Adaptive variational quantum eigensolvers for highly excited states
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2021-08-30
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Iowa State University Digital Repository, Ames IA (United States)
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Physics and AstronomyAmes Laboratory
Abstract
Highly excited states of quantum many-body systems are central objects in the study of quantum dynamics and
thermalization that challenge classical computational methods due to their volume-law entanglement content. In
this work, we explore the potential of variational quantum algorithms to approximate such states. We propose
an adaptive variational quantum eigensolver (VQE) for excited states (X) that self-generates a variational ansatz
for arbitrary eigenstates of a many-body Hamiltonian H by attempting to minimize the energy variance with
respect to H. We benchmark the method by applying it to an Ising spin chain with integrable and nonintegrable
regimes, where we calculate various quantities of interest, including the total energy, magnetization density,
and entanglement entropy. We also compare the performance of adaptive VQE-X to an adaptive variant of the
folded-spectrum method. For both methods, we find a strong dependence of the algorithm’s performance on the
choice of operator pool used for the adaptive construction of the ansatz. In particular, an operator pool including
long-range two-body gates accelerates the convergence of both algorithms in the nonintegrable regime. We also
study the scaling of the number of variational parameters with system size, finding that an exponentially large
number of parameters may be necessary to approximate individual highly excited states. Nevertheless, we argue
that these methods lay a foundation for the use of quantum algorithms to study finite-energy-density properties
of many-body systems.
Comments
This article is published as Zhang, Feng, Niladri Gomes, Yongxin Yao, Peter P. Orth, and Thomas Iadecola. "Adaptive variational quantum eigensolvers for highly excited states." Physical Review B 104, no. 7 (2021): 075159.
DOI: 10.1103/PhysRevB.104.075159.
Copyright 2021 American Physical Society.
Posted with permission.
DOE Contract Number(s): AC02-07CH11358; 2038010.