Christian Ospelkaus

We develop a theoretical and numerical framework to analyze the effect of transport on the motional states of ions in a trapped-ion quantum processor. We decompose the shuttling protocol into primitive operations and characterize these in terms of their heating performance. Instead of having to simulate the whole transport protocol for each complete ion trajectory, the method allows us to determine the heating properties of each primitive operation separately and obtain the global result through an algebraic expression. We demonstrate our method by applying it to an 8-qubit quantum processor design based on linear transport and swap operations for all-to-all connectivity. We show how to incorporate the price of motional operations at the level of the compiler as a cost function.

Microfabricated surface-electrode traps are a scalable platform for trapped-ion quantum processors. Recent advances in fabrication techniques have enabled the design of increasingly complex multi-layer structures. Yet the control electrodes remain mostly unchanged and of rectangular shape. We systematically analyze asymmetric inner control electrode shapes for simultaneous axial and radial control in multi-layer surface traps, characterize and compare a selection of different shapes, and verify their capabilities in realistic use-case scenarios for ion transport and micromotion compensation. Eliminating the need for the commonly used additional outer control electrodes, asymmetric inner control electrodes increase the compactness and space efficiency of surface-electrode traps while concurrently reducing the number of control signals. The improved control voltage efficiency of using solely inner electrodes enables the device's entire direct-current (DC) supply to be provided by integrated Cryo-CMOS circuits, further enhancing the scalability of the processor.

Manipulating individual trapped ions at the single quantum level has become standard practice in radio-frequency ion traps, enabling applications from quantum information processing to precision metrology. The key ingredient is ground-state cooling of the particle's motion through resolved-sideband laser cooling. Ultra-high-presicion experiments using Penning ion traps will greatly benefit from the reduction of systematic errors offered by full motional control, with applications to atomic masses and $g$-factor measurements, determinations of fundamental constants or related tests of fundamental physics. In addition, it will allow to implement quantum logic spectroscopy, a technique that has enabled a new class of precision measurements in radio-frequency ion traps. Here we demonstrate resolved-sideband laser cooling of the axial motion of a single $^9$Be$^+$ ion in a cryogenic 5 Tesla Penning trap system using a two-photon stimulated-Raman process, reaching a mean phonon number of $\bar{n}_z = 0.10(4)$. This is a fundamental step in the implementation of quantum logic spectroscopy for matter-antimatter comparison tests in the baryonic sector of the Standard Model and a key step towards improved precision experiments in Penning traps operating at the quantum limit.

Trapped ions in radio-frequency traps are among the leading approaches for realizing quantum computers, due to high-fidelity quantum gates and long coherence times. However, the use of radio-frequencies presents a number of challenges to scaling, including requiring compatibility of chips with high voltages, managing power dissipation and restricting transport and placement of ions. By replacing the radio-frequency field with a 3 T magnetic field, we here realize a micro-fabricated Penning ion trap which removes these restrictions. We demonstrate full quantum control of an ion in this setting, as well as the ability to transport the ion arbitrarily in the trapping plane above the chip. This unique feature of the Penning micro-trap approach opens up a modification of the Quantum CCD architecture with improved connectivity and flexibility, facilitating the realization of large-scale trapped-ion quantum computing, quantum simulation and quantum sensing.

In recent years, the number of hybrid algorithms that combine quantum and classical computations has been continuously increasing. These two approaches to computing can mutually enhance each others' performances thus bringing the promise of more advanced algorithms that can outmatch their pure counterparts. In order to accommodate this new class of codes, a proper environment has to be created, which enables the interplay between the quantum and classical hardware. For many of these hybrid processes the coherence time of the quantum computer arises as a natural time constraint, making it crucial to minimize the classical overhead. For ion-trap quantum computers however, this is a much less limiting factor than with superconducting technologies, since the relevant timescale is on the order of seconds instead of microseconds. In fact, this long coherence time enables us to develop a scheme for real-time control of quantum computations in an interpreted programming language like Python. In particular, compilation of all instructions in advance is not necessary, unlike with superconducting qubits. This keeps the implementation of hybrid algorithms simple and also lets users benefit from the rich environment of existing Python libraries. In order to show that this approach of interpreted quantum-classsical computations (IQCC) is feasible, we bring real-world examples and evaluate them in realistic benchmarks.

