Matrix Product State on a Quantum Computer

TL;DR

This paper introduces a quantum version of matrix product states (qMPS) and develops variational algorithms to efficiently simulate quantum many-body systems on near-term quantum devices, reducing qubit requirements and mitigating barren plateau issues.

Contribution

The paper proposes a novel quantum matrix product state framework and variational algorithms that improve efficiency and accuracy over existing methods like VQE, suitable for near-term quantum hardware.

Findings

Reduces qubit requirements compared to VQE

Mitigates barren plateau effects in variational algorithms

Achieves comparable or better accuracy in simulating quantum systems

Abstract

Solving quantum many-body systems is one of the most significant regimes where quantum computing applies. Currently, as a hardware-friendly computational paradigms, variational algorithms are often used for finding the ground energy of quantum many-body systems. However, running large-scale variational algorithms is challenging, because of the noise as well as the obstacle of barren plateaus. In this work, we propose the quantum version of matrix product state (qMPS), and develop variational quantum algorithms to prepare it in canonical forms, allowing to run the variational MPS method, which is equivalent to the Density Matrix Renormalization Group method, on near term quantum devices. Compared with widely used methods such as variational quantum eigensolver, this method can greatly reduce the number of qubits required, and thus can mitigate the effects of Barren Plateaus while obtain comparable or even better accuracy. Our method holds promise for distributed quantum computing, offering possibilities for fusion of different computing systems.