living worm to receive a global and precise picture of the volumes of all the gonad cells, as well as the exchange of fluids between the cells. Stephan Grill, Speaker of the PoL and director at the MPI-CBG and supervisor of the multidisciplinary work, adds: “These findings are very exciting because they reveal that the life and death decision in the cells is of mechanical nature and related to tissue hydraulics. It helps to understand how the organism auto-selects a cell that will become an egg. Furthermore, the study is another example of the excellent cooperation between biologists, physicists and mathematicians in Dresden.”

T. Chartier et al., Nature Physics (2021)

Disorder-free localization has been recently introduced as a mechanism for ergodicity breaking in low-dimensional homogeneous lattice gauge theories caused by local constraints imposed by gauge invariance. We show that also genuinely interacting systems in two spatial dimensions can become nonergodic as a consequence of this mechanism. This result is all the more surprising since the conventional many-body localization is conjectured to be unstable in two dimensions; hence the gauge invariance represents an alternative robust localization mechanism surviving in higher dimensions in the presence of interactions. Specifically, we demonstrate nonergodic behavior in the quantum link model by obtaining a bound on the localization-delocalization transition through a classical correlated percolation problem implying a fragmentation of Hilbert space on the nonergodic side of the transition. We study the quantum dynamics in this system by introducing the method of “variational classical networks,” an efficient and perturbatively controlled representation of the wave function in terms of a network of classical spins akin to artificial neural networks. We identify a distinguishing dynamical signature by studying the propagation of line defects, yielding different light cone structures in the localized and ergodic phases, respectively. The methods we introduce in this work can be applied to any lattice gauge theory with finite-dimensional local Hilbert spaces irrespective of spatial dimensionality.

P. Karpov et al., Phys. Rev. Lett. 126, 130401 (2021).

We study in detail the properties of $\pi$-fluxes embedded in a state with a finite density of anyons that form either a Fermi liquid or a Bose-Einstein condensate. By employing a recently developed exact lattice bosonization in 2D, we demonstrate that such $\pi$-flux remains a fully deconfined quasi-particle with a finite energy cost in a Fermi liquid of emergent fermions coupled to a $\mathbb{Z}_2$ gauge field. This $\pi$-flux is accompanied by a screening cloud of fermions, which in the case of a Fermi gas with a parabolic dispersion binds exactly 1/8 of a fermionic hole. In addition there is a long-ranged power-law oscillatory disturbance of the liquid surrounding the $\pi$-flux akin to Friedel oscillations. These results carry over directly to the $\pi$-flux excitations in orthogonal metals. In sharp contrast, when the $\pi$-flux is surrounded by a Bose-Einstein condensate of particles coupled to a $\mathbb{Z}_2$ gauge field, it binds a superfluid half-vortex, becoming a marginally confined excitation with a logarithmic energy cost divergence.

O. Pozo et al., Phys. Rev. B 103, 035145 (2021)

Driven quantum systems may realize novel phenomena absent in static systems, but driving-induced heating can limit the timescale on which these persist. We study heating in interacting quantum many-body systems driven by random sequences with n-multipolar correlations, corresponding to a polynomially suppressed low-frequency spectrum. For $n\geq 1$, we find a prethermal regime, the lifetime of which grows algebraically with the driving rate, with exponent $2n+1$. A simple theory based on Fermi’s golden rule accounts for this behavior. The quasiperiodic Thue-Morse sequence corresponds to the $n\to \infty$ limit and, accordingly, exhibits an exponentially long-lived prethermal regime. Despite the absence of periodicity in the drive, and in spite of its eventual heat death, the prethermal regime can host versatile nonequilibrium phases, which we illustrate with a random multipolar discrete time crystal.

H. Zhao et al., Phys. Rev. Lett. 126, 040601 (2021).

We address the ground-state properties of the long-standing and much-studied three-dimensional quantum spin liquid candidate, the $S=1/2$ pyrochlore Heisenberg antiferromagnet. By using SU(2) density-matrix renormalization group (DMRG), we are able to access cluster sizes of up to 128 spins. Our most striking finding is a robust spontaneous inversion symmetry breaking, reflected in an energy density difference between the two sublattices of tetrahedra, familiar as a starting point of earlier perturbative treatments. We also determine the ground-state energy, $E_0/N_{sites}=-0.490(6)$, by combining extrapolations of DMRG with those of a numerical linked cluster expansion. These findings suggest a scenario in which a finite-temperature spin liquid regime gives way to a symmetry-broken state at low temperatures.

I. Hagymási et al., Phys. Rev. Lett. 126, 117204 (2021)

Many proteins form small droplets that separate out of the cell’s cytoplasm, just like oil de-mixes from water. Since their discovery, these liquid-like protein droplets have been identified in myriad important biological phenomena ranging from embryonic development over neuro-degeneration to DNA regulation. For instance, the localization of protein droplets in a specific location during early development of a worm is believed to determine which cells will become the sexual organs of the adult worm. In another example, protein condensation into droplets under cell stress is associated with the growth of fibers related to neurodegeneration as seen in ALS (Amyotrophic lateral sclerosis) disease.
Observations have shown that the material properties of these protein condensates change with time. However, an appropriate measurement and description of the material properties and their evolution over time was missing so far. Researchers from the MPI of Molecular Cell Biology and Genetics (MPI-CBG) and the MPI for the Physics of Complex Systems (MPI-PKS), together with their colleagues from the TU Dresden, EMBL Heidelberg and the IMBA Vienna have now filled this gap. In their study, recently published in Science, the scientists show that protein droplets exhibit aging behavior in which they change slowly from liquid-like behavior to a more solid-like state.
Louise Jawerth, postdoc in the Frank Jülicher and Tony Hyman groups and first author of the publication, explains, “In order to carefully measure and characterize the time-dependent material properties we first developed a new optical trap technique (Jawerth et al physical review letters 2018 121 (25), 258101)”. The former ELBE postdoctoral fellow at the CSBD continues, ”We then found that droplet aging shows a strongly increasing viscosity, which leads to more solid-like behaviour. Our study suggests that the time-dependent material properties arise from unspecific mechanisms such as jamming of molecules.”
Frank Jülicher, director at the MPI-PKS and member of the CSBD and the “Physics of Life” (PoL) Cluster of Excellence at the TU Dresden, adds, “Similar aging has been seen in other materials with time-dependent properties such as traditional glass, plastics, rubbers, or common household items like toothpaste or mayonnaise. By establishing a connection to glass forming systems, we open a new window in which we can utilize a wealth of understanding of these other systems to understand protein droplets.”
The second supervisor of the study, Anthony Hyman, director at the MPI-CBG and member of the CSBD, summarizes, “The analogy to traditional glasses also suggests that the unspecific interactions resulting in a solid-like state require less energy to dissolve than, for instance, in comparison to a gel comprised of very strong bonds. Furthermore, it may be used in cells as novel stress sensors. Further study on aging in protein droplets may help to answer fundamental biological questions, for example in embryonic development or DNA transcription, and to better understand neurodegenerative diseases. Vice versa, it may also lead to insights into glass-like aging more generally, which is considered one of the big unsolved questions in condensed matter physics.”

L. Jawerth et al., Science 370, 1317 (2020)