Tensor Network enhanced Dynamic Multiproduct Formulas

TL;DR

This paper introduces a novel algorithm that synergistically combines tensor networks and quantum computation via multiproduct formulas to enhance the accuracy of quantum simulations, demonstrated on 50-qubit systems using IBM quantum computers.

Contribution

It presents a new hybrid algorithm integrating tensor networks and quantum computing with multiproduct formulas, improving simulation accuracy beyond existing methods.

Findings

Achieved higher accuracy in quantum simulations using the combined approach.

Successfully demonstrated the workflow on 50-qubit systems with IBM quantum computers.

Provided detailed error analysis of the hybrid algorithm.

Abstract

Tensor networks and quantum computation are two of the most powerful tools for the simulation of quantum many-body systems. Rather than viewing them as competing approaches, here we consider how these two methods can work in tandem. We introduce a novel algorithm that combines tensor networks and quantum computation to produce results that are more accurate than what could be achieved by either method used in isolation. Our algorithm is based on multiproduct formulas (MPF) - a technique that linearly combines Trotter product formulas to reduce algorithmic error. Our algorithm uses a quantum computer to calculate the expectation values and tensor networks to calculate the coefficients used in the linear combination. We present a detailed error analysis of the algorithm and demonstrate the full workflow on a one-dimensional quantum simulation problem on $50$ qubits using two IBM quantum computers: $ibm\_torino$ and $ibm\_kyiv$.