Using quantum computers to test Jarzynski’s equality for many interacting particles
Statistical mechanics is a branch of physics that uses statistical and probabilistic methods to understand the behaviour of large numbers of microscopic particles, such as atoms and molecules, in a system. Instead of focusing on the individual motion of each particle, statistical mechanics analyses the collective properties of the system. It provides a bridge between the microscopic world of particles and the macroscopic world that we can observe, explaining phenomena like the behaviour of liquids and gases, phase transitions, and the thermodynamic properties of materials. Through the statistical distribution of particle properties, such as energy and velocity, statistical mechanics helps us make predictions about how physical systems behave on a larger scale, contributing to our understanding of fundamental principles in physics and chemistry.
One of the most remarkable relations in statistical mechanics is Jarzynski's equality, connecting the irreversible work performed in an arbitrary thermodynamic process with the energy and entropy of the system in thermodynamic equilibrium. Because the system is free to leave the equilibrium state during its evolution, Jarzynski’s equality is a prime example of how equilibrium physics can constrain the outcome of nonequilibrium processes. Remarkably, the familiar Second Law of Thermodynamics – a fundamental principle of physics – follows directly from Jarzynski’s equality. The Second Law is a statement about the average properties of particles in a system undergoing a thermodynamic process, and postulates that heat always flows spontaneously from hotter to colder regions of the system. Intriguingly, Jarzynski’s equality shows that this fundamental law of Thermodynamics can be “violated” in individual realizations of a process (but never on average!).
Despite its fundamental importance, experimental tests of Jarzynski’s equality for classical and quantum systems are extremely challenging, since they require complete control in manipulating and measuring the system. Even more so, a test for many quantum interacting particles was until recently completely missing.
In a new joint study, an international team from the Max Planck Institute for the Physics of Complex Systems, the University of California at Berkeley, the Lawrence Berkeley National Laboratory, the German Cluster of Excellence ML4Q and the Universities of Cologne, Bonn, and Sofia identified quantum computers as a natural platform to test the validity of Jarzynski’s equality for many interacting quantum particles. (A quantum computer is a computing device that uses the principles of Quantum Mechanics to perform certain types of calculations at speeds and efficiency levels that are unattainable by classical computers. Quantum computers use quantum bits, or qubits, as the basic unit of information. Hence, any quantum computer is, at its core, a system of interacting quantum particles.) The researchers used the quantum bits of the quantum processor to simulate the behaviour of many quantum particles undergoing nonequilibrium processes, as is desired for an experimental verification of Jarzynski’s equality. They tested this fundamental principle of nature on multiple devices and using different quantum computing platforms. To their surprise, they found that the agreement between theory and quantum simulation was more accurate than originally expected due to the presence of computational errors, which are omnipresent in current quantum computers. The results demonstrate a direct link between certain types of errors that can occur in quantum computations and violations of Jarzynski’s equality, revealing a fascinating connection between quantum computing technology and this fundamental principle of physics.
Dominik Hahn, Maxime Dupont, Markus Schmitt, David J. Luitz, and Marin Bukov, Physical Review X 13, 041023 (2023)
Investigating the impact of a defect basepair on DNA melting
As temperature is increased, the two strands of DNA separate. This DNA melting is described by a powerful model of statistical physics, the Poland–Scheraga model. It is exactly solvable for homogeneous DNA (with only one type of basepairs), and predicts a first-order phase transition.
Arthur Genthon of the Max Planck Institute for the Physics of Complex Systems, Albertas Dvirnas and Tobias Ambjörnsson (Lund University, Sweden) have now derived an exact equilibrium solution of an extended Poland–Scheraga model that describes DNA with a defect site that could, for instance, result from DNA basepair mismatching, cross-linking, or the chemical modifications from attaching fluorescent labels, such as fluorescent-quencher pairs, to DNA. This defect was characterized by a change in the Watson–Crick basepair energy of the defect basepair, and in the associated two stacking (nearest-neighbour) energies for the defect compared to the remaining parts of the DNA. The exact solution yields the probability that the defect basepair and its neighbors are separated at different temperatures. In particular, the authors investigated the impact of the defect on the phase transition, and the number of base pairs away from the defect at which its impact is felt. This work has implications for studies in which fluorophore-quencher pairs are used to analyse single-basepair fluctuations of designed DNA molecules.
