<!--HTML--> In this talk, I will review the fundamental principles of quantum information processing and provide an update on the Innsbruck trapped-ion quantum computer [1]. Using strings of trapped ions, we realize a programmable quantum processor capable of performing universal operations. I will give an overview of the experimental quantum toolbox and discuss current strategies for scaling the system to larger sizes. The versatility of this platform is illustrated through both analog and digital quantum simulations. By exploiting the trapped-ion toolbox for entanglement-enhanced Ramsey interferometry, we identify optimal parameters for quantum metrology [2]. Employing universal quantum computation, we explore the dynamics of the Lattice Schwinger model [3] - a one-dimensional gauge theory of quantum electrodynamics - and, using a hybrid quantum-classical variational approach, we determine steady-state properties of the corresponding Hamiltonian [4]. Finally, with a trapped-ion qudit quantum processor, in which quantum information is encoded in multiple internal states, we simulate a two-dimensional lattice gauge theory [5}. [1] I. Pogorelov et al., PRX Quantum 2, 020343 (2021) [2] C. D. Marciniak et al., Nature 603, 604 (2022) [3] E. A. Martinez et al., Nature 534, 516 (2016) [4] C. Kokail et al., Nature 569, 355–360 (2019) [5] M. Meth et al., Nature Physics 21, 570 (2025)
<!--HTML--> In this talk, I will review the fundamental principles of quantum information processing and provide an update on the Innsbruck trapped-ion quantum computer [1]. Using strings of trapped ions, we realize a programmable quantum processor capable of performing universal operations. I will give an overview of the experimental quantum toolbox and discuss current strategies for scaling the system to larger sizes. The versatility of this platform is illustrated through both analog and digital quantum simulations. By exploiting the trapped-ion toolbox for entanglement-enhanced Ramsey interferometry, we identify optimal parameters for quantum metrology [2]. Employing universal quantum computation, we explore the dynamics of the Lattice Schwinger model [3] - a one-dimensional gauge theory of quantum electrodynamics - and, using a hybrid quantum-classical variational approach, we determine steady-state properties of the corresponding Hamiltonian [4]. Finally, with a trapped-ion qudit quantum processor, in which quantum information is encoded in multiple internal states, we simulate a two-dimensional lattice gauge theory [5}. [1] I. Pogorelov et al., PRX Quantum 2, 020343 (2021) [2] C. D. Marciniak et al., Nature 603, 604 (2022) [3] E. A. Martinez et al., Nature 534, 516 (2016) [4] C. Kokail et al., Nature 569, 355–360 (2019) [5] M. Meth et al., Nature Physics 21, 570 (2025)
The state-of-the-art of the Innsbruck trapped-ion quantum computer [1] is briefly reviewed. We present an overview on the available quantum toolbox and discuss the scalability of the approach. With up to 50 fully controlled ion qubits we perform quantum simulations investigating quantum transport [2] and emerging hydrodynamics features [3]. Employing the quantum toolbox for entanglement-enhanced Ramsey interferometry, we find optimal parameters for quantum metrology [4]. Quantum computers can be protected from noise by encoding the logical quantum information redundantly into multiple qubits using error-correcting codes. Manipulating logical quantum states by imperfect operations requires that all operations on the quantum register obey a fault-tolerant circuit design to avoid spreading uncontrolled errors. We demonstrate a fault-tolerant universal set of gates on two logical qubits in the trapped-ion quantum computer [5].
