MOR+EC: Efficient Computation of Correlation Functions of Quantum Systems Across Many Parameter Regimes using Model Order Reduction and Quantum Subspaces

Correlation functions (CF) are fundamental to analyzing quantum systems and are widely used in many scientific fields. In some cases, especially with exponentially scaling vector spaces, calculating CFs is computationally expensive and often infeasible when many evaluations are required. This limits the ability to explore multiple parameter regimes, which is important in studying phases of matter or optimizing system parameters. Usually, the entire vector space doesn't affect CF dynamics, so using a smaller, relevant subspace is advantageous. Inspired by the moment matching of Model Order Reduction (MOR) and the construction of a low-energy subspace of quantum states with Eigenvector Continuation (EC), we propose MOR+EC, where projections into the reduced model space are constructed from low-energy vectors, "training" response frequencies, and "training" Hamiltonians. At the cost of initializing a more expressive projection, this setup yields significant speed-ups and maintains high accuracy across many parameters, outperforming traditional MOR.