Quantum Engineering with Trapped Ions

Topological phases are governed by discrete symmetries that protect boundary modes against local perturbations. When translational periodicity is absent, the bulk states also become localized, so that a topological edge state can no longer be distinguished from them by spatial localization alone. Here, we investigate the topological edge state (TES) and bulk eigenstates of the anisotropic quantum Rabi model (AQRM) in a trapped-ion quantum simulator. The AQRM hosts a topological phase in a one-dimensional synthetic lattice, whose translational symmetry is broken by the non-uniform couplings scaling with the site index. While both the TES and bulk states show localized distributions, we find that the TES exhibits well-defined chirality and near-complete spin--boson separability as signatures of the topological phase, in contrast to the bulk states. Phase-space tomography further reveals that the bosonic component of the TES is a squeezed vacuum state, with squeezing up to 6.45 dB. These results identify the TES through its intrinsic topological signatures and establish eigenstate-level characterization as a route to probing topological phenomena.

Trapped-ion quantum networks rely on efficient ion-photon interfaces, while objective-based free-space collection systems must balance high photon collection with sufficient working distance for practical integration with ion-trap hardware. Here, we design and characterize an ion-photon interface with a long working distance of 26.15 mm and a high numerical aperture of 0.5. The core of the interface is a photon-collection objective consisting of six commercial spherical lenses with optimized spacing. The interface achieved an overall fiber-coupled photon-detection efficiency of (1.29$\pm$0.09)% from the ion to the detector and maintains fiber coupling over several hours without active realignment, supporting stable operation of the ion-to-fiber interface. Photon-correlation measurements show clear antibunching in the fiber-coupled fluorescence, confirming the preservation of non-classical photon statistics. These results demonstrate a practical implementation of a long-working-distance photon collection interface for trapped-ion quantum network experiments.

Multi-controlled gates are essential primitives in quantum algorithms, yet implementing them via standard gate-level decompositions remains resource-intensive. We develop efficient pulse-level implementations of multi-controlled gates in trapped-ion systems using the Cirac-Zoller scheme. We first show that the Cirac-Zoller construction admits a freedom in the sign choice of red-sideband (RSB) pulses, which leaves the logical operation invariant up to a local Pauli-$Z$ correction. By exploiting this freedom, we construct equivalent realizations of multi-controlled gates and develop pulse cancellation for more efficient implementations of successive gates. We perform numerical simulations and show that pulse cancellation reduces the gate time and improves the state fidelity. Furthermore, we propose ancilla-free circuits for general $N$-controlled gates that use a single-controlled gate primitive and $\mathcal{O}(N)$ RSB pulses. As a key application, we apply our pulse cancellation to the linear combination of unitaries (LCU) method for block encoding. We show that the RSB-pulse cost of the select operator over $L$ unitaries can be reduced from $\mathcal{O}(L\log L)$ to $\mathcal{O}(L)$, which improves the efficiency and scalability of LCU-based quantum circuits.

We present a compact design for a beam-steering system based on acousto-optic-deflectors (AODs) used as an individual addressing system for trapped-ion quantum computing. The design targets to minimize the optomechanical degrees of freedom and the optical beam paths to improve optical stability, and we successfully implemented a solution with a compact footprint of less than 1 square foot. The system characterization results show that we achieve clean Gaussian beams at 355nm wavelength with a beam steering range of $\sim$50 times the beam diameter, and an intensity crosstalk of $< 9 \times 10^{-4}$ at all neighboring ions in a five-ion chain. Based on these capabilities, we experimentally demonstrate individual addressing of a 30-ion chain. We estimate the beam switching time of the AOD to be $\sim$240 ns. The compact system design is expected to provide high optical stability, providing the potential for high-fidelity trapped-ion quantum computing with long ion chains.

We propose Shuttling-based Distributed Quantum Computing (SDQC), a hybrid architecture that combines the strengths of physical qubit shuttling and distributed quantum computing to enable scalable trapped-ion quantum computing. SDQC performs non-local quantum operations by distributing entangled ion qubits via deterministic shuttling, combining the high-fidelity and deterministic operations of shuttling-based architectures with the parallelism and pipelining advantages of distributed quantum computing. We present (1) a practical architecture incorporating quantum error correction (QEC), (2) pipelining strategies to exploit parallelism in entanglement distribution and measurement, and (3) a performance evaluation in terms of logical error rate and clock speed. For a 256-bit elliptic-curve discrete logarithm problem (ECDLP) instance, which requires 2,871 logical qubits at code distance 13, SDQC achieves a logical error rate which is $1.20^{+0.94}_{-0.45}\times10^{-8}$ of Photonic DQC error rate and $3.79^{+5.09}_{-2.84}\times10^{-3}$ of Quantum Charge-Coupled Device (QCCD) error rate, while providing 2.82 times faster logical clock speed than QCCD.

Vibrational modes of trapped ions have traditionally served as quantum buses to mediate internal qubits. However, with recent advances in quantum control, it has become possible to use these vibrational modes directly as quantum computational resources, such as bosonic qubits. Here, we propose a dual-rail encoding scheme in which a dual-rail qubit is encoded by two vibrational modes that share a single phonon. We present the preparation, measurement, and implementation of single- and two-qubit gates, enabling universal quantum computation. The dual-rail qubit system offers scalability and all-to-all connectivity. Moreover, we extend the dual-rail qubit system to a logical internal qubit--dual-rail qubit hybrid system by incorporating internal qubits into the dual-rail qubit system as another type of logical qubit. The hybrid system nearly doubles the number of available logical qubits compared to conventional trapped-ion quantum computers while maintaining all-to-all connectivity. Additionally, we propose a method for implementing multi-qubit controlled gates and discuss potential applications that can leverage the advantages of the hybrid system. Our scheme provides a practical framework for an internal qubit-boson qubit hybrid system.

We report the direct measurement of isotope shifts of the barium 6s$^2$ $^1$S$_0$ --5d6p $^3$D$^\text{o}_1$ 413-nm electric quadrupole transition, which is utilized for efficient barium ion trapping via photoionization using a single coherent light source. The measured isotope shifts relative to $^{138}$Ba are $392.9\pm0.9$ MHz, $178.1\pm0.8$ MHz, $401.4\pm1.2$ MHz, and $124.3\pm1.3$ MHz for isotopes with atomic numbers 137, 136, 135, and 134, respectively. We verify the measured isotopes with King plot analysis and compare the result with the formerly known shifts inferred from previous studies on neighboring transitions. The results can be used for efficient isotope selective loading of low-abundant barium ions, while careful suppression of line broadening is required for successful isotopic selectivity.

Molecules are the most demanding quantum systems to be simulated by quantum computers because of their complexity and the emergent role of quantum nature. The recent theoretical proposal of Huh et al. (Nature Photon., 9, 615 (2015)) showed that a multi-photon network with a Gaussian input state can simulate a molecular spectroscopic process. Here, we report the first experimental demonstration of molecular vibrational spectroscopy of SO$_{2}$ with a trapped-ion system. In our realization, the molecular scattering operation is decomposed to a series of elementary quantum optical operations, which are implemented through Raman laser beams, resulting in a multimode Gaussian (Bogoliubov) transformation. The molecular spectroscopic signal is reconstructed from the collective projection measurements on phonon modes of the trapped-ion system. Our experimental demonstration would pave the way to large-scale molecular quantum simulations, which are classically intractable.