Journal Article FZJ-2022-04047

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Using gradient-based algorithms to determine ground-state energies on a quantum computer

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2022
Inst. Woodbury, NY

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Abstract: Variational algorithms are promising candidates to be implemented on near-term quantum computers. In our work, we investigate the variational Hamiltonian ansatz (VHA), where a parametrized trial state of the quantum mechanical wave function is optimized to obtain the ground-state energy. In the VHA, the trial state is given by a noninteracting reference state modified by unitary rotations using generators that are part of the Hamiltonian describing the system. The lowest energy is obtained by optimizing the angles of those unitary rotations. A standard procedure to optimize the variational parameters is to use gradient-based algorithms. However, shot noise and the intrinsic noise of the quantum device affect the evaluation of the required gradients. We study how different methods for obtaining the gradient, specifically the finite-difference and the parameter-shift rule, are affected by shot noise and the noise of the quantum computer. To this end, we simulate a simple quantum circuit, as well as the two-site and six-site Hubbard models.

Classification:

Contributing Institute(s):
  1. Quantum Computing Analytics (PGI-12)
Research Program(s):
  1. 5223 - Quantum-Computer Control Systems and Cryoelectronics (POF4-522) (POF4-522)

Appears in the scientific report 2022
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Medline ; American Physical Society Transfer of Copyright Agreement ; OpenAccess ; Clarivate Analytics Master Journal List ; Current Contents - Electronics and Telecommunications Collection ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; SCOPUS ; Science Citation Index Expanded ; Web of Science Core Collection
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 Record created 2022-10-31, last modified 2023-01-23


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