# A polynomial-time algorithm for ground states of spin trees

@article{Abrahamsen2019APA, title={A polynomial-time algorithm for ground states of spin trees}, author={Nilin Abrahamsen}, journal={arXiv: Quantum Physics}, year={2019} }

We prove that the ground states of a local Hamiltonian satisfy an area law and can be computed in polynomial time when the interaction graph is a tree with discrete fractal dimension $\beta<2$. This condition is met for generic trees in the plane and for established models of hyperbranched polymers in 3D. This work is the first to prove an area law and exhibit a provably polynomial-time classical algorithm for local Hamiltonian ground states beyond the case of spin chains. Our algorithm outputs…

## 5 Citations

Sub-exponential algorithm for 2D frustration-free spin systems with gapped subsystems

- Mathematics, Physics
- 2020

We show that in the setting of the subvolume law of [Anshu, Arad, Gosset '19] for 2D locally gapped frustration-free spin systems there exists a randomized classical algorithm which computes the…

Sharp implications of AGSPs for degenerate ground spaces

- Physics
- 2020

We generalize the `off-the-rack' AGSP$\Rightarrow$entanglement bound implication of [Arad, Landau, and Vazirani '12] from unique ground states to degenerate ground spaces. Our condition…

Area law of noncritical ground states in 1D long-range interacting systems

- Medicine, PhysicsNature communications
- 2020

This work shows that for generic non-critical one-dimensional ground states with locally bounded Hamiltonians, the area law robustly holds without any corrections, even under long-range interactions, which guarantees an efficient description of ground states by the matrix-product state in experimentally relevant long- range systems, which justifies the density-matrix renormalization algorithm.

From communication complexity to an entanglement spread area law in the ground state of gapped local Hamiltonians

- Computer Science, PhysicsArXiv
- 2020

This work construction provides evidence for a conjecture in physics by Li and Haldane on the entanglement spectrum of lattice Hamiltonians, and uses recent advances in Hamiltonian simulation algorithms along with quantum phase estimation to give a new construction for an approximate ground space projector over arbitrary interaction graphs.

Improved Thermal Area Law and Quasilinear Time Algorithm for Quantum Gibbs States

- Physics, Mathematics
- 2020

One of the most fundamental problems in quantum many-body physics is the characterization of correlations among thermal states. Of particular relevance is the thermal area law, which justifies the…

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