Trapped Ion Quantum Computing

High-fidelity two-qubit entangling gates are essential for the realization of useful quantum algorithms on quantum processors. The Mølmer-Sørensen (MS) gate has become a common choice for trapped-ion quantum computing due to its resilience to ion temperature and its demonstrated record fidelities. However, the spectral impurity of the driving laser field impacts gate performance, with phase noise influencing the qubit dynamics through mechanisms operating on different timescales. In this work, we present a comprehensive theoretical analysis of laser phase noise in the MS gate, identifying two spectral ranges which influence the gate fidelity the most: "fast" noise at frequencies near the motional mode spectrum, and "slow" noise at frequencies on the order of the inverse gate time. We derive the noise Hamiltonians for two common laser beam geometries and obtain analytical expressions for the average gate error in terms of the laser noise power spectral density and gate parameters. For slowly varying noise spectra, we provide simplified error estimates. In addition, we validate our findings against previously published numerical simulations.

Sympathetic cooling of data qubits by coolant ions is an essential technique for trapped-ion quantum computing. Conventionally a second ion species is used, requiring additional lasers and complicating optical setups. We propose a scheme for sympathetic cooling using the same species and test it for $^{43}$Ca$^+$ ions. Pulsed sideband cooling and ion addressing are implemented via integrated microwave control, further simplifying optical requirements. We cool a two-ion gate mode close to its ground state ($\bar{n}\approx 0.16$) and benchmark an induced error on the data qubit of $1.7(4)\times 10^{-4}$ per cooling cycle.

Modularity underpins classical computing; as quantum processors encounter limits on fabrication yield, reliability, and size, they will also need it acutely. The bottleneck to linking modules is producing shared entanglement at sufficient rate, density, and fidelity. Trapped ions hold the best demonstrated photonic links, yet they rely on bulky collection optics that cap how densely links can be packed, and remote entanglement operations trail local gates by two orders of magnitude in rate and fidelity. We synthesize several enabling results $\unicode{x2014}$ single-photon heralding, coherent recoil correction, projective distillation, and trap-integrated photonics $\unicode{x2014}$ into one comprehensive architecture that substantially narrows this gap. Single-photon heralding leads to linear scaling of success probability with detection efficiency, allowing compact integrated photonics to saturate the entanglement rate at a local-operation limit in dense, easy-to-parallelize channels. Addressing its inherent error mechanisms at their source, we project a Bell-pair fidelity of 99.9% at rates and densities compatible with fault-tolerant operations. Remote entanglement then need not remain the bottleneck for modular trapped-ion computing; the limit shifts to the local operations that must improve regardless.

Towards the scalable realization of a quantum computer, a quantum charge-coupled device (QCCD) based on ion shuttling has been considered a promising approach. However, the processes of detaching an ion from an array, reintegrating it, and driving non-uniform motion introduce severe heating, requiring significant time and laser power for re-cooling and stabilization. To mitigate these challenges, we propose a novel entangling scheme between a stationary ion qubit and a continuously transported mobile ion, which remains in uniform motion and minimizes motional heating. We theoretically demonstrate a gate error on the order of 0.01%, within reach of current technology. This approach enables resource-efficient quantum operations and facilitates long-distance entanglement distribution, where stationary trapped-ion arrays serve as memory units and mobile ions act as communication qubits passing beside them. Our results pave the way for an alternative trapped-ion architecture beyond the QCCD paradigm.

We present a theoretical model for realizing squeezed lasing in a trapped-ion system without relying on engineered baths or tailored dissipative reservoirs. Our approach leverages the intrinsic ion-phonon interactions, where two trapped ions, each interacting with a shared vibrational mode, are driven on both red- and blue-sideband transitions. This enables the creation of a squeezed state of motion through the dynamic coupling between the ions' internal states and the phonon mode. Unlike traditional methods that require bath engineering, our model demonstrates that squeezed lasing can be achieved through a direct manipulation of ion-phonon interactions, with no external reservoirs required. We explore the steady-state behavior of the system, analyzing the onset of lasing, gain-loss balance, and the role of the squeezing parameter in shaping the phonon field's statistical properties. Furthermore, we show how external coherent drives can stabilize phase coherence and achieve controlled quadrature squeezing, offering a simple yet effective method for achieving squeezed lasing in quantum mechanical systems. Our findings provide new insights into the realization of squeezed states in phonon-based systems, with potential applications in quantum metrology and information processing.

Electric-field-induced ion heating is a major obstacle in scalable trapped-ion quantum computing. We present a theoretical study of a novel 3D-printed ion trap with a skeleton electrode structure, designed to reduce heating by minimizing surface area near the ion. Compared to a conventional blade trap with identical confinement parameters, the skeleton trap achieves over 50% reduction in total heating rate. Patch-by-patch analysis reveals that heating is dominated by surfaces within 500 μm of the ion. For axial motion, the peak heating occurs approximately 110 μm away due to electric field directionality. We demonstrate that minor geometric optimization, in which the electrode gaps are realigned with these hotspots, can further suppress heating despite the associated increase in surface area. A linear relationship between ion-to-electrode distance and peak heating location is also established. These results highlight the potential of 3D-printed electrode designs for achieving both strong confinement and reduced noise in future quantum systems.