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The performance of the Quantum Approximate Optimisation Algorithm (QAOA)relies on the setting of optimal parameters in each layer of the circuit. Thisis no trivial task, and much literature has focused on the challenge of findingoptimal parameters when the landscape is plagued with problems such as "barrenplateaus". There are many choices of optimisation heuristics that can be usedto search for optimal parameters, each with its own parameters andinitialisation choices that affect performance. More recently, the question ofwhether such optimal parameter search is even necessary has been posed, withsome studies showing that optimal parameters tend to be concentrated on certainvalues for specific types of problem instances. However, these existing studieshave only examined specific instance classes of MaxCut, so it is uncertain ifthe claims of instance independence apply to a diverse range of instances. Inthis paper, we use Instance Space Analysis to study the dependence of instancecharacteristics on the performance of QAOA. Focusing on the MaxCut problem, weassess the effectiveness of parameter initialisation strategies and introduce anew initialisation approach based on instance characteristics called QuantumInstance-Based Parameter Initialisation (QIBPI). This study reveals that usinginsights about instance characteristics in choosing initialisation parameterscan improve QAOA performance. We also show that, within certain instanceclasses, parameters from smaller instances can be transferred to larger ones.This research provides a foundation for further instance space analysis forquantum algorithms and encourages a broader class of instances to be consideredto ensure conclusions are not limited to particular well-studied test problemsor classes.

On the Instance Dependence of Optimal Parameters for the Quadratic Approximate Optimisation Algorithm: Insights via Instance Space Analysis