Error suppression for Hamiltonian-based quantum computation

In this talk, I will present recent results on using quantum codes for error suppression. In particular, I present general conditions for quantum error suppression for Hamiltonian-based quantum computation using subsystem codes. This involves encoding the Hamiltonian performing the computation using an error detecting subsystem code and the addition of a penalty term that commutes with the encoded Hamiltonian. I illustrate the power of subsystem-based error suppression with several examples of two-local constructions for protection against local errors, which circumvent an earlier no-go theorem about two-local commuting Hamiltonians. I also discuss the generalization of the quantum error suppression results of Jordan, Farhi, and Shor to arbitrary Markovian dynamics. In this setting, we show that it is possible to suppress the initial decay out of the encoded ground state with an energy penalty strength that grows only logarithmically in the system size, at a fixed temperature.

Joint work with Daniel Lidar
PRL 118, 030504 (2017)
PRA 95, 032302 (2017)