Quantum Computational Matter

          @misc{ pirsa_PIRSA:11100070,
            doi = {10.48660/11100070},
            url = {https://pirsa.org/11100070},
            author = {Bartlett, Stephen},
            keywords = {},
            language = {en},
            title = {Quantum Computational Matter},
            publisher = {Perimeter Institute},
            year = {2011},
            month = {oct},
            note = {PIRSA:11100070 see, \url{https://pirsa.org}}
          }
          

Abstract

Low-temperature phases of strongly-interacting quantum many-body systems can exhibit a range of exotic quantum phenomena, from superconductivity to fractionalized particles. One exciting prospect is that the ground or low-temperature thermal state of an engineered quantum system can function as a quantum computer. The output of the computation can be viewed as a response, or 'susceptibility', to an applied input (say in the form of a magnetic field). For this idea to be sensible, the usefulness of a ground or low-temperature thermal state for quantum computation cannot be critically dependent on the details of the system's Hamiltonian; if so, engineering such systems would be difficult or even impossible. A much more powerful result would be the existence of a robust ordered phase which is characterised by its ability to perform quantum computation. I'll discuss some recent results on the existence of such a quantum computational phase of matter. I'll outline some positive results on a phase of a toy model that allows for quantum computation, including a recent result that provides sufficient conditions for fault-tolerance. I'll also introduce a more realistic model of antiferromagnetic spins, and demonstrate the existence of a quantum computational phase in a two-dimensional system. Together, these results reveal that the characterisation of quantum computational matter has a rich and complex structure, with connections to renormalisation and recently-proposed concepts of 'symmetry-protected topological order'.