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We explore how diffusion models factorize and compose concepts.

High-fidelity operation of quantum computers requires precise knowledge of the physical system through characterization. For motion-mediated entanglement generation in trapped ions, it is crucial to have precise knowledge of the motional-mode parameters such as the mode frequencies and the Lamb-Dicke parameters.

Diffusion models are capable of impressive feats of image generation with uncommon juxtapositions such as astronauts riding horses on the moon with properly placed shadows. These outputs indicate the ability to perform compositional generalization, but how do the models do so?

Progress in fault-tolerant quantum computation (FTQC) has driven the pursuit of practical applications with early fault-tolerant quantum computers (EFTQC). These devices, limited in their qubit counts and fault-tolerance capabilities, require algorithms that can accommodate some degrees of error, which are known as EFTQC algorithms.

To achieve high-fidelity operations on a large-scale quantum computer, the parameters of the physical system must be efficiently characterized with high accuracy.

Two-qubit gates in trapped-ion quantum computers are generated by applying spin-dependent forces that temporarily entangle the internal state of the ion with its motion.Laser pulses are carefully designed to generate a maximally entangling gate between the ions while minimizing any residual entanglement between the motion and the ion.

In a large scale trapped atomic ion quantum computer, high-fidelity two-qubit gates need to be extended over all qubits with individual control. We realize and characterize high-fidelity two-qubit gates in a system with up to four ions using radial modes.