非交换酉查询量子复杂性的半定规划刻画和谱对抗方法
Semidefinite programming characterization and spectral adversary method for quantum complexity with noncommuting unitary queries
摘要：
推广早期的工作，表征计算从一组这样的黑盒函数中提取的未知经典"黑盒“函数的函数的量子查询复杂性，我们研究了一个更一般的量子查询模型，其中目标是计算从一组这样的矩阵中提取的N乘N”黑盒“酉矩阵的函数，一个应用于确定量子物理系统性质的问题。我们的特点是存在这样一个查询问题的算法，与给定的错误和查询次数，相当于一组半定规划约束的可行性，或等价的不可行性，这些约束的对偶，我们构造。放松原始约束对应于量子计算机的最终状态的仅仅成对近正交性，条件是黑箱输入具有不同的函数值，而不是通过对输出状态的单个测量的函数值的有界误差确定性，我们得到一个放松的原始程序，其对偶的可行性仍然意味着量子算法的不存在。我们用这个来获得一个泛化，我们不一定交换设置，量子查询下限的“光谱对手的方法”。
英文摘要：
Generalizing earlier work characterizing the quantum query complexity of computing a function of an unknown classical ``black box'' function drawn from some set of such black box functions, we investigate a more general quantum query model in which the goal is to compute functions of N by N ``black box'' unitary matrices drawn from a set of such matrices, a problem with applications to determining properties of quantum physical systems. We characterize the existence of an algorithm for such a query problem, with given error and number of queries, as equivalent to the feasibility of a certain set of semidefinite programming constraints, or equivalently the infeasibility of a dual of these constraints, which we construct. Relaxing the primal constraints to correspond to mere pairwise near-orthogonality of the final states of a quantum computer, conditional on black-box inputs having distinct function values, rather than bounded-error determinability of the function value via a single measurement on the output states, we obtain a relaxed primal program the feasibility of whose dual still implies the nonexistence of a quantum algorithm. We use this to obtain a generalization, to our not-necessarily-commutative setting, of the ``spectral adversary method'' for quantum query lower bounds.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
