Incorporating protection against quantum errors into adiabatic quantum computing (AQC) is an important task due to the inevitable presence of decoherence. Here, we investigate an error-protected encoding of the AQC Hamiltonian, where qubit ensembles are used in place of qubits. Our Hamiltonian only involves total spin operators of the ensembles, offering a simpler route towards error-corrected quantum computing. Our scheme is particularly suited to neutral atomic gases where it is possible to realize large ensemble sizes and produce ensemble-ensemble entanglement. We identify a critical ensemble size N_c where the nature of the first excited state becomes a single particle perturbation of the ground state, and the gap energy is predictable by mean-field theory. For ensemble sizes larger than N_c, the ground state becomes protected due to the presence of logically equivalent states and the AQC performance improves with N, as long as the decoherence rate is sufficiently low.

由于不可避免地存在退相干，因此将对量子错误的保护纳入绝热量子计算（AQC）是一项重要的任务。在这里，我们研究了AQC哈密顿量的受错误保护的编码，其中使用了qubit集成来代替qubit。我们的哈密顿量仅涉及合奏的全部自旋算符，从而提供了一种更简单的方法来进行纠错的量子计算。我们的方案特别适用于中性原子气体，在其中可以实现大的合奏尺寸并产生合奏-合奏纠缠。我们确定了临界集合大小N _c，其中第一激发态的性质变为基态的单个粒子扰动，并且间隙能量可以通过平均场理论预测。对于大于N _c，只要退相干率足够低，由于存在逻辑上相等的状态，基态将受到保护，并且AQC性能会随着N的提高而提高。