2023/06/20 by Cheng-Lin Hong, Luis Colmenárez, Hong, Cheng-Lin +7 · 3 citations
Computer Science · Physics and Astronomy · #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum and electron transport phenomena #Strongly Correlated Electrons (cond-mat.str-el)
paper · pdf · doi:10.48550/arxiv.2306.11844
openalex publication_date 2023/06/20 · openalex created_date 2023/06/24 · openalex updated_date 2026/07/28
The weighted subspace-search variational quantum eigensolver (SSVQE) is a prominent algorithm for calculating excited-state properties of molecular quantum systems. In this work, we elaborate on some of its fundamental features with the aim of improving its practical realization. First, we demonstrate that the initial ansätze for various excited states could be prepared into a single pure state through a minimal number of ancilla qubits, followed by the optimization of a subsequent global unitary rotation in the targeted subspace. Since the ancillas' sole purpose is to purify an underlying ensemble ρ_\boldsymbolw state with spectral weights \boldsymbolw, their measurement would just collapse ρ_\boldsymbolw with probabilities wj to one of its eigenstates |Ψj ⟩. We thus observe that our realization of SSVQE is equivalent to the original SSVQE improved by importance sampling. Then, we elaborate by numerical means on the potential influence of the auxiliary weights \boldsymbolw on the accuracy of the sought-after eigenstates and eigenenergies. Clear trends are discovered which are contrasted with some recent mathematical results concerning the ensemble variational principle that underlies SSVQE.