Improved iterative quantum algorithm for ground-state preparation
- URL: http://arxiv.org/abs/2210.08454v2
- Date: Mon, 24 Oct 2022 07:52:27 GMT
- Title: Improved iterative quantum algorithm for ground-state preparation
- Authors: Jin-Min Liang, Qiao-Qiao Lv, Shu-Qian Shen, Ming Li, Zhi-Xi Wang, and
Shao-Ming Fei
- Abstract summary: We propose an improved iterative quantum algorithm to prepare the ground state of a Hamiltonian system.
Our 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.
- Score: 4.921552273745794
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Finding the ground state of a Hamiltonian system is of great significance in
many-body quantum physics and quantum chemistry. We propose an improved
iterative quantum algorithm to prepare the ground state of a Hamiltonian. The
crucial point is to optimize a cost function on the state space via the quantum
gradient descent (QGD) implemented on quantum devices. We provide practical
guideline on the selection of the learning rate in QGD by finding a fundamental
upper bound and establishing a relationship between our algorithm and the
first-order approximation of the imaginary time evolution. Furthermore, we
adapt a variational quantum state preparation method as a subroutine to
generate an ancillary state by utilizing only polylogarithmic quantum
resources. The performance of our algorithm is demonstrated by numerical
calculations of the deuteron molecule and Heisenberg model without and with
noises. Compared with the existing algorithms, our 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.
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