论文标题
量子多体基态的Bang-Bang算法：张量网络探索
Bang-bang algorithms for quantum many-body ground states: a tensor network exploration
论文作者
论文摘要
我们使用矩阵产品技术来研究两种算法的性能，用于获得无限系统中量子多体汉密尔顿$ h = h_a + h_b $的基态。第一种算法是对量子近似优化算法（QAOA）的概括，并使用量子计算机将初始产品状态演变为$ h $的基态近似，通过在$ h_a $和$ h_b $之间交替。我们为1D量子模型展示了表示间隙基态的准确性随着交替的数量而呈指数增长。第二个算法是变异的想象时间ansatz（VITA），该算法使用经典计算机通过$ H_A $和$ H_B $的交替虚构时间步骤模拟基态。我们发现，对于1D量子iSing模型，可以通过总的假想时间$τ$获得与基态获得的准确近似值，该$τ$仅在逆向能差距$ 1/δ$ $ h $的情况下生长。这比假想时间的演变要比$ h $快得多，这将需要$τ\ sim 1/δ$。
We use matrix product techniques to investigate the performance of two algorithms for obtaining the ground state of a quantum many-body Hamiltonian $H = H_A + H_B$ in infinite systems. The first algorithm is a generalization of the quantum approximate optimization algorithm (QAOA) and uses a quantum computer to evolve an initial product state into an approximation of the ground state of $H$, by alternating between $H_A$ and $H_B$. We show for the 1D quantum Ising model that the accuracy in representing a gapped ground state improves exponentially with the number of alternations. The second algorithm is the variational imaginary time ansatz (VITA), which uses a classical computer to simulate the ground state via alternating imaginary time steps with $H_A$ and $H_B$. We find for the 1D quantum Ising model that an accurate approximation to the ground state is obtained with a total imaginary time $τ$ that grows only logarithmically with the inverse energy gap $1/ Δ$ of $H$. This is much faster than imaginary time evolution by $H$, which would require $τ\sim 1/ Δ$.
