ICML 2025

A Sub-Problem Quantum Alternating Operator Ansatz for Correlation
Clustering
Lucas Fabian Naumann 1 Jannik Irmai 1 Bjoern Andres 1 2
Abstract
The Quantum Alternating Operator Ansatz
(QAOA) is a hybrid quantum-classical variational
algorithm for approximately solving combinato-
rial optimization problems on Noisy Intermediate-
Scale Quantum (NISQ) devices. Although it has
been successfully applied to a variety of problems,
there is only limited work on correlation cluster-
ing due to the difficulty of modelling the problem
constraints with the ansatz. Motivated by this, we
present a generalization of QAOA that is more
suitable for this problem. In particular, we mod-
ify QAOA in two ways: Firstly, we use nucleus
sampling for the computation of the expected cost.
Secondly, we split the problem into sub-problems,
solving each individually with QAOA. We call
this generalization the Sub-Problem Quantum Al-
ternating Operator Ansatz (SQAOA) and show
theoretically that optimal solutions to correlation
clustering instances can be obtained with certainty
when the depth of the ansatz tends to infinity.
Further, we show experimentally that SQAOA
achieves better approximation ratios than QAOA
for correlation clustering, while using only one
qubit per node of the respective problem instance
and reducing the runtime (of simulations).
1. Introduction
The term “quantum supremacy” (Preskill, 2012) refers to
the ability of quantum computers to perform tasks efficiently
that classical computers cannot. From a theoretical point
of view, algorithms achieving this supremacy for problems
of practical interest have long been established. However,
applying these algorithms to problem instances of classi-
cally intractable sizes is not possible on current quantum
1Faculty of Computer Science, TU Dresden 2Center for Scal-
able Data Analytics and AI, Dresden/Leipzig. Correspondence to:
Bjoern Andres <bjoern.andres@tu-dresden.de>.
Proceedings of the 42 nd International Conference on Machine
Lea...