Automatically differentiable quantum circuit for many-qubit state preparation
Peng-Fei Zhou, Rui Hong, Shi-Ju Ran
Abstract
Constructing quantum circuits for efficient state preparation are central topics in the field of quantum information and computation. As the number of qubits grows quickly, methods to derive large-scale quantum circuits are strongly desired. In this article, we propose the automatically differentiable quantum circuit (ADQC) approach to efficiently prepare quantum many-qubit states in the form of a matrix product state (MPS). A key ingredient is to introduce latent gates whose decompositions give unitary gates that form a quantum circuit. The circuit is optimized by updating the latent gates using backpropagation to minimize the distance between the evolved and target states. Taking the ground states of one-dimensional spin lattice models and random matrix product states as examples, with the number of qubits where processing the full coefficients is unlikely, ADQC obtains high fidelities with small numbers of layers ${N}_{L}\ensuremath{\sim}O(1)$. Much higher fidelities are obtained compared with the existing state-preparation approach based on the matrix product disentangler. In addition, ADQC provides an efficient representation of many-qubit states, whose number of parameters can be compressed to about $0.1%\text{--}1%$ of that in the MPS. Our work sheds light on the ``intelligent construction'' of quantum circuits for many-qubit systems by combining them with machine learning methods.