标题： 一阶相变与随机优化问题中量子算法的性能 显示英文标题

标题： First-order transitions and the performance of quantum algorithms in random optimization problems

摘要： 我们研究了在存在量子涨落的情况下随机优化问题的相图。 我们的主要结果是对相变性质的表征，我们发现这是一阶量子相变。 我们提供了证据表明，在转变处，能隙随着系统大小呈指数级消失。 这表明，量子绝热算法需要随系统大小指数增长的时间才能找到该问题的基态。 显示英文摘要

摘要： We present a study of the phase diagram of a random optimization problem in presence of quantum fluctuations. Our main result is the characterization of the nature of the phase transition, which we find to be a first-order quantum phase transition. We provide evidence that the gap vanishes exponentially with the system size at the transition. This indicates that the Quantum Adiabatic Algorithm requires a time growing exponentially with system size to find the ground state of this problem.