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Sponsors

Pauli Center for Theoretical Studies

The Swiss National Science Foundation

ETH Zurich (Computer Science and Physics Department)

Quantum Science and Technology

CQT Singapore

QAP European Project

Sandia National Laboratories

Institute for Quantum Computing

id Quantique

Local Hamiltonians in quantum computation

Daniel Nagaj, Slovak Academy of Sciences

This talk is about two Hamiltonian Complexity questions. First, how hard is it to compute the ground state properties of quantum systems with local Hamiltonians? Second, which spin systems with time-independent (and perhaps, translationally-invariant) local interactions could be used for universal computation?

Aiming at a participant without previous understanding of complexity theory, we will discuss two locally-constrained quantum problems: k-local Hamiltonian and quantum k-SAT. Learning the techniques of Kitaev and others along the way, our first goal is the understanding of QMA-completeness of these problems. The second goal is an up-to-date review of results in this field, including QMA-complete problems with restricted geometry of interactions and new universal constructions with a connection to Adiabatic Quantum Computing.