Data alone could fix quantum circuit design choices before training

Manav Seksaria, Advith Desu and Anil Prabhakar of the Indian Institute of Technology Madras and the Singapore University of Technology and Design report a method for predetermining optimal variational quantum circuit structure. Their work establishes three rules that fix choices of circuit design, ansätze and depths, from data and the gate set alone, before any training begins. A singular value decomposition of a dataset’s Fourier coefficients indicates whether entanglement is needed, identifying which qubits should connect, while the rank of the quantum Fisher information matrix grows predictably with circuit depth. For the Madelon dataset, these rules prescribed a 239-parameter classifier with 78.5% test accuracy, found without a grid search. This approach bypasses traditional methods of searching for optimal circuit designs, or ansätze and depths through trial and error. The analysis centers on the rank of the Fourier coefficient tensor, revealing whether a circuit lacking entangling gates can accurately represent the data; a rank exceeding one on any qubit subset signals the need for entanglement. From a labelled dataset,…