NLTS Hamiltonians from good quantum codes


Anshu, A. (2022). NLTS Hamiltonians from good quantum codes. Perimeter Institute. https://pirsa.org/22090094


Anshu, Anurag. NLTS Hamiltonians from good quantum codes. Perimeter Institute, Sep. 28, 2022, https://pirsa.org/22090094


          @misc{ pirsa_PIRSA:22090094,
            doi = {10.48660/22090094},
            url = {https://pirsa.org/22090094},
            author = {Anshu, Anurag},
            keywords = {Quantum Information},
            language = {en},
            title = {NLTS Hamiltonians from good quantum codes},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {sep},
            note = {PIRSA:22090094 see, \url{https://pirsa.org}}

Anurag Anshu Harvard University


The NLTS (No Low-Energy Trivial State) conjecture of Freedman and Hastings [2014] posits that there exist families of Hamiltonians with all low energy states of non-trivial complexity (with complexity measured by the quantum circuit depth preparing the state). Our recent work https://arxiv.org/abs/2206.13228 (with Nikolas Breuckmann and Chinmay Nirkhe) proves this conjecture by showing that the recently discovered families of constant-rate and linear-distance QLDPC codes correspond to NLTS local Hamiltonians. This talk will provide background on the conjecture, its relevance to quantum many-body physics and quantum complexity theory, and touch upon the proof techniques.

Zoom link: https://pitp.zoom.us/j/94224635225?pwd=SUovNXA3MWlkRUJlcTIxV0pLQzQxdz09