Kirill Lakhmanskiy

In trapped-ion chains, multipartite GHZ states can be prepared natively with the help of a single bichromatic laser pulse. However, higher-order terms in the expansion in the Lamb-Dicke parameter $η$ limit the GHZ state preparation infidelity for rectangular and bell-like pulses to the order of $η^4$. For tens of ions, the infidelity caused by out-of-Lamb-Dicke effects can reach several percents. We propose an amplitude and phase-modulated pulse shape, an "echoed lemniscate pulse", which cancels this contribution into error in the leading order. For the proposed pulse, the infidelity scales as $η^6$. The improved scaling is achieved because of a special phase trajectory of a collective motional mode following the figure-eight curve (lemniscate). We demonstrate that the lemniscate pulse allows achieving lower infidelity than bell-like pulses, which can be as low as $10^{-4}$ for $20$-ion chains.

Carrier transition is one of the major factors hindering the high-speed implementation of the Mølmer-Sørensen gates in trapped-ion quantum processors. We present an approach to design laser pulse shapes for the Mølmer-Sørensen gate in ion chains which accounts for the effect of carrier transition on qubit-phonon dynamics. We show that the fast-oscillating carrier term effectively modifies the spin-dependent forces acting on ions, and this can be compensated by a simple nonlinear transformation of a laser pulse. Using numerical simulations for short ion chains and perturbation theory for longer chains up to $20$ ions, we demonstrate that our approach allows to reach the infidelity below $10^{-4}$ while keeping the gate duration of the order of tens of microseconds.

We propose a new method of individual single-qubit addressing of linear trapped-ion chains utilizing two ultrastable femtosecond frequency combs. For that, we suggest implementing the single-qubit gates with two counter-propagating frequency combs overlapping on the target ion and causing the AC Stark shift between the qubit levels. With analytical calculations and numerical modeling, we show that the arbitrary single-qubit rotations can be indeed realized using only laser fields propagating along the ion chain. We analyze the error sources for the proposed addressing method and prove that it allows implementing the single-qubit gates with high fidelity.

We describe the design and operation of a surface-electrode Paul trap for parallel entangling gate implementation. In particular, we demonstrate the possibility of separating or coupling ion motion by adjusting the DC-voltages on a set of electrodes and show the possibility of parallel MS-gate operations for specific voltage configurations. We verify the scalability of this approach and characterize the performance of these gates in the presence of the finite phonon mode occupation and of the finite drift of the phonon frequencies. Additionally, we investigate how the number of ions per individual trapping site and anharmonic potential terms affect the coupling between the wells.

Scaling up trapped-ion quantum computers requires new trap materials to be explored. Here, we present experiments with a surface ion trap made from the high-temperature superconductor YBCO, a promising material for future trap designs. We show that voltage noise from superconducting electrode leads is negligible within the sensitivity $S_V=9\times 10^{-20}\,\mathrm{V}^2\mathrm{Hz}^{-1}$ of our setup, and for lead dimensions typical for advanced trap designs. Furthermore, we investigate the frequency and temperature dependence of electric field noise above a YBCO surface. We find a $1/f$ spectral dependence of the noise and a non-trivial temperature dependence, with a plateau in the noise stretching over roughly $60\,\mathrm{K}$. The onset of the plateau coincides with the superconducting transition, indicating a connection between the dominant noise and the YBCO trap material. We exclude the YBCO bulk as origin of the noise and suggest further experiments to decide between the two remaining options explaining the observed temperature dependence: noise screening within the superconducting phase, or surface noise activated by the YBCO bulk through some unknown mechanism.

Quantum information processing is steadily progressing from a purely academic discipline towards applications throughout science and industry. Transitioning from lab-based, proof-of-concept experiments to robust, integrated realizations of quantum information processing hardware is an important step in this process. However, the nature of traditional laboratory setups does not offer itself readily to scaling up system sizes or allow for applications outside of laboratory-grade environments. This transition requires overcoming challenges in engineering and integration without sacrificing the state-of-the-art performance of laboratory implementations. Here, we present a 19-inch rack quantum computing demonstrator based on $^{40}\textrm{Ca}^+$ optical qubits in a linear Paul trap to address many of these challenges. We outline the mechanical, optical, and electrical subsystems. Further, we describe the automation and remote access components of the quantum computing stack. We conclude by describing characterization measurements relevant to digital quantum computing including entangling operations mediated by the Molmer-Sorenson interaction. Using this setup we produce maximally-entangled Greenberger-Horne-Zeilinger states with up to 24 ions without the use of post-selection or error mitigation techniques; on par with well-established conventional laboratory setups.

We present the design and construction of a new experimental apparatus for the trapping of single Ba$^+$ ions in the center of curvature of an optical-quality hemispherical mirror. We describe the layout, fabrication and integration of the full setup, consisting of a high-optical access monolithic `3D-printed' Paul trap, the hemispherical mirror, a diffraction-limited in-vacuum lens (NA = 0.7) for collection of atomic fluorescence and a state-of-the art ultra-high vacuum vessel. This new apparatus enables the study of quantum electrodynamics effects such as strong inhibition and enhancement of spontaneous emission, and achieves a collection efficiency of the emitted light in a single optical mode of 31%.

We present an ion-lattice quantum processor based on a two-dimensional arrangement of linear surface traps. Our design features a tunable coupling between ions in adjacent lattice sites and a configurable ion-lattice connectivity, allowing one, e.g., to realize rectangular and triangular lattices with the same trap chip. We present detailed trap simulations of a simplest-instance ion array with $2\times9$ trapping sites and report on the fabrication of a prototype device in an industrial facility. The design and the employed fabrication processes are scalable to larger array sizes. We demonstrate trapping of ions in rectangular and triangular lattices and demonstrate transport of a $2\times2$ ion-lattice over one lattice period.

Trapped ions are pre-eminent candidates for building quantum information processors and quantum simulators. They have been used to demonstrate quantum gates and algorithms, quantum error correction, and basic quantum simulations. However, to realise the full potential of such systems and make scalable trapped-ion quantum computing a reality, there exist a number of practical problems which must be solved. These include tackling the observed high ion-heating rates and creating scalable trap structures which can be simply and reliably produced. Here, we report on cryogenically operated silicon ion traps which can be rapidly and easily fabricated using standard semiconductor technologies. Single $^{40}$Ca$^+$ ions have been trapped and used to characterize the trap operation. Long ion lifetimes were observed with the traps exhibiting heating rates as low as $\dot{\bar{n}}=$ 0.33 phonons/s at an ion-electrode distance of 230 $μ$m. These results open many new avenues to arrays of micro-fabricated ion traps.