Arthur Genthon, Albertas Dvirnas, and Tobias Ambjörnsson, J, Chem. Phys. 159, 145102 (2023)
In 1983, the two physicists Page and Wootters postulated a timeless entangled quantum state of the universe in which time emerges for a subsystem in relation to the rest of the universe. This radical perspective of one quantum system serving as the other’s temporal reference resembles our traditional use of celestial bodies’ relative motion to
track time. However, a vital piece has been missing: the inevitable interaction of physical systems.
Forty years later, Sebastian Gemsheim and Jan M. Rost from the Max Planck Institute for the Physics of Complex Systems have finally shown how a static global state, a solution of the time-independent Schrödinger equation, gives rise to the time-dependent Schrödinger equation for the state of the subsystem once it is separated from its environment to which it retains arbitrary static couplings. Exposing a twofold role, the environment additionally provides a time-dependent effective potential governing the system dynamics, which is intricately encoded in the entanglement of the global state. Since no approximation is required, intriguing applications beyond the question of time are within reach for heavily entangled quantum systems, which are elusive but relevant for processing quantum information.
Sebastian Gemsheim and Jan M. Rost, Phys. Rev. Lett. 131, 140202 (2023)
New Max Planck Fellow group established at the institute
The Max Planck Fellows Programme promotes cooperation between universities and Max Planck institutes and enables a university professor to install a research group at an MPI. We are glad to announce that Prof. Jan Budich from TU Dresden has started a new Max Planck Fellow group "Dissipative Quantum Matter" at MPI-PKS. The research group will explore quantum many-body systems in which dissipation plays a crucial role, for example inducing novel phases of topological matter or enabling the controlled preparation of complex quantum states in the context of quantum simulators. Regarding physical platforms, the spectrum of interest ranges from quantum condensed matter to atomic and quantum-optical many-body systems.
Welcome at the institute, Jan!
When a liquid is cooled to form a glass, its dynamic slows down significantly, resulting in its unique properties. This process, known as “glass transition”, has puzzled scientists for decades. One of its intriguing aspects is the emergence of “dynamical heterogeneities”, when the dynamics become increasingly correlated and intermittent as the liquid cools down and approaches the glass transition temperature.
In a new collaborative study, Ali Tahaei and Marko Popovic from the Max Planck Institute for the Physics of Complex Systems, with colleagues from EPFL Lausanne, ENS Paris, and Université Grenoble Alpes, propose a new theoretical framework to explain the origin of the dynamical heterogeneities in glass-forming liquids.
Based on the premise that relaxation in these materials occurs occurs through local rearrangements of particles that interact via elastic interactions, the researchers formulated a scaling theory that predicts a growing length-scale of dynamical heterogeneties upon decreasing temperature. The proposed mechanism is an example of extremal dynamics that leads to self-organised critical behavior. The proposed scaling theory also accounts for the Stokes-Einstein breakdown, which is a phenomenon observed in glass-forming liquids in which the viscosity becomes uncoupled from the diffusion coefficient. To validate their theoretical predictions, the researchers conducted extensive numerical simulations that confirmed the predictions of the scaling theory.
Ali Tahaei, Giulio Biroli, Misaki Ozawa, Marko Popovic, and Matthieu Wyart, Phys. Rev. X 13, 031034 (2023).
