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Quantum signal processing (QSP) has emerged as a promising framework to manipulate and determine properties of quantum systems. QSP not only unifies most existing quantum algorithms but also provides tools to discover new ones. Quantum signal processing is applicable to single-qubit or multiqubit systems that can be “qubitized” so one can exploit the SU(2) structure of system evolution within special invariant two-dimensional subspaces. In the context of quantum algorithms, this SU(2) structure is artificially imposed on the system through highly nonlocal evolution operators that are difficult to implement on near-term quantum devices. In this work, we propose QSP protocols for the infinite-dimensional Onsager Lie algebra, which is relevant to the physical dynamics of quantum devices that can simulate the transverse-field Ising model. To this end, we consider QSP sequences in the Heisenberg picture, allowing us to exploit the emergent SU(2) structure in momentum space and “synthesize” QSP sequences for the Onsager algebra. Our results demonstrate a concrete connection between QSP techniques and noisy intermediate scale quantum protocols. We provide examples and applications of our approach in diverse fields ranging from space-time dual quantum circuits and quantum simulation to quantum control. 

Trapped-ion quantum information processing may benefit from qubits encoded in isotopes that are practically available in only small quantities, e.g., due to low natural abundance or radioactivity. Laser ablation provides a method of controllably liberating neutral atoms or ions from low-volume targets, but energetic ablation products can be difficult to confine in the small ion-electrode distance, micron-scale microfabricated traps amenable to high-speed, high-fidelity manipulation of ion arrays. Here, we investigate ablation-based ion loading into surface-electrode traps of different sizes to test a model describing ion loading probability as a function of effective trap volume and other trap parameters. We characterize loading of ablated barium from a metallic source in two cryogenic surface-electrode traps with 730 and 50 μm ion-electrode distances. Our loading rate agrees with a predictive analytical model, providing insight for the confinement of limited-quantity species of interest for quantum computing, simulation, and sensing.