Molecular Properties from Quantum Krylov Subspace Diagonalization

Understand

Quantum Krylov subspace diagonalization is a prominent candidate for early fault tolerant quantum simulation of many-body and molecular systems, but so far the focus has been mainly on computing ground-state energies.

• We go beyond this by deriving analytical first-order derivatives for quantum Krylov methods and show how to obtain relaxed one and two particle reduced density matrices of the Krylov eigenstates.
• The direct approach to measuring these matrices requires a number of distinct measurement that scales quadratically with the Krylov dimension $D$.
• Here, we show how to reduce this scaling to a constant.