Quantum algorithms for optimal effective theory of many-body systems
- URL: http://arxiv.org/abs/2211.14854v2
- Date: Wed, 6 Sep 2023 07:09:25 GMT
- Title: Quantum algorithms for optimal effective theory of many-body systems
- Authors: Yongdan Yang, Zongkang Zhang, Xiaosi Xu, Bing-Nan Lu, Ying Li
- Abstract summary: We propose two approaches that apply quantum computing to find the optimal effective theory of a quantum many-body system.
The first algorithm searches the space of effective Hamiltonians by quantum phase estimation and amplitude amplification.
The second algorithm is based on a variational approach that is promising for near-future applications.
- Score: 3.4918110778972458
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A common situation in quantum many-body physics is that the underlying
theories are known but too complicated to solve efficiently. In such cases one
usually builds simpler effective theories as low-energy or large-scale
alternatives to the original theories. Here the central tasks are finding the
optimal effective theories and proving their equivalence to the original
theories. Recently quantum computing has shown the potential of solving quantum
many-body systems by exploiting its inherent parallelism. It is thus an
interesting topic to discuss the emergence of effective theories and design
efficient tools for finding them based on the results from quantum computing.
As the first step towards this direction, in this paper, we propose two
approaches that apply quantum computing to find the optimal effective theory of
a quantum many-body system given its full Hamiltonian. The first algorithm
searches the space of effective Hamiltonians by quantum phase estimation and
amplitude amplification. The second algorithm is based on a variational
approach that is promising for near-future applications.
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