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Symmetry Breaking Slows Convergence of the ADAPT Variational Quantum Eigensolver
Luke W Bertels1, Harper R Grimsley1, Sophia E Economou2
1Department of Chemistry, Virginia Tech, Blacksburg, Virginia24061, United States.
Journal of Chemical Theory and Computation
|October 14, 2022
Summary
Investigating strongly correlated systems with adaptive variational quantum eigensolver (ADAPT-VQE) reveals that symmetry breaking, while improving classical energy calculations, hinders quantum algorithm performance. This increases ansatz length and exacerbates gradient troughs in quantum simulations.
Area of Science:
- Quantum computing
- Computational chemistry
- Condensed matter physics
Background:
- Quantum simulation offers advantages for strongly correlated systems.
- Classical methods face challenges with strong correlation, leading to the
- symmetry dilemma
- .
Purpose of the Study:
- Assess the performance of the adaptive-variational quantum eigensolver (ADAPT-VQE) for strongly correlated systems.
- Explore the impact of symmetry breaking on ADAPT-VQE performance.
Main Methods:
- Studied two strongly correlated systems: the anisotropic Heisenberg model and stretched linear H4.
- Analyzed the role of symmetry breaking in reference states and orbital mappings.
- Investigated the effect on ansatz length and convergence.
Main Results:
- Increasing system correlation led to spontaneous symmetry breaking in mean-field solutions.
- Symmetry breaking in reference states negatively impacted ADAPT-VQE.
- Observed increased ansatz length and exacerbated
- gradient troughs
- .
Conclusions:
- Symmetry breaking in reference states is detrimental to ADAPT-VQE performance.
- The
- symmetry dilemma
- poses challenges for quantum simulation of strongly correlated systems.
- Further research is needed to mitigate these effects in quantum algorithms.
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