Chiang Chen-Fu, Alsing Paul M
Department of Computer Science, State University of New York Polytechnic Institute, Utica, NY 13203, USA.
Information Directorate, Air Force Research Laboratory, Rome, NY 13441, USA.
Entropy (Basel). 2023 Aug 31;25(9):1287. doi: 10.3390/e25091287.
We investigate the irreconcilability issue that arises when translating the search algorithm from the Continuous Time Quantum Walk (CTQW) framework to the Adiabatic Quantum Computing (AQC) framework. For the AQC formulation to evolve along the same path as the CTQW, it requires a constant energy gap in the Hamiltonian throughout the AQC schedule. To resolve the constant gap issue, we modify the CTQW-inspired AQC catalyst Hamiltonian from an XZ operator to a oracle operator. Through simulation, we demonstrate that the total running time for the proposed approach for AQC with the modified catalyst Hamiltonian remains optimal as CTQW. Inspired by this solution, we further investigate adaptive scheduling for the catalyst Hamiltonian and its coefficient function in the adiabatic path of Grover-inspired AQC to improve the adiabatic local search.
我们研究了将搜索算法从连续时间量子行走（CTQW）框架转换到绝热量子计算（AQC）框架时出现的不可调和问题。为了使AQC公式沿着与CTQW相同的路径演化，在整个AQC调度过程中，哈密顿量需要有一个恒定的能隙。为了解决恒定能隙问题，我们将受CTQW启发的AQC催化剂哈密顿量从XZ算子修改为预言算子。通过模拟，我们证明了采用修改后的催化剂哈密顿量的AQC方法的总运行时间与CTQW一样保持最优。受此解决方案的启发，我们进一步研究了在受格罗弗启发的AQC绝热路径中催化剂哈密顿量及其系数函数的自适应调度，以改进绝热局部搜索。