The John Atanasoff Award, named after the creator of the first electronic computer - the famous scholar of Bulgarian descent, John Atanasoff, was first awarded in 2003 in support of the personal achievements of young Bulgarian researchers working in the fields of informatics and information technology. Marin Bukov, group leader at MPI-PKS, is among this year's awardees ”for his outstanding contributions to the field of artificial intelligence applied to quantum technologies, and for his role in the development of efficient innovative research and education tools used worldwide”. Congratulations, Marin!
Call for Distinguished PKS Postdoctoral Fellowship 2024 open!
Application deadline: 10 November 2023. Distinguished PKS postdoctoral fellows appear personally along with the departments and groups on the main research page of the institute and are expected to have at least one year of postdoctoral experience at an institution other than the one at which their PhD was awarded. Applications for this fellowship directly after completion of the PhD might be considered in exceptional cases.
Please click on the link- button to see the full advertisement!
Cell Lineage Statistics with Incomplete Population Trees
Cell lineage statistics is a powerful tool for inferring cellular parameters, such as division rate, death rate, fitness landscape and selection. Yet, in practice such an analysis suffers from a basic problem: how should we treat incomplete lineages that do not survive until the end of the experiment? Examples of such lineages are found in experiments in which cells can die (antibiotic experiments, ...) and in experiments in which cells are diluted to maintain the population constant (microchannels, cytometers, ...).
Arthur Genthon of the Max Planck Institute for the Physics of Complex Systems, Takashi Nozoe (U. Tokyo, Japan), Luca Peliti (Santa Marinella Research Institute, Italy), and David Lacoste (Gulliver, Paris) have now developed a model-independent theoretical framework to address this issue.
They show how to quantify fitness landscape, survivor bias, and selection for arbitrary cell traits from cell lineage statistics in the presence of death, and they test this method using an experimental data set in which a cell population is exposed to a drug that kills a large fraction of the population. This analysis reveals that failing to properly account for dead lineages can lead to misleading fitness estimations. For simple trait dynamics, they prove and illustrate numerically that the fitness landscape and the survivor bias can in addition be used for the nonparametric estimation of the division and death rates, using only lineage histories. Their framework provides universal bounds on the population growth rate, and a fluctuation-response relation that quantifies the change in population growth rate due to the variability in death rate. Further, in the context of cell size control, they obtain generalizations of Powell's relation that link the distributions of generation times with the population growth rate, and they show that the survivor bias can sometimes conceal the adder property, namely the constant increment of volume between birth and division.
Arthur Genthon, Takashi Nozoe, Luca Peliti, and David Lacoste, PRX Life 1, 013014 (2023)
Two ERC Starting Grants awarded to group leaders at MPI-PKS
The European Research Council (ERC) has announced early-career top researchers across Europe who will receive a starting grant. The prestigious grants enable the best young researchers in Europe to build their own teams and to conduct pioneering research across all disciplines. This year, two of these grants were awarded to research group leaders at the MPI-PKS: Marin Bukov for his proposal "Nonequilibrium Many Body Control of Quantum Simulators" and Ricard Alert for his proposal "The Spectrum of Fluctuations in Living Matter". Congratulations!!
The hydrogen atom is one of the few exactly solvable quantum systems. Its well-known properties are shared by highly excited Rydberg atoms, albeit to such an exaggerated degree that their behavior is often wholly unexpected.
Scientists at the Max Planck Institute for the Physics of Complex Systems have now investigated a Rydberg atom perturbed by ground state atoms, exploiting hydrogen's infinite spectrum and high degeneracy to show that the Rydberg electron localizes in the same fashion as electrons in a disordered solid. This unexpected manifestation of Anderson localization is enabled by the existence of a well-defined thermodynamic limit of the single Rydberg electron as its principle quantum number and the number of ground state atoms increase in tandem. Myriad localization regimes can be realized as a function of the geometry of the system.
Matthew T. Eiles, Alexander Eisfeld, and Jan M. Rost, Phys. Rev. Research 5, 033032 (2023)