Improved Iterative Quantum Algorithm for Ground‐State Preparation. Issue 12 (20th October 2022) - Liang, Jin‐Min; Lv, Qiao‐Qiao; Shen, Shu‐Qian; Li, Ming; Wang, Zhi‐Xi; Fei, Shao‐Ming
Abstract: Finding the ground state of a Hamiltonian system is of great significance in many‐body quantum physics and quantum chemistry. An improved iterative quantum algorithm to prepare the ground state of a Hamiltonian is proposed. The crucial point is to optimize a cost function on the state space via the quantum gradient descent (QGD) implemented on quantum devices. Practical guideline on the selection of the learning rate in QGD are provided by finding a fundamental upper bound and establishing a relationship between the algorithm and the first‐order approximation of the imaginary time evolution. Furthermore, a variational quantum state preparation method is adapted as a subroutine to generate an ancillary state by utilizing only polylogarithmic quantum resources. The performance of the algorithm is demonstrated by numerical calculations of the deuteron molecule and Heisenberg model without and with noises. Compared with the existing algorithms, the approach has advantages including the higher success probability at each iteration, the measurement precision‐independent sampling complexity, the lower gate complexity, and only quantum resources are required when the ancillary state is well prepared. Abstract : This work reports an improved iterative quantum algorithm for preparing the ground state of a Hamiltonian. Upper bound on the learning rate, variational quantum state preparation, and the equivalence to the imaginary time evolution enable the ground state preparation method via linear combinational of unitary operators more suitable on near‐term quantum devices.