# Quantum Simulation

Many-particle quantum systems challenge us with a large number of fundamental open questions, such as the mechanisms behind high-temperature superconductivity or quark confinement. One obstacle for developing a full theoretical understanding of quantum many-body systems is the difficulty of solving them on classical computers, as the required computing resources grow exponentially with the number of constituents. In 1982, Feynman proposed an alternative approach to tackle such problems, namely to encode them in specifically engineered experimental systems that themselves are governed by the laws of quantum mechanics, a concept now termed “quantum simulation”. With their high degree of precision and controllability, current experimental platforms such as cold atomic gases, trapped ions, or superconducting qubits, are perfectly suited for this purpose.

In this project, we aim at identifying difficult problems and interesting phenomena that are worthy targets of quantum simulations, and to develop schemes to realize them in realistic experiments. Currently, we are especially interested in quantum transport and thermalization, strongly-correlated systems, topological phases of matter, and lattice gauge theories. We are also addressing a crucial challenge for the further development of the field, namely how to ensure the reliability of quantum simulators once they explore regimes where benchmarks with classical computers are no longer possible.

##### Kevin T. Geier

###### PhD Student (2018 – 2022)

Postdoc (2022 – 2024)

Now Senior Researcher at Technology Innovation Institute, Abu Dhabi

## Publications

### Quantifying non-Hermiticity using single- and many-particle quantum properties

### Miscibility-immiscibility transition of strongly interacting bosonic mixtures in optical lattices

### Unraveling the emergence of quantum state designs in systems with symmetry

### Beyond braid statistics: Constructing a lattice model for anyons with exchange statistics intrinsic to one dimension

### Variational quantum simulation of U(1) lattice gauge theories with qudit systems

### Observation of microscopic confinement dynamics by a tunable topological $\theta$-angle

### Many-body magic via Pauli–Markov chains — from criticality to gauge theories

### Spin-$S$ $U(1)$ Quantum Link Models with Dynamical Matter on a Quantum Simulator

### A cavity quantum electrodynamics implementation of the Sachdev--Ye--Kitaev model

### Absence of operator growth for average equal-time observables in charge-conserved sectors of the Sachdev-Ye-Kitaev model

**2023**, 126 (2023)

### Engineering random spin models with atoms in a high-finesse cavity

### Quantum Hall and Synthetic Magnetic-Field Effects in Ultra-Cold Atomic Systems

### Stabilizing Gauge Theories in Quantum Simulators: A Brief Review

### Tuning the Topological $\theta$-Angle in Cold-Atom Quantum Simulators of Gauge Theories

### Probing confinement in a $\mathbb{Z}_2$ lattice gauge theory on a quantum computer

### Robust quantum many-body scars in lattice gauge theories

### Disorder-free localization with Stark gauge protection

### Dynamical quantum phase transitions in spin-$S$ $U(1)$ quantum link models

### Achieving the quantum field theory limit in far-from-equilibrium quantum link models

**6**, 878 (2022)

### Ground-state phase diagram of quantum link electrodynamics in $(2+1)$-d

**13**, 017 (2022)

### Enhancing disorder-free localization through dynamically emergent local symmetries

**3**, 020345 (2022)

### Stabilizing Disorder-Free Localization

### Suppressing nonperturbative gauge errors in the thermodynamic limit using local pseudogenerators

### Stabilizing lattice gauge theories through simplified local pseudo generators

**4**, 033120 (2022)

### Universal equilibration dynamics of the Sachdev-Ye-Kitaev model

**7**, 1022 (2023)

### Engineering a $\mathrm{U}(1)$ lattice gauge theory in classical electric circuits

### Thermalization dynamics of a gauge theory on a quantum simulator

**377**, 311-314 (2022)

### Gauge protection in non-Abelian lattice gauge theories

**24**033015 (2022)

### Dynamical phase transitions in quantum spin models with antiferromagnetic long-range interactions

**104**, 115133 (2021)

### Generalized Discrete Truncated Wigner Approximation for Nonadiabtic Quantum-Classical Dynamics

### Reliability of lattice gauge theories in the thermodynamic limit

**107**, 035153 (2023)

### Towards the continuum limit of a $(1+1)$d quantum link Schwinger model

**106**, L091502 (2022)

### Gauge-Symmetry Violation Quantum Phase Transition in Lattice Gauge Theories

### Diffusive-to-ballistic crossover of symmetry violation in open many-body systems

### Fate of Lattice Gauge Theories Under Decoherence

### Analog cosmological reheating in an ultracold Bose gas

**104**, 023302 (2021)

### Gauge-Symmetry Protection Using Single-Body Terms

**2**, 040311 (2021)

### Robustness of gauge-invariant dynamics against defects in ultracold-atom gauge theories

**2**, 033361 (2020)

### Origin of staircase prethermalization in lattice gauge theories

### Staircase prethermalization and constrained dynamics in lattice gauge theories

### Observation of gauge invariance in a 71-site quantum simulator

**587**, 392–396 (2020)

### Reliability of lattice gauge theories

**125**, 030503 (2020)

### A scalable realization of local U(1) gauge invariance in cold atomic mixtures

**367**(6482) (2020)

### Many-body localization in a quantum simulator with programmable random disorder

**12**, 907–911 (2016)

### Can one trust quantum simulators?

**75**082401 (2012)