A promising architecture for scaling up quantum computers based on trapped ions are so called Quantum Charged-Coupled Devices (QCCD). These consist of multiple ion traps, each designed for solving specific tasks, that are connected by transport links. In this paper we present the backend compiler phases needed for running quantum circuits on a QCCD architecture, while providing strategies to solve the optimization problems that occur when generating assembly instructions. We implement and test these strategies for the QVLS-Q1 chip architecture.

Two-ion crystals constitute a platform for investigations of quantum nature that can be extended to any ion species or charged particle provided one of the ions in the crystal can be directly laser-cooled and manipulated with laser radiation. This paper presents the formation of two-ion crystals for quantum metrology in a 7-tesla open-ring Penning trap. $^{40}$Ca$^+$ ions are produced either internally by photoionization or externally in a (Paul-trap) source, transported through the strong magnetic field gradient of the superconducting solenoid, and captured in-flight with a mean kinetic energy of a few electronvolts with respect to the minimum of the Penning-trap potential well. Laser cooling of the two-ion crystal in a strong magnetic field towards reaching the quantum regime is also presented with particular emphasis on the cooling of the radial modes.

We demonstrate phase locking of two ultraviolet laser sources by modulating a fundamental infrared laser with 4th-order sidebands using an electro-optic modulator and phase locking of one sideband to a second fundamental infrared laser. Subsequent sum frequency generation and second harmonic generation successfully translates the frequency offset to the ultraviolet domain. The phase lock at 139 GHz is confirmed through stimulated Raman transitions for thermometry of $^9$Be$^+$ ions confined in a cryogenic Penning trap. This technique might be used for sideband cooling of single $^9$Be$^+$ ions as well as sympathetic cooling schemes and quantum logic based measurements in Penning traps in the future.

Cosmological observations as well as theoretical approaches to physics beyond the Standard Model provide strong motivations for experimental tests of fundamental symmetries, such as CPT invariance. In this context, the availability of cold baryonic antimatter at CERN has opened an avenue for ultrahigh-precision comparisons of protons and antiprotons in Penning traps. This work discusses an experimental method inspired by quantum logic techniques that will improve particle localization and readout speed in such experiments. The method allows for sympathetic cooling of the (anti-)proton to its quantum-mechanical ground state as well as the readout of its spin alignment, replacing the commonly used continuous Stern-Gerlach effect. Both of these features are achieved through coupling to a laser-cooled `logic' ion co-trapped in a double-well potential. This technique will boost the measurement sampling rate and will thus provide results with lower statistical uncertainty, contributing to stringent searches for time dependent variations in the data. Such measurements ultimately yield extremely high sensitivities to CPT violating coefficients acting on baryons in the Standard-Model Extension, will allow the exploration of previously unmeasured types of symmetry violations, and will enable antimatter-based axion-like dark matter searches with improved mass resolution.

We describe the design, commissioning and operation of an ultra-low-vibration closed-cycle cryogenic ion trap apparatus. One hundred lines for low-frequency signals and eight microwave / radio frequency coaxial feed lines offer the possibility of implementing a small-scale ion-trap quantum processor or simulator. With all supply cables attached, more than 1.3 W of cooling power at 5 K is still available for absorbing energy from electrical pulses introduced to control ions. The trap itself is isolated from vibrations induced by the cold head using a helium exchange gas interface. The performance of the vibration isolation system has been characterized using a Michelson interferometer, finding residual vibration amplitudes on the order of 10 nm rms. Trapping of $^9$Be$^+$ ions has been demonstrated using a combination of laser ablation and photoionization.

