Variational Quantum Circuits to Prepare Low Energy Symmetry States
Variational Quantum Circuits to Prepare Low Energy Symmetry States
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DOI：
10.3390/sym14030457
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发表时间：
2021-12
期刊：
影响因子：
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通讯作者：
R. Selvarajan;M. Sajjan;S. Kais
中科院分区：
文献类型：
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作者：
R. Selvarajan;M. Sajjan;S. Kais
我们探索如何构建量子电路，通过将对称子空间内给定哈密顿量显式编码到电路中来计算对应于给定哈密顿量的最低能态。我们创建一个显式酉元和一个变分训练酉元，将 ansatz A(α→) 输出的任何向量从定义的子空间映射到对称空间中的向量。对参数进行不同的训练以最小化能量，从而将输出保持在标记的对称值内。该方法使用旋转和反射对称性测试了自旋 XXZ 哈密顿量，并使用 S2 对称性测试了 Sz=0 子空间内的 H2 哈密顿量。我们发现变分训练的酉式在深度非常低的电路中给出了良好的结果，因此可以用于在近期量子计算机中准备对称态。
We explore how to build quantum circuits that compute the lowest energy state corresponding to a given Hamiltonian within a symmetry subspace by explicitly encoding it into the circuit. We create an explicit unitary and a variationally trained unitary that maps any vector output by ansatz A(α→) from a defined subspace to a vector in the symmetry space. The parameters are trained varitionally to minimize the energy, thus keeping the output within the labelled symmetry value. The method was tested for a spin XXZ Hamiltonian using rotation and reflection symmetry and H2 Hamiltonian within Sz=0 subspace using S2 symmetry. We have found the variationally trained unitary gives good results with very low depth circuits and can thus be used to prepare symmetry states within near term quantum computers.