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Journal Article
Variational quantum state eigensolver
2022
Overview
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
̃
=
V
ρ
V
†
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.
Publisher
Nature Publishing Group UK,Nature Publishing Group,Nature Partner Journals,Nature Portfolio
