Review of Variational Quantum Eigensolver: part 2
It is the sequel of "Review of Variational Quantum Eigensolver: part 1".
I will introduce you the advanced metyhod of VQE method with respect of modified processes.
Modifying evaluation function is the most popular way to establish the advanced VQE method.
Subspace-Search VQE(SSVQE) and Vartiational Quantum State Eigensolver(VQSE) are so. SSVQE optimizes the sum of multiple eigenenergies. And, VQSE optimize the trace of the product of density operator and hamiltonian. If quantum computer can process, whatever can be evaluation function.
Thus, novel advanced VQE that modify evaluation function may appear in the future.
Some advanced VQE method apply the algorithms that make the cluster in unique way.
ADAPT-VQE make the cluster by optimize the evaluational function and its derivaritive later. In the case the variation of evaluation function in not enough small after deriving the minimum of it, new cluster term is add and repeat the process. Multiobjective-Genetic VQE(MoG-VQE) optimizes the cluster by discrete-coded Genetic Algorithm that individual is optimized evaluation function using each cluster.
On the other hand, many types of cluster terms are proposed.
This type of advanced VQE method has very high accuracy.
Adding postcalculation treatment is proposed by some groups though they are minor to above two.
Multiscale-Contracted VQE(MCVQE) method make the superpositioned state after SSVQE method. It is called Configuration Intaraction Single (CIS) state. Energy levels are derived by diagonalizing CIS matrix made by CIS state. Quantum Subspace Expansion (QSE) method is also proposed. It is the method to correct errors on real quantum computers.
Other types of modification can be realized such as initial values and optimization methods.
I will propose the one of them I established in near future.
 K. M. Nakanishi, and. et. al., arXiv:1810.09434v2[quant-ph](2018)
 M. Cerezo, and et. al., arXiv:2004.01372[quant-ph](2020)
 H. R. Grimsey, and et. al., Nat. Comm.10.3007(2019)
 D. Chivilikhin, and et. al., arXiv:2007.04424[quant-ph](2020)
 R. Parrish et al., Phys. Rev. Lett. 122, 230401 (2019)
 J. R. McClean, and et. al., Nat. Comm. 11.636(2020)