Quantum Physics and Complexity
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Hamiltonian Complexity
Hamiltonians are the fundamental object of study in quantum mechanics; they give the energy, time-evolution and all other physical properties of a quantum system. Hamiltonian complexity seeks to understand the properties Hamiltonians from an information theory and computer science perspective. We ask whether many-body systems have metastable states? Can their ground state energies be efficiently computed, even with a quantum computer? Can we say anything about the phase transitions of a Hamiltonian? We can even show there are systems which have ‘undecidable’ properties – there is no algorithmic way of determining them. Hamiltonian complexity also plays a central role in adiabatic quantum computing, particularly in determining what Hamiltonians are “complex enough” for universal computation.