Online Seminar: Asst. Prof. Josh Combes, CU Boulder, USA
Bosonic mode error correcting codes: Quantum oscillators with an infinite Hilbert space.
Quantum Computing with Rotation-Symmetric Bosonic Codes
SPEAKER: Assistant Professor Josh Combes
AFFILIATION: University of Colorado Boulder, CO, USA
HOSTED BY: A/Prof Chris Ferrie, UTS Centre for Quantum Software and Information
ABSTRACT:
Bosonic mode error correcting codes are error correcting codes where a qubit (or qudit) is encoded into one or multiple bosonic modes, i.e., quantum oscillators with an infinite Hilbert space.
In the first part of this talk I will give an introduction codes that have a phase space translation symmetry, i.e. the Gottesman-Kitaev-Preskill aka GKP, and codes that obey a rotation symmetry. Moreover, I will survey the impressive experimental progress on these codes.
The second part of the talk I focus on single-mode codes that obey rotation symmetry in phase space, such as the the well known Cat and Binomial codes. I will introduce a universal scheme for this class of codes based only on simple and experimentally well-motivated interactions. The scheme is fault-tolerant in the sense that small errors are guaranteed to remain small under the considered gates. I will also introduce a fault-tolerant error correction scheme based on cross-Kerr interactions and imperfect destructive phase measurement (e.g., a marginal of heterodyne). Remarkably, the error correction scheme approaches the optimal recovery map for Cat and Binomial codes when the auxiliary modes are error free. We numerically compute break-even thresholds under loss and dephasing, with ideal auxiliary systems.
If time permits I will discuss the search for optimized codes and progress towards genuine fault tolerance.