Quantum computational phases of matter: measurement-based quantum computing in the Haldane phase

          @misc{ pirsa_PIRSA:09110025,
            doi = {10.48660/09110025},
            url = {https://pirsa.org/09110025},
            author = {Bartlett, Stephen},
            keywords = {Quantum Information},
            language = {en},
            title = {Quantum computational phases of matter: measurement-based quantum computing in the Haldane phase},
            publisher = {Perimeter Institute},
            year = {2009},
            month = {nov},
            note = {PIRSA:09110025 see, \url{https://pirsa.org}}
          }
          

Abstract

A recent breakthrough in quantum computing has been the realization that quantum computation can proceed solely through single-qubit measurements on an appropriate quantum state. One exciting prospect is that the ground or low-temperature thermal state of an interacting quantum many-body system can serve as such a resource state for quantum computation. The system would simply need to be cooled sufficiently and then subjected to local measurements. It would be unfortunate, however, if the usefulness of a ground or low-temperature thermal state for quantum computation was 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 characterized by the ability to perform measurement-based quantum computation. I’ll discuss some recent results on the existence of such a computational phase of matter. I’ll first outline some positive results on a phase of a toy model that contains the cluster state. Then, in a realistic model of coupled spin-1 particles, I’ll demonstrate the existence of a computational phase. This result is obtained by using a local measurement sequence to “renormalize” the state to a computationally-universal fixed point. Together, these results reveal that the characterization of computational phases of matter has a rich, complex structure – one which is still poorly understood. Joint work with Gavin Brennen, Akimasa Miyake, and Joseph Renes.