论文标题
Schrieffer-Wolff转换的量子算法
Quantum algorithms for Schrieffer-Wolff transformation
论文作者
论文摘要
Schrieffer-Wolff的转化旨在解决退化的扰动问题，并提供有效的汉密尔顿人，描述了在不易受扰动的汉密尔顿人低能的子空间中确切的汉密尔顿的低能动力学。这种统一的转化可以通过量子回路实现转化的汉密尔顿的低能和高能量子空间。我们给出了一种完全量子算法，以实现SW转换。我们还提出了一种混合量子古典算法，用于在NISQ硬件上找到有效的哈密顿量，该算法使用一般成本函数来指示脱钩度。在量子计算机上没有噪声和实验的数值模拟IBMQ_MANILA上是为Heisenberg链模型实施的。我们的结果验证了算法并在近期量子计算机上显示其有效性。
The Schrieffer-Wolff transformation aims to solve degenerate perturbation problems and give an effective Hamiltonian that describes the low-energy dynamics of the exact Hamiltonian in the low-energy subspace of unperturbed Hamiltonian. This unitary transformation decoupling the low-energy and high-energy subspaces for the transformed Hamiltonian can be realized by quantum circuits. We give a fully quantum algorithm for realizing the SW transformation. We also propose a hybrid quantum-classical algorithm for finding the effective Hamiltonian on NISQ hardware, where a general cost function is used to indicate the decoupling degree. Numerical simulations without or with noise and experiments on quantum computer ibmq_manila are implemented for a Heisenberg chain model. Our results verify the algorithm and show its validity on near-term quantum computers.
