Symmetry-adapted variational quantum eigensolver
Symmetry-adapted variational quantum eigensolver
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DOI：
10.1103/physreva.101.052340
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发表时间：
2019-12
影响因子：
2.9
通讯作者：
K. Seki;T. Shirakawa;S. Yunoki
中科院分区：
文献类型：
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作者：
K. Seki;T. Shirakawa;S. Yunoki
在变分量子本征求解（VQE）算法中，针对量子电路结构通常会破坏哈密顿对称性的问题，提出了一种恢复哈密顿空间对称性的方案。本文介绍的自对称VQE方案简单地应用投影算子，该算子是厄密的但不是酉的，以恢复空间群的不可约表示中的空间对称性。量子态的纠缠仍然在量子电路中表示，但投影算子的非一致性在VQE框架中被经典地视为后处理。通过对一维环上自旋- 1/2 Heisenberg模型的数值模拟，我们证明了具有较浅量子电路的对称自适应VQE方案与非对称自适应VQE方案相比，在基态保真度方面取得了显着改善，并且在基态能量方面具有很大的优势，并且具有良好的精度。我们还证明了该方案可以近似由对称扇区指定的低洼激发态，使用相同的电路结构进行基态计算。
We propose a scheme to restore spatial symmetry of Hamiltonian in the variational-quantum-eigensolver (VQE) algorithm for which the quantum circuit structures used usually break the Hamiltonian symmetry. The symmetry-adapted VQE scheme introduced here simply applies the projection operator, which is Hermitian but not unitary, to restore the spatial symmetry in a desired irreducible representation of the spatial group. The entanglement of a quantum state is still represented in a quantum circuit but the nonunitarity of the projection operator is treated classically as postprocessing in the VQE framework. By numerical simulations for a spin-$1/2$ Heisenberg model on a one-dimensional ring, we demonstrate that the symmetry-adapted VQE scheme with a shallower quantum circuit can achieve significant improvement in terms of the fidelity of the ground state and has a great advantage in terms of the ground-state energy with decent accuracy, as compared to the non-symmetry-adapted VQE scheme. We also demonstrate that the present scheme can approximate low-lying excited states that can be specified by symmetry sectors, using the same circuit structure for the ground-state calculation.