Vlad Negnevitsky

We present the design, fabrication, and characterization of a monolithic, segmented, three-dimensional linear Paul ion trap for quantum science applications. The trap is fabricated from a single fused-silica block using selective laser-induced etching (SLE) and is subsequently metallized, forming electrodes isolated by self-shadowing trench structures without the need for layer alignment or external shadow masks. The segmented electrodes allow for shaping of the axial potential, enabling the creation of anharmonic potential wells, such as those required for equidistant ion strings. In addition, they enable shuttling and splitting of ion chains. We discuss key design choices and SLE-imposed constraints on achievable feature sizes, and evaluate electron-beam evaporation and magnetron sputtering as metallization approaches. Across two independent experimental setups, we demonstrate stable trapping and control of linear chains of up to 33 $^{40}$Ca$^+$ ions, including approximately equally spaced configurations. The measured secular frequencies in both traps agree with boundary-element simulations at the percent level, with residual deviations attributed to stray electric fields in the presence of anharmonic axial potentials, rather than fabrication imperfections. We measure axial micromotion field strengths on the order of 100 V/m along the trap axis, in approximate agreement with simulations. For radial mode frequencies near 2 MHz and an ion-electrode distance of 300 um, we measure heating rates of the order of 10 quanta/s in all but one motional mode, which is elevated by a technical noise source. The presented trap design is thus suitable for a wide range of quantum science applications and demonstrates the viability of SLE for the fabrication of finely segmented, monolithic, three-dimensional ion traps.

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.

The stable operation of quantum computers will rely on error-correction, in which single quantum bits of information are stored redundantly in the Hilbert space of a larger system. Such encoded qubits are commonly based on arrays of many physical qubits, but can also be realized using a single higher-dimensional quantum system, such as a harmonic oscillator. A powerful encoding is formed from a periodically spaced superposition of position eigenstates. Various proposals have been made for realizing approximations to such states, but these have thus far remained out of reach. Here, we demonstrate such an encoded qubit using a superposition of displaced squeezed states of the harmonic motion of a single trapped Calcium ion, controlling and measuring the oscillator through coupling to an ancilliary internal-state qubit. We prepare and reconstruct logical states with an average square fidelity of $87.3 \pm 0.7 \%$, and demonstrate a universal logical single qubit gate set which we analyze using process tomography. For Pauli gates we reach process fidelities of $\approx 97\%$, while for continuous rotations we use gate teleportation achieving fidelities of $\approx 89 \%$. The control demonstrated opens a route for exploring continuous variable error-correction as well as hybrid quantum information schemes using both discrete and continuous variables. The code states also have direct applications in quantum sensing, allowing simultaneous measurement of small displacements in both position and momentum.

Quantum error correction will be essential for realizing the full potential of large-scale quantum information processing devices. Fundamental to its experimental realization is the repetitive detection of errors via projective measurements of quantum correlations among qubits, and correction using conditional feedback. Performing these tasks repeatedly requires a system in which measurement and feedback decision times are short compared to qubit coherence times, where the measurement reproduces faithfully the desired projection, and for which the measurement process has no detrimental effect on the ability to perform further operations. Here we demonstrate up to 50 sequential measurements of correlations between two beryllium-ion qubits using a calcium ion ancilla, and implement feedback which allows us to stabilize two-qubit subspaces as well as Bell states. Multi-qubit mixed-species gates are used to transfer information from qubits to the ancilla, enabling quantum state detection with negligible crosstalk to the stored qubits. Heating of the ion motion during detection is mitigated using sympathetic recooling. A key element of the experimental system is a powerful classical control system, which features flexible in-sequence processing to implement feedback control. The methods employed here provide a number of essential ingredients for scaling trapped-ion quantum computing, and provide new opportunities for quantum state control and entanglement-enhanced quantum metrology.

We present a versatile rf pulse control system that has been designed for multi-qubit quantum experiments. One instrument can be scaled to provide 32 channels of rf between 10 - 450 MHz. Synchronization can be achieved across multiple instruments. By using direct digital synthesis and custom control circuitry contained within a field-programmable gate array, sequences of transform-limited pulses can be produced. These have been used to carry out quantum gates that are able to meet fault-tolerant thresholds for single- and two-qubit gate fidelities, as published elsewhere. We have also extended the frequency to the gigahertz regime using additional mixers to address hyperfine transitions in atomic systems. The system uses an efficient memory management scheme and a low-latency communications protocol that allows pulse sequences to be updated in real-time. Together these can enable outcome-based algorithms such as quantum error correction to be executed. The system is fully programmable in C++, and other languages such as Python can be supported by the on-board CPU, offering a highly flexible platform for a wide variety of experimental systems, and has been proven in trapped-ion quantum information experiments.

We demonstrate single-qubit operations by transporting a beryllium ion with a controlled velocity through a stationary laser beam. We use these to perform coherent sequences of quantum operations, and to perform parallel quantum logic gates on two ions in different processing zones of a multiplexed ion trap chip using a single recycled laser beam. For the latter, we demonstrate individually addressed single-qubit gates by local control of the speed of each ion. The fidelities we observe are consistent with operations performed using standard methods involving static ions and pulsed laser fields. This work therefore provides a path to scalable ion trap quantum computing with reduced requirements on the optical control complexity.

Mesoscopic superpositions of distinguishable coherent states provide an analog to the Schrödinger's cat thought experiment. For mechanical oscillators these have primarily been realised using coherent wavepackets, for which the distinguishability arises due to the spatial separation of the superposed states. Here, we demonstrate superpositions composed of squeezed wavepackets, which we generate by applying an internal-state dependent force to a single trapped ion initialized in a squeezed vacuum state with 9 dB reduction in the quadrature variance. This allows us to characterise the initial squeezed wavepacket by monitoring the onset of spin-motion entanglement, and to verify the evolution of the number states of the oscillator as a function of the duration of the force. In both cases, we observe clear differences between displacements aligned with the squeezed and anti-squeezed axes. We observe coherent revivals when inverting the state-dependent force after separating the wavepackets by more than 19 times the ground-state root mean squared extent, which corresponds to 56 times the root mean squared extent of the squeezed wavepacket along the displacement direction. Aside from their fundamental nature, these states may be useful for quantum metrology or quantum information processing with continuous variables.