Early instances of quantum advantage in the realm of chemistry and physics which are expected to have a tangible impact will likely be a result from judicious choices of circuit ansatz and/or economical measurement schedule. The first half of this challenge finds in ADAPT-VQE a prominent frontrunner, prescribing a sparse ansatz that prioritizes terms based on their ability to variationally lower the ground state energy. However, this is achieved at the expense of an extensive measurement load in order to identify the best candidate term at each iteration of the algorithm. A contender in this regard is the family of expansions in terms of moments of the Hamiltonian. These approaches are not directly variational and are guaranteed to approach the ground state energy if the state from which the moments are computed has non-zero overlap with the ground state. Since the first-order expansion is the expectation value of the Hamiltonian itself, even at second-order one is likely to improve upon the energy estimate. Here we aim at taking advantage of such properties and propose a modification of the original ADAPT-VQE algorithm in which the underlying objective function is no longer the expectation value of the Hamiltonian with the ansatz at the current iteration. Instead, we employ the Peeters–Devreese–Soldatov energy functional at order K, PDS(K), as a variational quantum solver that resembles the typical VQE routine, hence termed PDS(K)-VQS. This solver is then employed as the objective function that guides ADAPT in its circuit ansatz construction, leading to the proposed ADAPT-PDS(K)-VQS algorithm. Building on our recent numerical analysis of ADAPT-VQE, we discuss the implementation of the novel ADAPT-PDS(K)-VQS algorithm, show the measurement profile of this variant, and describe how the PDS order and the circuit depth/number of ADAPT iterations affect its accuracy.

Adaptive variational quantum solver based on the PDS energy functional: ADAPT-PDS(K)-VQS

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