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Articles by Markus Heyl
Adaptive Trotterization for Time-Dependent Hamiltonian Quantum Dynamics Using Piecewise Conservation Laws
Digital quantum simulation relies on Trotterization to discretize time evolution into elementary quantum gates. On current quantum processors with notable gate imperfections, there is a critical trade-off between improved accuracy for finer time steps, and increased error rate on account of the larger circuit depth.
Empowering deep neural quantum states through efficient optimization - Nature Physics
Abstract Computing the ground state of interacting quantum matter is a long-standing challenge, especially for complex two-dimensional systems. Recent developments have highlighted the potential of neural quantum states to solve the quantum many-body problem by encoding the many-body wavefunction into artificial neural networks. However, this method has faced the critical limitation that existing optimization algorithms are not suitable for training modern large-scale deep network architectures.
Simplicity of mean-field theories in neural quantum states
The utilization of artificial neural networks to represent quantum many-body wave functions has garnered significant attention, with enormous recent progress for both ground states and nonequilibrium dynamics. However, quantifying state complexity within this neural quantum states framework remains elusive. In this study, we address this key open question from a complementary point of view: Which states are simple to represent with neural quantum states?
Vortex loop dynamics and dynamical quantum phase transitions in three-dimensional fermion matter
Over the past decade, dynamical quantum phase transitions (DQPTs) have emerged as a paradigm shift in understanding nonequilibrium quantum many-body systems. However, the challenge lies in identifying order parameters that effectively characterize the associated dynamic phases.
Dynamical Localization Transition of String Breaking in Quantum Spin Chains
The fission of a string connecting two charges is an astounding phenomenon in confining gauge theories. The dynamics of this process have been studied intensively in recent years, with plenty of numerical results yielding a dichotomy: the confining string can decay relatively fast or persist up to extremely long times. Here, we put forward a dynamical localization transition as the mechanism underlying this dichotomy.
Spectral Response of Disorder-Free Localized Lattice Gauge Theories
We show that certain lattice gauge theories exhibiting disorder-free localization have a characteristic response in spatially averaged spectral functions: a few sharp peaks combined with vanishing response in the zero frequency limit. This reflects the discrete spectra of small clusters of kinetically active regions formed in such gauge theories when they fragment into spatially finite clusters in the localized phase due to the presence of static charges.
Identifying Quantum Many-Body Integrability and Chaos Using Eigenstate Trace Distances
While the concepts of quantum many-body integrability and chaos are of fundamental importance for the understanding of quantum matter, their precise definition has so far remained an open question. In this Letter, we introduce an alternative indicator for quantum many-body integrability and chaos, which is based on the statistics of eigenstates by means of nearest-neighbor subsystem trace distances.
Hin per Rad, zurück zu Fuß: Jonas Deichmann durchquert USA zweimal
New York – Täglich rund 200 Kilometer auf dem Rad oder mehr als 50 zu Fuß. Es ist eine Wahnsinns-Leistung! Jonas Deichmann (36) aus Stuttgart (Baden-Württemberg) startete Anfang Juli zu einer Extrem-Tour. Der Athlet stieg in New York auf sein Fahrrad und fuhr quer durch die USA bis nach Los Angeles im Bundesstaat Kalifornien. Aber damit nicht genug ... Danach ging es zurück in den Big Apple. Zu Fuß! Dort kam er am Samstag wieder an, nahm sich Sonntag noch den berühmten New York Marathon vor.
Making Trotterization Adaptive and Energy-Self-Correcting for NISQ Devices and Beyond
Abstract Simulation of continuous-time evolution requires time discretization on both classical and quantum computers. A finer time step improves simulation precision but it inevitably leads to increased computational efforts. This is particularly costly for today’s noisy intermediate-scale quantum computers, where notable gate imperfections limit the circuit depth that can be executed at a given accuracy. Classical adaptive solvers are well developed to save numerical computation times.
Highly Resolved Spectral Functions of Two-Dimensional Systems with Neural Quantum States
Abstract Spectral functions are central to link experimental probes to theoretical models in condensed matter physics. However, performing exact numerical calculations for interacting quantum matter has remained a key challenge especially beyond one spatial dimension. In this work, we develop a versatile approach using neural quantum states to obtain spectral properties based on simulations of the dynamics of excitations initially localized in real or momentum space.
Anomalous relaxation of density waves in a ring-exchange system
Abstract We present the analysis of the slowing down exhibited by stochastic dynamics of a ring-exchange model on a square lattice, by means of numerical simulations. We find the preservation of coarse-grained memory of initial state of density-wave types for unexpectedly long times. This behavior is inconsistent with the prediction from a low frequency continuum theory developed by assuming a mean-field solution.
Bergsprinter im Himalya: Ein Gipfelsturm unter sieben Stunden
Kathmandu – Der Himlung Himal ragt im größten Bergmassiv der Welt 7126 Meter hoch. Er gilt als wenig bestiegen. Nun wurde er zum Schauplatz eines Geschwindigkeits-Projekts. Extrem-Bergsteiger Benedikt Böhm (45) und Prakash Sherpa (29) erklommen den Gipfel im Himalaya in nur sechs Stunden und 43 Minuten, von einem Basislager in 4850 Metern Höhe. Sonntag startete die Speed-Expedition mit Skiern mitten in der Nacht. Eine Tour mit der Gewissheit, auf sich gestellt zu sein.
Local measures of dynamical quantum phase transitions
Abstract In recent years, dynamical quantum phase transitions (DQPTs) have emerged as a useful theoretical concept to characterize nonequilibrium states of quantum matter. DQPTs are marked by singular behavior in an effective free energy λ(t), which, however, is a global measure, making its experimental or theoretical detection challenging in general. We introduce two local measures for the detection of DQPTs with the advantage of requiring fewer resources than the full effective free energy.
Digital quantum simulation, Trotter errors, and quantum chaos of the kicked top
Abstract This work aims at giving Trotter errors in digital quantum simulation (DQS) of collective spin systems an interpretation in terms of quantum chaos of the kicked top. In particular, for DQS of such systems, regular dynamics of the kicked top ensures convergence of the Trotterized time evolution, while chaos in the top, which sets in above a sharp threshold value of the Trotter step size, corresponds to the proliferation of Trotter errors.
Dynamical quantum phase transitions: a review
Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards the generation of quantum states beyond this equilibrium paradigm.
Quantum localization bounds Trotter errors in digital quantum simulation
Abstract A fundamental challenge in digital quantum simulation (DQS) is the control of an inherent error, which appears when discretizing the time evolution of a quantum many-body system as a sequence of quantum gates, called Trotterization. Here, we show that quantum localization-by constraining the time evolution through quantum interference-strongly bounds these errors for local observables, leading to an error independent of system size and simulation time.
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