论文标题
重新审视量子绝热定理
Quantum Adiabatic Theorem Revisited
论文作者
论文摘要
2004年，Ambainis和Regev制定了某种形式的量子绝热定理，并提供了一个基本证明，计算机科学家特别可以使用。他们的结果是通过将绝热进化分配为作用于量子系统的一系列单一转换序列来实现的。在这里，我们通过提供另一个基本和较短的证明，并以改进的界限来继续进行这一研究。我们的关键发现是目标和实际状态之间差异的简洁不可或缺的表示，这可以准确估计近似误差。我们的证明可以被Ambainis和Regev视为作品的“连续”版本。作为应用程序，我们将展示如何从初始状态中绝热地准备任意量子状态。
In 2004 Ambainis and Regev formulated a certain form of quantum adiabatic theorem and provided an elementary proof which is especially accessible to computer scientists. Their result is achieved by discretizing the total adiabatic evolution into a sequence of unitary transformations acting on the quantum system. Here we continue this line of study by providing another elementary and shorter proof with improved bounds. Our key finding is a succinct integral representation of the difference between the target and the actual states, which yields an accurate estimation of the approximation error. Our proof can be regarded as a "continuous" version of the work by Ambainis and Regev. As applications, we show how to adiabatically prepare an arbitrary qubit state from an initial state.
