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…
4 Citations
An Optimal Product-State Approximation for 2-Local Quantum Hamiltonians with Positive Terms
- PhysicsArXiv
- 2022
We resolve the approximability of the maximum energy of the Quantum Max Cut (QMC) problem using product states. A classical 0.498-approximation, using a basic semidefinite programming relaxation, is…
Application of the Level-$2$ Quantum Lasserre Hierarchy in Quantum Approximation Algorithms
- Computer ScienceICALP
- 2021
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
- Physics
- 2022
The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [14] 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
- Computer ScienceArXiv
- 2022
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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