A Quantum-Centric Super-Krylov Diagonalization Method

Abstract: The problem of estimating the ground-state energy of a quantum system is ubiquitous in chemistry and condensed matter physics. Krylov quantum diagonalization (KQD) methods have emerged as a promising approach for this task, although many existing methods rely on subroutines - particularly the Hadamard test - that are challenging to implement on near-term quantum computers. We present a KQD method that uses only real-time evolutions and recovery probabilities, making it very well adapted for existing quantum hardware. Additionally, we propose a classical post-processing derivative estimation algorithm. Under assumptions on the spectrum of the Hamiltonian, we prove that our algorithm converges exponentially quickly to the ground-state energy. Finally, we provide classical numerical simulations for the transverse-field Ising model on 100 qubits.