Université de Bordeaux Builds Stable Quantum Krylov Method

Researchers at Université de Bordeaux, CNRS, and LOMA have developed a new quantum computing method, Orthogonal Quantum Krylov Diagonalization (OQKD), that directly reformulates the classical Lanczos recursion at the operator level. Unlike existing Quantum Krylov Diagonalization methods, OQKD eliminates the need for overlap-matrix regularization, promising improved numerical stability and accuracy in quantum calculations. The team reports achieving this by expressing Lanczos vectors as polynomial transformations of the Hamiltonian. This increased stability comes without a computational penalty; using block encoding and Generalized Quantum Signal Processing, OQKD achieves the same asymptotic query complexity as…