We apply a modified version of the multistate contracted variational quantum eigensolver method to calculate vibrational eigenstates of ${\mathrm{CO}}_2$ on a quantum computer. A two-mode model of ${\mathrm{CO}}_2$ is employed, and the vibrational wave function is expanded using three harmonic-oscillator basis functions for each mode. The wave functions are mapped to four qubits by a compact mapping method. The Hamiltonian matrix elements are evaluated on a simulator including noise and on a quantum computer available at IBM Quantum, while the Hamiltonian matrix is diagonalized on a classical computer. We propose an error mitigation method by which the shift of the numerical values of the matrix elements originating from the noise can be corrected, and examine the dependence of the statistical uncertainties on the number of executions of each quantum circuit. We find that, at about $8\times {10}^6$ executions, the energy eigenvalues of the Fermi resonance states in ${\mathrm{CO}}_2$ can be obtained with an uncertainty within 1 ${\mathrm{cm}}^{-1}$.

中文翻译：

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在量子计算机上计算振动本征能：在 CO2 中的费米共振中的应用

我们应用多态收缩变分量子本征求解器方法的修改版本来计算振动本征态 ${\mathrm{二氧化碳}}_2$在量子计算机上。两种模式的模型${\mathrm{二氧化碳}}_2$被采用，并且振动波函数使用每个模式的三个谐波振荡器基函数进行扩展。波函数通过紧凑映射方法映射到四个量子位。哈密​​顿矩阵元素在包含噪声的模拟器和 IBM Quantum 提供的量子计算机上进行评估，而哈密顿矩阵在经典计算机上对角化。我们提出了一种错误缓解方法，通过该方法可以校正源自噪声的矩阵元素的数值偏移，并检查统计不确定性对每个量子电路执行次数的依赖性。我们发现，在大约$8\times {10}^6$ 执行，费米共振态的能量特征值 ${\mathrm{二氧化碳}}_2$ 可以在不确定度为 1 的情况下获得 ${\mathrm{厘米}}^{-1}$.