2022/07/22 by Jack Ceroni, Ceroni, Jack, Alain Delgado +5
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2207.11274
openalex publication_date 2022/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
To understand the chemical properties of molecules, it is often important to study derivatives of energies with respect to nuclear coordinates or external fields. Quantum algorithms for computing energy derivatives have been proposed, but only limited work has been done to address the specific challenges that arise in this context, where calculations are more complicated and involve more stringent requirements on accuracy compared to single-point energy calculations. In this work, we introduce a technique to improve the performance of variational quantum circuits calculating energy derivatives. The method, which we refer to as tailgating, is an adaptive procedure that selects gates based on their gradient with respect to the expectation value of Hamiltonian derivatives. These gates are then added at the end of a quantum circuit originally designed to calculate ground- or excited-state energies. A distinguishing feature of this approach is that the appended gates do not need to be optimized: their parameters can be set to zero and varied only for the purpose of computing energy derivatives, via calculating derivatives with respect to circuit parameters. We support the validity of this method by establishing sufficient conditions for a circuit to compute accurate energy gradients. This is achieved through a connection between energy derivatives and eigenstates of Taylor approximations of the Hamiltonian. We illustrate the advantages of the tailgating approach by performing simulations calculating the vibrational modes of beryllium hydride and water: quantities that depend on second-order energy derivatives.