Cryogenic setup for trapped ion quantum computing

Probabilistic Interpolation of Quantum Rotation Angles

Quantum computing requires a universal set of gate operations; regarding gates as rotations, any rotation angle must be possible. However a real device may only be capable of B bits of resolution, i.e., it might support only 2^{B} possible variants of a given physical gate. Naive discretization of an algorithm's gates to the nearest available options causes coherent errors, while decomposing an impermissible gate into several allowed operations increases circuit depth. Conversely, demanding higher B can greatly complexify hardware. Here, we explore an alternative: probabilistic angle interpolation (PAI). This effectively implements any desired, continuously parametrized rotation by randomly choosing one of three discretized gate settings and postprocessing individual circuit outputs. The approach is particularly relevant for near-term applications where one would in any case average over many runs of circuit executions to estimate expected values. While PAI increases that sampling cost, we prove that (a) the approach is optimal in the sense that PAI achieves the least possible overhead and (b) the overhead is remarkably modest even with thousands of parametrized gates and only seven bits of resolution available. This is a profound relaxation of engineering requirements for first generation quantum computers where even 5-6 bits of resolution may suffice and, as we demonstrate, the approach is many orders of magnitude more efficient than prior techniques. Moreover we conclude that, even for more mature late noisy intermediate-scale quantum era hardware, no more than nine bits will be necessary.

Experimental Realization of Nonunitary Multiqubit Operations

We demonstrate a novel experimental tool set that enables irreversible multiqubit operations on a quantum platform. To exemplify our approach, we realize two elementary nonunitary operations: the or and nor gates. The electronic states of two trapped ^{40}Ca^{+} ions encode the logical information, and a cotrapped ^{88}Sr^{+} ion provides the irreversibility of the gate by a dissipation channel through sideband cooling. We measure 87% and 81% success rates for the or and nor gates, respectively. The presented methods are a stepping stone toward other nonunitary operations such as in quantum error correction and quantum machine learning.

Native qudit entanglement in a trapped ion quantum processor

Quantum information carriers, just like most physical systems, naturally occupy high-dimensional Hilbert spaces. Instead of restricting them to a two-level subspace, these high-dimensional (qudit) quantum systems are emerging as a powerful resource for the next generation of quantum processors. Yet harnessing the potential of these systems requires efficient ways of generating the desired interaction between them. Here, we experimentally demonstrate an implementation of a native two-qudit entangling gate up to dimension 5 in a trapped-ion system. This is achieved by generalizing a recently proposed light-shift gate mechanism to generate genuine qudit entanglement in a single application of the gate. The gate seamlessly adapts to the local dimension of the system with a calibration overhead that is independent of the dimension.

Design and characterization of a cryogenic linear Paul ion trap for ion-neutral reaction studies

Ultra-high vacuum conditions are ideal for the study of trapped ions. They offer an almost perturbation-free environment, where ions confined in traps can be studied for extended periods of time-facilitating precision measurements and allowing infrequent events to be observed. However, if one wishes to study processes involving molecular ions, it is important to consider the effect of blackbody radiation (BBR). The vast majority of molecular ions interact with BBR. At 300 K, state selection in trapped molecular ions can be rapidly lost (in a matter of seconds). To address this issue, and to maintain state selectivity in trapped molecular ions, a cryogenic ion trap chamber has been constructed and characterized. At the center of the apparatus is a linear Paul ion trap, where Coulomb crystals can be formed for ion-neutral reaction studies. Optical access is provided, for lasers and for imaging of the crystals, alongside ion optics and a flight tube for recording time-of-flight mass spectra. The ion trap region, encased within two nested temperature stages, reaches temperatures below 9 K. To avoid vibrations from the cryocooler impeding laser cooling or imaging of the ions, vibration-damping elements are explicitly included. These components successfully inhibit the coupling of vibrations from the cold head to the ion trap-confirmed by accelerometer measurements and by the resolution of images recorded at the trap center (at 9 and 295 K). These results confirm that the cryogenic ion trap apparatus meets all requirements for studying ion-neutral reactions under cold, controlled conditions.

Coupling Two Laser-Cooled Ions via a Room-Temperature Conductor

We demonstrate coupling between the motions of two independently trapped ions with a separation distance of 620  μm. The ion-ion interaction is enhanced via a room-temperature electrically floating metallic wire which connects two surface traps. Tuning the motion of both ions into resonance, we show flow of energy with a coupling rate of 11 Hz. Quantum-coherent coupling is hindered by strong surface electric-field noise in our device. Our ion-wire-ion system demonstrates that room-temperature conductors can be used to mediate and tune interactions between independently trapped charges over distances beyond those achievable with free-space dipole-dipole coupling. This technology may be used to sympathetically cool or entangle remotely trapped charges and enable coupling between disparate physical systems.

Ultra-low-vibration closed-cycle cryogenic surface-electrode ion trap apparatus

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 ⁹Be⁺ ions has been demonstrated using a combination of laser ablation and photoionization.