Universal digital quantum computers are able to approximate any Hamiltonian evolution as a digital quantum circuit consisting of discrete time steps. Strongly interacting physics models, for example in high-energy physics or materials science, make this a challenging task for near-term devices as they place a high demand on the quantum resources required [1]. One alternative is analog quantum simulation where the native evolution of a quantum system can be tailored to mimic that of the model of interest. While more efficient at specific problems, there are limits on the types of evolution available and on the observables that can be measured. In this conference paper we present first results towards unifying these two concepts in a trapped-ion experiment. Trapped atomic ions are one of the most advanced experimental platforms for both analog quantum simulation and digital quantum computing. Typically, the internal spin degrees of freedom are used qubits or for the simulation of spin models. The harmonic oscillator modes given by the motion of the ions in the trap are only employed transiently to create quantum gates or spin-spin interactions. However, these motional modes constitute a large Hilbert space themselves and present a bosonic degree of freedom, which is costly to model with qubits. Many systems of interest, for example Lattice gauge theories, require both spin and boson degrees of freedom. It was recently shown that they can be encoded more efficiently using the harmonic oscillator modes directly [2].
Direct experimental access to some of the most intriguing quantum phenomena is not granted due to the lack of precise control of the relevant parameters in their naturally intricate environment. Their simulation on conventional computers is impossible, since quantum behaviour arising with superposition states or entanglement is not efficiently translatable into the classical language. However, one could gain deeper insight into complex quantum dynamics by experimentally simulating the quantum behaviour of interest in another quantum system, where the relevant parameters and interactions can be controlled and robust effects detected sufficiently well. Systems of trapped ions provide unique control of both the internal (electronic) and external (motional) degrees of freedom. The mutual Coulomb interaction between the ions allows for large interaction strengths at comparatively large mutual ion distances enabling individual control and readout. Systems of trapped ions therefore exhibit a prominent system in several physical disciplines, for example, quantum information processing or metrology. Here, we will give an overview of different trapping techniques of ions as well as implementations for coherent manipulation of their quantum states and discuss the related theoretical basics. We then report on the experimental and theoretical progress in simulating quantum many-body physics with trapped ions and present current approaches for scaling up to more ions and more-dimensional systems.
<!--HTML-->Trapped ions are one of the leading and furthest developed technologies in quantum computing. However, despite higher quality operations than on any other platform and the absence of variations in qubit quality, the road to fault-tolerant quantum computing remains long and steep. In this talk, I will briefly review the state of the art of the trapped-ion platform, illustrate the current attempts to scaling up to larger numbers of qubits and highlight the challenges faced in control electronics and reliable manufacturing.
Abstract The past few years have witnessed the concrete and fast spreading of quantum technologies for practical computation and simulation. In particular, quantum computing platforms based on either trapped ions or superconducting qubits have become available for simulations and benchmarking, with up to few tens of qubits that can be reliably initialized, controlled, and measured. The present Review aims at giving a comprehensive outlook on the state‐of‐the‐art capabilities offered from these near‐term noisy devices as universal quantum simulators, that is, programmable quantum computers potentially able to calculate the time evolution of many physical models. First, a pedagogic overview on the basic theoretical background pertaining digital quantum simulations is given, with a focus on hardware‐dependent mapping of spin‐type Hamiltonians into the corresponding quantum circuit as a key initial step toward simulating more complex models. Then, the main experimental achievements obtained in the last decade are reviewed, focusing on the digital quantum simulation of such spin models by employing two leading quantum architectures. Their performances are compared, and future challenges are outlined, also in view of prospective hybrid technologies, towards the ultimate goal of reaching the long‐sought quantum advantage for the simulation of complex many‐body models in the physical sciences.
Trapped atomic ions are among the most advanced platforms for quantum simulation, computation, and metrology, offering long coherence times and precise, individual control over both internal and motional degrees of freedom. In this review, we present a pedagogical introduction to trapped-ion systems, covering the physics of ion trapping, qubit encodings, and laser-ion interactions. We explain how spin-dependent forces generated by light fields enable both analog and digital quantum simulations of spin and spin-boson models, as well as high-fidelity quantum logic gates. We then highlight an emerging frontier in the simulation of chemical dynamics, summarizing recent experiments that demonstrate the capability of trapped ions to simulate vibronic models and excitation-transfer processes. Finally, we outline future directions in quantum simulation and discuss open challenges in scaling up trapped-ion architectures.