Linearly simplified QAOA parameters and transferability

TL;DR

This paper introduces a linear parameter simplification for QAOA that drastically reduces the parameter space and demonstrates transferability of parameters across different problem instances, potentially easing optimization.

Contribution

The work proposes a linear form of QAOA parameters that simplifies the optimization landscape and shows that these parameters can be transferred between instances, reducing computational effort.

Findings

Parameter space reduced from 2p to 4 dimensions.

Linearized parameters exhibit stability across different instances.

Transferability of parameters depends on instance features.

Abstract

Quantum Approximate Optimization Algorithm (QAOA) provides a way to solve combinatorial optimization problems using quantum computers. QAOA circuits consist of time evolution operators by the cost Hamiltonian and of state mixing operators, and embedded variational parameter for each operator is tuned so that the expectation value of the cost function is minimized. The optimization of the variational parameters is taken place on classical devices while the cost function is measured in the sense of quantum. To facilitate the classical optimization, there are several previous works on making decision strategies for optimal/initial parameters and on extracting similarities among instances. In our current work, we consider simplified QAOA parameters that take linear forms along with the depth in the circuit. Such a simplification, which would be suggested from an analogy to quantum annealing, leads to a drastic reduction of the parameter space from 2p to 4 dimensions with the any number of QAOA layers p. In addition, cost landscapes in the reduced parameter space have some stability on differing instances. This fact suggests that an optimal parameter set for a given instance can be transferred to other instances. In this paper we present some numerical results that are obtained for instances of the random Ising model and of the max-cut problem. The transferability of linearized parameters is demonstrated for randomly generated source and destination instances, and its dependence on features of the instances are investigated.