Quantum simulation with hybrid tensor networks

TL;DR

This paper introduces hybrid tensor networks combining quantum states and classical tensors to enable efficient quantum simulation of large many-body systems on smaller quantum computers, with promising applications across physics and chemistry.

Contribution

The paper presents a novel hybrid tensor network framework that leverages quantum and classical components for efficient simulation of many-body wave functions.

Findings

Successfully simulated 8x8 and 9x8 spin systems.

Performed ground state calculations with reduced quantum resources.

Demonstrated potential for large-scale quantum simulations.

Abstract

Tensor network theory and quantum simulation are respectively the key classical and quantum computing methods in understanding quantum many-body physics. Here, we introduce the framework of hybrid tensor networks with building blocks consisting of measurable quantum states and classically contractable tensors, inheriting both their distinct features in efficient representation of many-body wave functions. With the example of hybrid tree tensor networks, we demonstrate efficient quantum simulation using a quantum computer whose size is significantly smaller than the one of the target system. We numerically benchmark our method for finding the ground state of 1D and 2D spin systems of up to $8\times 8$ and $9\times 8$ qubits with operations only acting on $8+1$ and $9+1$ qubits,~respectively. Our approach sheds light on simulation of large practical problems with intermediate-scale quantum computers, with potential applications in chemistry, quantum many-body physics, quantum field theory, and quantum gravity thought experiments.