论文标题
在量子计算机上模拟Lipkin模型的激发态
Simulating excited states of the Lipkin model on a quantum computer
论文作者
论文摘要
我们使用最近提出的运动量子方程（QEOM）方法模拟Lipkin模型的激发态。 QEOM在经典计算机上概括了EOM，并访问了基于准玻色子操作员的集体激发$ \ hat {o}^\ dagger_n（α）$，以增加配置复杂性$α$。我们特别表明，准确性在很大程度上取决于Qubit编码的费用。标准编码会导致较大的错误，但是使用对称性和灰色代码可减少量子资源，并显着改善当前嘈杂的量子设备的结果。使用此编码方案，我们使用IBM量子机来计算$ n = 2、3 $和$ 4 $粒子系统的能量谱，并将精度与精确解决方案进行比较。我们发现，使用$α= 2 $的方法的结果是第二个随机相位近似（SRPA）的类似物，在原则上比$α= 1 $更准确，这对应于随机相位近似（RPA），但SRPA对大耦合强度的噪声更为相关。因此，如果应用适当的缓解方法，则提出的方案通过具有较高配置复杂性的实现来实现较高的光谱准确性。
We simulate the excited states of the Lipkin model using the recently proposed Quantum Equation of Motion (qEOM) method. The qEOM generalizes the EOM on classical computers and gives access to collective excitations based on quasi-boson operators $\hat{O}^\dagger_n(α)$ of increasing configuration complexity $α$. We show, in particular, that the accuracy strongly depends on the fermion to qubit encoding. Standard encoding leads to large errors, but the use of symmetries and the Gray code reduces the quantum resources and improves significantly the results on current noisy quantum devices. With this encoding scheme, we use IBM quantum machines to compute the energy spectrum for a system of $N=2, 3$ and $4$ particles and compare the accuracy against the exact solution. We found that the results of the approach with $α= 2$, an analog of the second random phase approximation (SRPA), are, in principle, more accurate than with $α= 1$, which corresponds to the random phase approximation (RPA), but the SRPA is more amenable to noise for large coupling strengths. Thus, the proposed scheme shows potential for achieving higher spectroscopic accuracy by implementations with higher configuration complexity, if a proper error mitigation method is applied.
