Department of Computer Science, Purdue University, West Lafayette, Indiana 47907, USA.
J Chem Phys. 2011 Apr 14;134(14):144112. doi: 10.1063/1.3575402.
Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems.
构建新量子算法的适当幺正矩阵运算符，并找到实现这些幺正运算符的最小代价门序列，这在量子信息和量子计算领域至关重要。量子电路的演化面临两个主要挑战：复杂且庞大的搜索空间以及在经典计算机上模拟量子电路的高成本。在这里，我们使用群组领导者优化算法将给定的幺正矩阵分解为适当的最小代价量子门序列。我们在托弗里门、格罗弗搜索算法的放大步骤、量子傅里叶变换以及量子隐形传态的发送方部分的已知分解上测试了该方法。使用此过程，我们提出了模拟氢和水分子哈密顿量幺正传播子的电路设计。该方法具有通用性，可用于生成更大分子系统的量子门序列。
