QAOA-PCA: Enhancing Efficiency in the Quantum Approximate Optimization Algorithm via Principal Component Analysis
This work addresses efficiency issues for researchers and practitioners using QAOA on near-term quantum devices, but it is incremental as it builds on existing QAOA methods with a dimensionality reduction approach.
The paper tackles the computational burden of optimizing many parameters in the Quantum Approximate Optimization Algorithm (QAOA) by introducing QAOA-PCA, a reparameterization technique using Principal Component Analysis (PCA) to reduce dimensionality, which empirically requires fewer iterations and achieves substantial efficiency gains on the MaxCut problem, though with a slight reduction in approximation ratio.
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.