We published our preprint paper
I am pleased to announce that I have submitted a paper titled "Tangent Vector Variational Quantum Eigensolver: A Robust Variational Quantum Eigensolver against the inaccuracy of derivatives" with Prof. Suksmoto of the University of Bandung. derivative" with Prof. Suskmoto, University of Bandung. This paper describes our method, Tangent-Vector VQE (TVVQE), and shows its computational results and advantages. In this method, after optimizing the energy eigenvalues, the desired energy eigenvalues and their states are calculated accurately by minimizing their first derivative instead of the trial energy, avoiding local solutions. As a result, it was found that the calculation can be done with much higher accuracy than other well-known methods in two iterations for only a few excited states. Looking at the convergence, for the exact solution of the bond length in the hydrogen molecule (0.7414 Å), the calculation results exceeded the chemical accuracy in all states (Figure 1). This method can be a powerful algorithm for a 100-qubit NISQ computer that can be used as a Fault-Tolerant-Quantum-Computer (FTCC), which will be released in the future, if the time can be reduced by computing the first derivative in parallel.
Figure 1: Convergence of each state in molecular hydrogen.