A sequentially generated variational quantum circuit with polynomial complexity

TL;DR

This paper introduces a sequentially generated variational quantum circuit ansatz that efficiently adapts to different dimensions of quantum many-body problems, enabling accurate state reconstruction and ground state finding with polynomial complexity.

Contribution

It proposes a novel sequentially generated circuit ansatz that naturally adapts to 1D, 2D, and 3D quantum problems, with polynomial complexity and broad applicability.

Findings

Efficiently generates matrix product states in 1D.

Accurately reconstructs unknown quantum states.

Outperforms alternatives in finding ground states.

Abstract

Variational quantum algorithms have been a promising candidate to utilize near-term quantum devices to solve real-world problems. The powerfulness of variational quantum algorithms is ultimately determined by the expressiveness of the underlying quantum circuit ansatz for a given problem. In this work, we propose a sequentially generated circuit ansatz, which naturally adapts to 1D, 2D, 3D quantum many-body problems. Specifically, in 1D our ansatz can efficiently generate any matrix product states with a fixed bond dimension, while in 2D our ansatz generates the string-bond states. As applications, we demonstrate that our ansatz can be used to accurately reconstruct unknown pure and mixed quantum states which can be represented as matrix product states, and that our ansatz is more efficient compared to several alternatives in finding the ground states of some prototypical quantum many-body systems as well as quantum chemistry systems, in terms of the number of quantum gate operations.