The Quantum Approximate Optimization Algorithm (QAOA) is a promising variational algorithm for solving combinatorial optimization problems on near-term devices. However, as the number of layers in a QAOA circuit increases, which is correlated with the quality of the solution, the number of parameters to optimize grows linearly. This results in more iterations required by the classical optimizer, which results in an increasing computational burden as more circuit executions are needed. To mitigate this issue, we introduce QAOA-PCA, a novel reparameterization technique that employs Principal Component Analysis (PCA) to reduce the dimensionality of the QAOA parameter space. By extracting principal components from optimized parameters of smaller problem instances, QAOA-PCA facilitates efficient optimization with fewer parameters on larger instances. Our empirical evaluation on the prominent MaxCut problem demonstrates that QAOA-PCA consistently requires fewer iterations than standard QAOA, achieving substantial efficiency gains. While this comes at the cost of a slight reduction in approximation ratio compared to QAOA with the same number of layers, QAOA-PCA almost always outperforms standard QAOA when matched by parameter count. QAOA-PCA strikes a favorable balance between efficiency and performance, reducing optimization overhead without significantly compromising solution quality.

We provide a method to prepare a warm-started quantum state from measurements with an iterative framework to enhance the quantum approximate optimisation algorithm (QAOA). The numerical simulations show the method can effectively address the "stuck issue" of the standard QAOA using a single-string warm-started initial state described in [Cain et al., 2023]. When applied to the $3$-regular MaxCut problem, our approach achieves an improved approximation ratio, with a lower bound that iteratively converges toward the best classical algorithms for $p=1$ standard QAOA. Additionally, in the context of the discrete global minimal variance portfolio (DGMVP) model, simulations reveal a more favourable scaling of identifying the global minimal compared to the QAOA standalone, the single-string warm-started QAOA and a classical constrained sampling approach.