Tensor Network Assisted Distributed Variational Quantum Algorithm for Large Scale Combinatorial Optimization Problem

TL;DR

This paper introduces a scalable distributed quantum algorithm that effectively solves large combinatorial optimization problems by preserving inter-variable dependencies and localizing noise, demonstrated through simulations and real quantum hardware.

Contribution

The paper presents the DVQA, a novel distributed variational quantum algorithm utilizing tensor network techniques to handle large-scale COPs on limited hardware.

Findings

DVQA solves 1,000-variable instances on constrained hardware.

Achieves state-of-the-art performance in simulations.

Validated experimentally on Wu Kong quantum computer.

Abstract

Although quantum computing holds promise for solving Combinatorial Optimization Problems (COPs), the limited qubit capacity of NISQ hardware makes large-scale instances intractable. Conventional methods attempt to bridge this gap through decomposition or compression, yet they frequently fail to capture global correlations of subsystems, leading to solutions of limited quality. We propose the Distributed Variational Quantum Algorithm (DVQA) to overcome these limitations, enabling the solution of 1,000-variable instances on constrained hardware. A key innovation of DVQA is its use of the truncated higher-order singular value decomposition to preserve inter-variable dependencies without relying on complex long-range entanglement, leading to a natural form of noise localization where errors scale with subsystem size rather than total qubit count, thus reconciling scalability with accuracy. Theoretical bounds confirm the algorithm's robustness for p-local Hamiltonians. Empirically, DVQA achieves state-of-the-art performance in simulations and has been experimentally validated on the Wu Kong quantum computer for portfolio optimization. This work provides a scalable, noise-resilient framework that advances the timeline for practical quantum optimization algorithms.