论文标题
通过代数表达绝热仪的电势来控制和探索量子系统
Controlling and exploring quantum systems by algebraic expression of adiabatic gauge potential
论文作者
论文摘要
绝热规范的潜力是非绝热过渡的起源。在抵绝热的驾驶中，这是对绝热性的快捷方式的方法，可以使用绝热规格电位实现与绝热时间演化相同的动态，而无需慢速变化参数。我们引入了绝热规范电位的代数表达。然后，我们发现，绝热规格电位的明确形式可以通过一些代数计算很容易确定。我们通过使用单旋链系统，两旋链系统和横向iSing链来证明这种方法。此外，我们根据量子速度限制得出了对绝热时间演变的延误。这使我们能够知道近似绝热仪势的最坏情况。我们还可以使用这种约束，以在绝热规范的潜力中找到主要的术语来抑制非绝热过渡。我们将此结合应用于两旋链系统的磁化逆转和横向iSing链的量子退火。绝热规格的电势反映了能量本征状结构，因此我们还通过使用绝热仪势讨论了量子相变的检测。我们发现横向iSing链中量子相变的特征。
Adiabatic gauge potential is the origin of nonadiabatic transitions. In counterdiabatic driving, which is a method of shortcuts to adiabaticity, adiabatic gauge potential can be used to realize identical dynamics to adiabatic time evolution without requiring slow change of parameters. We introduce an algebraic expression of adiabatic gauge potential. Then, we find that the explicit form of adiabatic gauge potential can be easily determined by some algebraic calculations. We demonstrate this method by using a single-spin system, a two-spin system, and the transverse Ising chain. Moreover, we derive a lower bound for fidelity to adiabatic time evolution based on the quantum speed limit. This bound enables us to know the worst case performance of approximate adiabatic gauge potential. We can also use this bound to find dominant terms in adiabatic gauge potential to suppress nonadiabatic transitions. We apply this bound to magnetization reversal of the two-spin system and to quantum annealing of the transverse Ising chain. Adiabatic gauge potential reflects structure of energy eigenstates, and thus we also discuss detection of quantum phase transitions by using adiabatic gauge potential. We find a signature of a quantum phase transition in the transverse Ising chain.