An optically heated atomic source for compact ion trap vacuum systems

We present a design for an atomic oven suitable for loading ion traps, which is operated via optical heating with a continuous-wave multimode diode laser. The absence of the low-resistance electrical connections necessary for Joule heating allows the oven to be extremely well thermally isolated from the rest of the vacuum system. Extrapolating from high-flux measurements of an oven filled with calcium, we calculate that a target region number density of 100 cm^-3, suitable for rapid ion loading, will be produced with 175(10) mW of heating laser power, limited by radiative losses. With simple feedforward to the laser power, the turn-on time for the oven is 15 s. Our measurements indicate that an oven volume 1000 times smaller could still hold enough source metal for decades of continuous operation.

Quantum Walks of a Phonon in Trapped Ions

We report the observation of the quantum walks of a phonon, a vibrational quantum, in a trapped-ion crystal. By employing the capability to prepare and observe the localized wave packet of a phonon, the propagation of a single radial local phonon in a four-ion linear crystal is observed with single-site resolution. The results show an agreement with numerical calculations, indicating the predictability and reproducibility of the phonon system. These characteristics may contribute advantageously in the advanced studies of quantum walks, as well as boson sampling and quantum simulation.

A cryogenic radio-frequency ion trap for quantum logic spectroscopy of highly charged ions

A cryogenic radio-frequency ion trap system designed for quantum logic spectroscopy of highly charged ions (HCI) 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 ⁹Be⁺ 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 Ar¹³⁺ (Ar XIV) ions concurrently with single Be⁺ ions, a key prerequisite for the first quantum logic spectroscopy of a HCI. This major stepping stone allows us to push highly-charged-ion spectroscopic precision from the gigahertz to the hertz level and below.

Closed-cycle, low-vibration 4 K cryostat for ion traps and other applications

In vacuo cryogenic environments are ideal for applications requiring both low temperatures and extremely low particle densities. This enables reaching long storage and coherence times, for example, in ion traps, essential requirements for experiments with highly charged ions, quantum computation, and optical clocks. We have developed a novel cryostat continuously refrigerated with a pulse-tube cryocooler and providing the lowest vibration level reported for such a closed-cycle system with 1 W cooling power for a <5 K experiment. A decoupling system suppresses vibrations from the cryocooler by three orders of magnitude down to a level of 10 nm peak amplitudes in the horizontal plane. Heat loads of about 40 W (at 45 K) and 1 W (at 4 K) are transferred from an experimental chamber, mounted on an optical table, to the cryocooler through a vacuum-insulated massive 120 kg inertial copper pendulum. The 1.4 m long pendulum allows installation of the cryocooler in a separate, acoustically isolated machine room. At the experimental chamber, we measured the residual vibrations using an interferometric setup. The positioning of the 4 K elements is reproduced to better than a few micrometer after a full thermal cycle to room temperature. Extreme high vacuum on the 10^-15 mbar level is achieved. In collaboration with the Max-Planck-Institut für Kernphysik, such a setup is now in operation at the Physikalisch-Technische Bundesanstalt for a next-generation optical clock experiment using highly charged ions.

Magnetic field stabilization system for atomic physics experiments

Atomic physics experiments commonly use millitesla-scale magnetic fields to provide a quantization axis. As atomic transition frequencies depend on the magnitude of this field, many experiments require a stable absolute field. Most setups use electromagnets, which require a power supply stability not usually met by commercially available units. We demonstrate the stabilization of a field of 14.6 mT to 4.3 nT rms noise (0.29 ppm), compared to noise of >100 nT without any stabilization. The rms noise is measured using a field-dependent hyperfine transition in a single ⁴³Ca⁺ ion held in a Paul trap at the center of the magnetic field coils. For the ⁴³Ca⁺ "atomic clock" qubit transition at 14.6 mT, which depends on the field only in second order, this would yield a projected coherence time of many hours. Our system consists of a feedback loop and a feedforward circuit that control the current through the field coils and could easily be adapted to other field amplitudes, making it suitable for other applications such as neutral atom traps.

Measuring Anomalous Heating in a Planar Ion Trap with Variable Ion-Surface Separation

Cold ions trapped in the vicinity of conductive surfaces experience heating of their oscillatory motion. Typically, the rate of this heating is orders of magnitude larger than expected from electric field fluctuations due to thermal motion of electrons in the conductors. This effect, known as anomalous heating, is not fully understood. One of the open questions is the heating rate's dependence on the ion-electrode separation. We present a direct measurement of this dependence in an ion trap of simple planar geometry. The heating rates are determined by taking images of a single ^{172}Yb^{+} ion's resonance fluorescence after a variable heating time and deducing the trapped ion's temperature from measuring its average oscillation amplitude. Assuming a power law for the heating rate versus ion-surface separation dependence, an exponent of -3.79±0.12 is measured.