Cooling and detection schemes using laser cooling and methods of quantum logic can contribute to high precision CPT symmetry tests in the baryonic sector. This work introduces an experiment to sympathetically cool protons and antiprotons using the Coulomb interaction with a $^9$Be$^+$ ion trapped in a nearby but separate potential well. We have designed and set up an apparatus to show such coupling between two identical ions for the first time in a Penning trap. In this paper, we present evidence for successful loading and Doppler cooling of clouds and single ions. Our coupling scheme has applications in a range of high-precision measurements in Penning traps and has the potential to substantially improve motional control in these experiments.

We demonstrate the experimental realization of a two-qubit Mølmer-Sørensen gate on a magnetic field-insensitive hyperfine transition in $^9$Be$^+$ ions using microwave-near fields emitted by a single microwave conductor embedded in a surface-electrode ion trap. The design of the conductor was optimized to produce a high oscillating magnetic field gradient at the ion position. The measured gate fidelity is determined to be $98.2\pm1.2\,\%$ and is limited by technical imperfections, as is confirmed by a comprehensive numerical error analysis. The conductor design can potentially simplify the implementation of multi-qubit gates and represents a self-contained, scalable module for entangling gates within the quantum CCD architecture for an ion-trap quantum computer.

A cryogenic radio-frequency ion trap system designed for quantum logic spectroscopy of highly charged ions is presented. It includes a segmented linear Paul trap, an in-vacuum imaging lens and a helical resonator. We demonstrate ground state cooling of all three modes of motion of a single $^9$Be$^+$ ion and determine their heating rates as well as excess axial micromotion. The trap shows one of the lowest levels of electric field noise published to date. We investigate the magnetic-field noise suppression in cryogenic shields made from segmented copper, the resulting magnetic field stability at the ion position and the resulting coherence time. Using this trap in conjunction with an electron beam ion trap and a deceleration beamline, we have been able to trap single highly charged Ar$^{13+}$ (Ar XIV) ions concurrently with single Be$^+$ ions, a key prerequisite for the first quantum logic spectroscopy of a highly charged ion.

Simulating computationally intractable many-body problems on a quantum simulator holds great potential to deliver insights into physical, chemical, and biological systems. While the implementation of Hamiltonian dynamics within a quantum simulator has already been demonstrated in many experiments, the problem of initialization of quantum simulators to a suitable quantum state has hitherto remained mostly unsolved. Here, we show that already a single dissipatively driven auxiliary particle can efficiently prepare the quantum simulator in a low-energy state of largely arbitrary Hamiltonians. We demonstrate the scalability of our approach and show that it is robust against unwanted sources of decoherence. While our initialization protocol is largely independent of the physical realization of the simulation device, we provide an implementation example for a trapped ion quantum simulator.

We present a multilayer surface-electrode ion trap with embedded 3D microwave circuitry for implementing entangling quantum logic gates. We discuss the electromagnetic full-wave simulation procedure that has led to the trap design and the characterization of the resulting microwave field-pattern using a single ion as a local field probe. The results agree with simulations within the uncertainty; compared to previous traps, this design reduces detrimental AC Zeeman shifts by three orders of magnitude. The design presented here can be viewed as an entangling gate component in a library for surface-electrode ion traps intended for quantum logic operations.

We present a novel ion trap fabrication method enabling the realization of multilayer ion traps scalable to an in principle arbitrary number of metal-dielectric levels. We benchmark our method by fabricating a multilayer ion trap with integrated three-dimensional microwave circuitry. We demonstrate ion trapping and microwave control of the hyperfine states of a laser cooled $\,^{9}$Be$^{+}$ ion held at a distance of 35$\,μ$m above the trap surface. This method can be used to implement large-scale ion trap arrays for scalable quantum information processing and quantum simulation.

We present a solid-state laser system that generates 750 mW of continuous-wave single-frequency output at 313 nm. Sum-frequency generation with fiber lasers at 1550 nm and 1051 nm produces up to 2 W at 626 nm. This visible light is then converted to UV by cavity-enhanced second-harmonic generation. The laser output can be tuned over a 495 GHz range, which includes the 9Be+ laser cooling and repumping transitions. This is the first report of a narrow-linewidth laser system with sufficient power to perform fault-tolerant quantum-gate operations with trapped 9Be+ ions by use of stimulated Raman transitions.