Quantum computers are supposed to revolutionize quantum chemistry by achieving polynomial computational scaling. Due to the noise of quantum hardware, the variational quantum eigensolver (VQE) is proposed accordingly. However, the circuit depth is expected to grow significantly with problem size. Increased depth can both degrade the accuracy of the results and reduce trainability due to the noises. Besides, near-term quantum devices have a limited number of qubits. This work proposes a novel approach to reduce ansatz circuit depth and the number of qubits by mutual-information-based permutation of qubits and iterative folding of ansatz into an effective Hamiltonian. This breaks the original VQE algorithm into a series of VQE simulations with shallower circuit depth and fewer qubits. Proof-of-principles demonstration is presented across several molecular systems. The efficiency is compared with other state-of-the-art methods to obtain variational ground state energies of molecules on NISQ devices. Besides, the VQE-type methods suffer from optimization problems, and most of the current VQE algorithms only focus on the ground state. To overcome these obstacles, we developed an efficient quantum Krylov subspace algorithm by leveraging the iterative growth of Krylov subspace. Such subspace methods remove the optimization problems suffered in the VQE-type of methods. The newly proposed quantum Krylov subspace algorithm is employed to study the excited-state properties of various systems on both simulators and quantum devices. The complexity of the quantum Krylov subspace method is also analyzed. We believe the newly developed quantum Krylov algorithm provides a feasible tool for studying excited-state phenomena on quantum computers.

Quantum Krylov subspace methods for excited states on quantum computers

ACS Spring 2022

The official archive and repository for all ACS Meetings & Expositions abstracts and select posters or presentations.