Preparation of Many-body Ground States by Time Evolution with Variational Microscopic Magnetic Fields and Incomplete Interactions

TL;DR

This paper introduces a variational approach using time evolution with fixed couplings and optimized magnetic fields to prepare many-body ground states, improving precision and stability over baseline methods.

Contribution

It proposes a novel optimization method for magnetic fields in quantum state preparation, enabling high-precision ground state engineering with incomplete interactions.

Findings

Outperforms baseline optimization strategies in ground state preparation.

Effective on Heisenberg chains with XY and Ising interactions.

Applicable to higher-dimensional quantum models.

Abstract

State preparation is of fundamental importance in quantum physics, which can be realized by constructing the quantum circuit as a unitary that transforms the initial state to the target, or implementing a quantum control protocol to evolve to the target state with a designed Hamiltonian. In this work, we study the latter on quantum many-body systems by the time evolution with fixed couplings and variational magnetic fields. In specific, we consider to prepare the ground states of the Hamiltonians containing certain interactions that are missing in the Hamiltonians for the time evolution. An optimization method is proposed to optimize the magnetic fields by "fine-graining" the discretization of time, in order to gain high precision and stability. The back propagation technique is utilized to obtain the gradients of the fields against the logarithmic fidelity. Our method is tested on preparing the ground state of Heisenberg chain with the time evolution by the XY and Ising interactions, and its performance surpasses two baseline methods that use local and global optimization strategies, respectively. Our work can be applied and generalized to other quantum models such as those defined on higher dimensional lattices. It enlightens to reduce the complexity of the required interactions for implementing quantum control or other tasks in quantum information and computation by means of optimizing the magnetic fields.