Variational quantum state eigensolver

Cerezo de la Roca, Marco Vinicio Sebastian; Sharma, Kunal; Arrasmith, Andrew Thomas; Coles, Patrick Joseph

doi:10.1038/s41534-022-00611-6

Variational quantum state eigensolver

Journal Article · Wed Sep 21 00:00:00 EDT 2022 · npj Quantum Information

DOI:https://doi.org/10.1038/s41534-022-00611-6· OSTI ID:1993221

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Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
Los Alamos National Laboratory (LANL), Los Alamos, NM (United States); Louisiana State University, Baton Rouge, LA (United States)

Extracting eigenvalues and eigenvectors of exponentially large matrices will be an important application of near-term quantum computers. The variational quantum eigensolver (VQE) treats the case when the matrix is a Hamiltonian. Here, we address the case when the matrix is a density matrix ρ. We introduce the variational quantum state eigensolver (VQSE), which is analogous to VQE in that it variationally learns the largest eigenvalues of ρ as well as a gate sequence V that prepares the corresponding eigenvectors. VQSE exploits the connection between diagonalization and majorization to define a cost function C=Tr(ρ~H) where H is a non-degenerate Hamiltonian. Due to Schur-concavity, C is minimized when ρ~=VρV† is diagonal in the eigenbasis of H. VQSE only requires a single copy of ρ (only n qubits) per iteration of the VQSE algorithm, making it amenable for near-term implementation. We heuristically demonstrate two applications of VQSE: (1) Principal component analysis, and (2) Error mitigation.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1993221

Report Number(s):: LA-UR-20-22660

Journal Information:: npj Quantum Information, Journal Name: npj Quantum Information Journal Issue: 1 Vol. 8; ISSN 2056-6387

Publisher:: Nature Partner JournalsCopyright Statement

Country of Publication:: United States

Language:: English

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