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

arXiv: https://arxiv.org/abs/2106.01779 · HTML: https://mlsanity.com/paper/2106.01779/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 65 references that are in the map.
- First posted on arXiv 3 Jun 2021.

## Builds on (most cited first, 6 of 6)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Universal Quantum Control through Deep Reinforcement Learning](https://mlsanity.com/paper/1803.01857/) (2018)
- [Deep Reinforcement Learning Control of Quantum Cartpoles](https://mlsanity.com/paper/1910.09200/) (2019)
- [Approximation of quantum control correction scheme using deep neural networks](https://mlsanity.com/paper/1803.05193/) (2018)
- [Automatically Differentiable Quantum Circuit for Many-qubit State Preparation](https://mlsanity.com/paper/2104.14949/) (2021)
- [Glassy Phase of Optimal Quantum Control](https://mlsanity.com/paper/1803.10856/) (2018)

## Built on by (most cited first, 2 of 2)

- [Quantum compiling with a variational instruction set for accurate and fast quantum computing](https://mlsanity.com/paper/2203.15574/) (2022)
- [Persistent Ballistic Entanglement Spreading with Optimal Control in Quantum Spin Chains](https://mlsanity.com/paper/2307.11609/) (2023)

## Abstract (arXiv)

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.