Quantum Error Correction via Hamiltonian Learning

          @misc{ pirsa_PIRSA:19070026,
            doi = {10.48660/19070026},
            url = {https://pirsa.org/19070026},
            author = {Greplova, Eliska},
            keywords = {Condensed Matter},
            language = {en},
            title = {Quantum Error Correction via Hamiltonian Learning},
            publisher = {Perimeter Institute},
            year = {2019},
            month = {jul},
            note = {PIRSA:19070026 see, \url{https://pirsa.org}}
          }
          

Abstract

Successful implementation of error correction is imperative for fault-tolerant quantum computing. At present, the toric code, surface code and related stabilizer codes are state of the art techniques in error correction. Standard decoders for these codes usually assume uncorrelated single qubit noise, which can prove problematic in a general setting. In this work, we use the knowledge of topological phases of modified toric codes to identify the underlying Hamiltonians for certain types of imperfections. The Hamiltonian learning is employed to adiabatically remove the underlying noise and approach the ideal toric code Hamiltonian. This approach can be used regardless of correlations. Our method relies on a neural network reconstructing the Hamiltonian given as input a linear amount of expectation values. The knowledge of the Hamiltonian offers significant improvement of standard decoding techniques Eliska Greplova, Agnes Valenti, Evert van Nieuwenburg, Sebastian Huber