Rubin Nicholas C, Lee Joonho, Babbush Ryan
Google Quantum AI, San Francisco, California 94105, United States.
Department of Chemistry, Columbia University, New York, New York 10027, United States.
J Chem Theory Comput. 2022 Mar 8;18(3):1480-1488. doi: 10.1021/acs.jctc.1c00912. Epub 2022 Feb 15.
The most efficient known quantum circuits for preparing unitary coupled cluster states and applying Trotter steps of the arbitrary basis electronic structure Hamiltonian involve interleaved sequences of Fermionic Gaussian circuits and Ising interaction-type circuits. These circuits arise from factorizing the two-body operators generating those unitaries as a sum of squared one-body operators that are simulated using product formulas. We introduce a numerical algorithm for performing this factorization that has an iteration complexity no worse than single particle basis transformations of the two-body operators and often results in many times fewer squared one-body operators in the sum of squares, compared to the analytical decompositions. As an application of this numerical procedure, we demonstrate that our protocol can be used to approximate generic unitary coupled cluster operators and prepare the necessary high-quality initial states for techniques (like ADAPT-VQE) that iteratively construct approximations to the ground state.
用于制备酉耦合簇态以及应用任意基电子结构哈密顿量的 Trotter 步的已知最有效量子电路，涉及费米子高斯电路和伊辛相互作用型电路的交错序列。这些电路源于将生成那些酉矩阵的两体算符分解为平方一体算符之和，而这些平方一体算符是使用乘积公式进行模拟的。我们引入了一种用于执行这种分解的数值算法，其迭代复杂度不高于两体算符的单粒子基变换，并且与解析分解相比，在平方和中通常会使平方一体算符的数量减少许多倍。作为该数值程序的一个应用，我们证明我们的协议可用于近似一般的酉耦合簇算符，并为迭代构建基态近似的技术（如 ADAPT-VQE）制备必要的高质量初始态。
