Quantum information platforms made great progress in the control of many-body entanglement and the implementation of quantum error correction, but it remains a challenge to realize both in the same setup. Here, we propose a mixture of two ultracold atomic species as a platform for universal quantum computation with long-range entangling gates, while providing a natural candidate for quantum error-correction. In this proposed setup, one atomic species realizes localized collective spins of tunable length, which form the fundamental unit of information. The second atomic species yields phononic excitations, which are used to entangle collective spins. Finally, we discuss a finite-dimensional version of the Gottesman–Kitaev–Preskill code to protect quantum information encoded in the collective spins, opening up the possibility to universal fault-tolerant quantum computation in ultracold atom systems.

量子信息平台在控制多体纠缠和实现量子纠错方面取得了很大进展，但在同一设置中实现两者仍然是一个挑战。在这里，我们提出了两种超冷原子物种的混合物，作为具有远程纠缠门的通用量子计算平台，同时为量子纠错提供了自然的候选者。在这个提议的设置中，一个原子种类实现了长度可调的局部集体自旋，形成了信息的基本单位。第二个原子种类产生声子激发，用于纠缠集体自旋。最后，我们讨论了 Gottesman-Kitaev-Preskill 代码的有限维版本，以保护集体自旋中编码的量子信息，