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SUMMARY:The Computational Complexity of the Ground State Energy Density Pr
 oblem - James Watson (UCL)
DTSTART:20190530T131500Z
DTEND:20190530T141500Z
UID:TALK124006@talks.cam.ac.uk
CONTACT:Johannes Bausch
DESCRIPTION:Over the past decade there has been a merging of condensed mat
 ter physics and computational complexity theory has given rise to the fiel
 d of Hamiltonian Complexity. The fundamental problem of study is approxima
 ting the ground state energy of many-body Hamiltonians (known as the local
  Hamiltonian problem). Other properties such as the form of the ground sta
 te subspace and excited state have also been characterised. However\, desp
 ite certain phenomena such a phase transitions happening only in the therm
 odynamic limit\, there has little work investigating this limit from a Ham
 iltonian complexity perspective. In this work we characterise the complexi
 ty of finding the ground state energy density in the thermodynamic limit a
 nd show that it is classically hard\, but quantumly is likely only of QMA-
 intermediate hardness. We also note that our result is the first complexit
 y result we know of that investigates how hard it is to improve the precis
 ion to which a value is known.
LOCATION:MR11\,  Centre for Mathematical Sciences\, Wilberforce Road\, Cam
 bridge
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