Complexity growth for one-dimensional free-fermionic lattice models

• URL: http://arxiv.org/abs/2302.06305v3
• Date: Wed, 9 Aug 2023 12:32:20 GMT
• Title: Complexity growth for one-dimensional free-fermionic lattice models
• Authors: S. Aravinda and Ranjan Modak
• Abstract summary: We study the unitary dynamics of the one-dimensional lattice models of non-interacting fermions. We find analytically using quasiparticle formalism, the bound grows linearly in time and followed by a saturation for short-ranged tight-binding Hamiltonians. The upper bound of the complexity in non-interacting fermionic lattice models is calculated, which grows linearly in time even beyond the saturation time of the lower bound, and finally, it also saturates.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Complexity plays a very important part in quantum computing and simulation where it acts as a measure of the minimal number of gates that are required to implement a unitary circuit. We study the lower bound of the complexity [Eisert, Phys. Rev. Lett. 127, 020501 (2021)] for the unitary dynamics of the one-dimensional lattice models of non-interacting fermions. We find analytically using quasiparticle formalism, the bound grows linearly in time and followed by a saturation for short-ranged tight-binding Hamiltonians. We show numerical evidence that for an initial Neel state the bound is maximum for tight-binding Hamiltonians as well as for the long-range hopping models. However, the increase of the bound is sub-linear in time for the later, in contrast to the linear growth observed for short-range models. The upper bound of the complexity in non-interacting fermionic lattice models is calculated, which grows linearly in time even beyond the saturation time of the lower bound, and finally, it also saturates.

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