One of the distinct features of quantum mechanics is that the probability amplitude can have both positive and negative signs, which has no classical counterpart as the classical probability must be positive. Consequently, one possible way to achieve quantum speedup is to explicitly harness this feature. Unlike a stoquastic Hamiltonian whose ground state has only positive amplitudes (with respect to the computational basis), a non-stoquastic Hamiltonian can be eventually stoquastic or properly non-stoquastic when its ground state has both positive and negative amplitudes. In this paper, we describe that, for some hard instances which are characterized by the presence of an anti-crossing (AC) in a stoquastic quantum annealing (QA) algorithm, how to design an appropriate XX-driver graph (without knowing the prior problem structure) with an appropriate XX-coupler strength such that the resulting non-stoquastic QA algorithm is proper-non-stoquastic with two bridged anti-crossings (a double-AC) where the spectral gap between the first and second level is large enough such that the system can be operated diabatically in polynomial time. The speedup is exponential in the original AC-distance, which can be sub-exponential or exponential in the system size, over the stoquastic QA algorithm, and possibly the same order of speedup over the state-of-the-art classical algorithms in optimization. This work is developed based on the novel characterizations of a modified and generalized parametrization definition of an anti-crossing in the context of quantum optimization annealing introduced in [4].
翻译:量子力学的一个明显特征是概率振幅既可能有正反两种偏差,而经典概率则没有典型的正反对等迹象。因此,实现量加速的一个可能办法是明确利用这一特性。与一个地面状态只有正振振幅(在计算基础方面)的可口喜汉密尔顿人不同的是,一个非夸度的汉密尔顿人最终可以具有正反振幅或非正反振幅。在本文中,我们描述的是,对于一些以反交替(AC)为特征的硬例,量加速度的加速度必须具有正正反正。与一个地面状态只有正振振幅(在计算基础方面不了解先前的问题结构)的可口味汉密尔密尔顿人不同,如何设计一个合适的正振动图,因此所产生的非夸度的QA算法与两个连接的正反正反正反正振幅(双向AC)不相近。对于第一个和第二个直径直径直径直的直径直径直值环境环境差异,在一个直径直径向直径直径直径直方平方平方的直径直径直径直方平方平方平方平方平段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段段内,在一个直的直的直直的直的直的直的直至直直直直至直至直至直直直至直至直至直直直直直直直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直直直直直直至直至直至直直直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直至直直