Improved approximation algorithms for bounded-degree local Hamiltonians

@article{Anshu2021ImprovedAA,
  title={Improved approximation algorithms for bounded-degree local Hamiltonians},
  author={Anurag Anshu and David Gosset and Karen J. Morenz Korol and Mehdi Soleimanifar},
  journal={ArXiv},
  year={2021},
  volume={abs/2105.01193}
}
Anurag Anshu, David Gosset, Karen J. Morenz Korol, and Mehdi Soleimanifar 1 Department of EECS & Challenge Institute for Quantum Computation, University of California, Berkeley, USA and Simons Institute for the Theory of Computing, Berkeley, California, USA. 2 Department of Combinatorics and Optimization and Institute for Quantum Computing, University of Waterloo, Canada 3 Department of Chemistry, University of Toronto, Canada and 4 Center for Theoretical Physics, Massachusetts Institute of… 
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4 Citations

4 Citations

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This work provides the first ever use of the level-2 hierarchy in an approximation algorithm for a particular QMA-complete problem, so-called Quantum Max Cut, and indicates that higher levels of the quantum Lasserre Hierarchy may be very useful tools in the design of approximation algorithms for Q MA-complete problems.
A construction of Combinatorial NLTS
The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [FH14] posits that there exist families of Hamiltonians with all low energy states of high complexity (with complexity…
The Quantum and Classical Streaming Complexity of Quantum and Classical Max-Cut
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The first application of Boolean Fourier analysis methods to sequential one-way quantum communication, in which each player receives a quantum message from the previous player, and can then perform arbitrary quantum operations on it before sending it to the next.

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