The Quantum Approximate Optimization Algorithm (QAOA) is a promising
variational algorithm for solving combinatorial optimization problems on
near-term devices. Cependant, 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.

Cet article explore les excursions dans le temps et leurs implications.

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