A Noise-Aware Scalable Subspace Classical Optimizer for the Quantum Approximate Optimization Algorithm
Kwassi Joseph Dzahini, Jeffrey M. Larson, Matt Menickelly, Stefan M. Wild
TL;DR
ANASTAARS tackles the challenge of optimizing high-dimensional QAOA parameters under noisy measurements by introducing a noise-aware stochastic trust-region optimizer that uses adaptive random subspaces and interpolation models built via Johnson-Lindenstrauss. The method reuses past interpolation data to reduce shot costs and increments subspace dimension after unsuccessful iterations, with explicit noise estimation integrated into the ratio test. MFN and diagonal-Hessian nonlinear subspace models are employed to capture curvature within small subspaces, enabling scalable high-dimensional optimization. Numerical results on MaxCut benchmarks demonstrate competitive performance and scalability compared with established DFO solvers, highlighting practical potential for near-term quantum applications.
Abstract
We introduce ANASTAARS, a noise-aware scalable classical optimizer for variational quantum algorithms such as the quantum approximate optimization algorithm (QAOA). ANASTAARS leverages adaptive random subspace strategies to efficiently optimize the ansatz parameters of a QAOA circuit, in an effort to address challenges posed by a potentially large number of QAOA layers. ANASTAARS iteratively constructs random interpolation models within low-dimensional affine subspaces defined via Johnson--Lindenstrauss transforms. This adaptive strategy allows the selective reuse of previously acquired measurements, significantly reducing computational costs associated with shot acquisition. Furthermore, to robustly handle noisy measurements, ANASTAARS incorporates noise-aware optimization techniques by estimating noise magnitude and adjusts trust-region steps accordingly. Numerical experiments demonstrate the practical scalability of the proposed method for near-term quantum computing applications.