Adaptive Variational Quantum Imaginary Time Evolution Approach for Ground State Preparation

Date
2021-12
Authors
Gomes, Niladri
Mukherjee, Anirban
Zheng, Feng
Iadecola, Thomas
Wang, Cai-Zhuang
Ho, Kai-Ming
Orth, Peter
Yao, Yong-Xin
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Wiley-VCH GmbH
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Orth, Peter
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Physics and Astronomy
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Ames Laboratory
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Physics and AstronomyAmes Laboratory
Abstract
An adaptive variational quantum imaginary time evolution (AVQITE) approach is introduced that yields efficient representations of ground states for interacting Hamiltonians on near-term quantum computers. It is based on McLachlan's variational principle applied to imaginary time evolution of variational wave functions. The variational parameters evolve deterministically according to equations of motions that minimize the difference to the exact imaginary time evolution, which is quantified by the McLachlan distance. Rather than working with a fixed variational ansatz, where the McLachlan distance is constrained by the quality of the ansatz, the AVQITE method iteratively expands the ansatz along the dynamical path to keep the McLachlan distance below a chosen threshold. This ensures the state is able to follow the quantum imaginary time evolution path in the system Hilbert space rather than in a restricted variational manifold set by a predefined fixed ansatz. AVQITE is used to prepare ground states of H4, H2O, and BeH2 molecules, where it yields compact variational ansätze and ground state energies within chemical accuracy. Polynomial scaling of circuit depth with system size is shown through a set of AVQITE calculations of quantum spin models. Finally, quantum Lanczos calculations are demonstrated alongside AVQITE without additional quantum resource costs.
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This is the published version of the following article: Gomes, Niladri, Anirban Mukherjee, Feng Zhang, Thomas Iadecola, Cai‐Zhuang Wang, Kai‐Ming Ho, Peter P. Orth, and Yong‐Xin Yao. "Adaptive variational quantum imaginary time evolution approach for ground state preparation." Advanced Quantum Technologies 4, no. 12 (2021): 2100114. DOI: 10.1002/qute.202100114. Copyright 2021 The Author(s). Attribution 4.0 International (CC BY 4.0). Posted with permission.
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