Various methods have been developed for the quantum computation of the ground and excited states of physical and chemical systems, but many of them require either large numbers of ancilla qubits or high-dimensional optimization in the presence of noise. The quantum imaginary-time evolution (QITE) and quantum Lanczos (QLanczos) methods proposed in Motta et al. (2020) eschew the aforementioned issues. In this study, we demonstrate the practical application of these algorithms to challenging quantum computations of relevance for chemistry and nuclear physics, using the deuteron-binding energy and molecular hydrogen binding and excited state energies as examples. With the correct choice of initial and final states, we show that the number of timesteps in QITE and QLanczos can be reduced significantly, which commensurately simplifies the required quantum circuit and improves compatibility with NISQ devices. We have performed these calculations on cloud-accessible IBM Q quantum computers. With the application of readout-error mitigation and Richardson error extrapolation, we have obtained ground and excited state energies that agree well with exact results obtained from diagonalization.

已经开发了各种方法来对物理和化学系统的基态和激发态进行量子计算，但是其中许多方法需要大量的辅助量子比特或在存在噪声的情况下进行高维优化。Motta等人提出的量子虚时演化（QITE）和量子Lanczos（QLanczos）方法。（2020）避免了上述问题。在这项研究中，我们以氘键结合能，分子氢键和激发态能为例，论证了这些算法在挑战化学和核物理相关量子计算中的实际应用。通过正确选择初始状态和最终状态，我们证明了QITE和QLanczos中的时间步数可以大大减少，相应地简化了所需的量子电路，并提高了与NISQ器件的兼容性。我们已经在可访问云的IBM Q Quantum计算机上执行了这些计算。通过应用减少读出误差和Richardson误差外推法，我们获得了基态和激发态能量，这些能量与对角化获得的精确结果非常吻合。