Concurrent quantum eigensolver for multiple low-energy eigenstates
Guanglei Xu, Yang Guo, Xishun Li, K. Wang, Z. Fan, Zhenjing Zhou, Haijun Liao, Tao Xiang · Physical Review A · 2023
We propose a quantum algorithm that diagonalizes a Hamiltonian by implementing an ansatz that satisfies the generalized Rayleigh-Ritz variational principle. This algorithm uses a purification technique to target many quantum states in one quantum circuit and allows multiple eigenstates to be optimized and determined simultaneously. Moreover, it requires a reasonable circuit depth compared to existing algorithms and enables flexible postprocessing on the accurately determined eigensubspace. Using the transverse-field Ising model, we confirm that the eigenvalues obtained with the algorithm converge efficiently and uniformly with the iteration steps, tested by both simulations and IBM platform measurements. As limited quantum resources are needed, this algorithm is promising for noise resilience, better performances, and versatile applications.