meQuanics - QSI@UTS Seminar Series - S17 - Josh Combes (University of Colorado)

During this time of lockdown, the centre for quantum software and information (QSI) at the University of Technology Sydney has launched an online seminar series.  With talks once or twice a week from leading researchers in the field, meQuanics is supporting this series by mirroring the audio from each talk.  I would encourage if you listen to this episode, to visit and subscribe to the UTS:QSI YouTube page to see each of these talks with the associated slides to help it make more sense.

https://youtu.be/L_VldJN_k-4

Bosonic mode error correcting codes: Quantum oscillators with an infinite Hilbert space  

TITLE: 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.  

Joint work with Arne Grimsmo, USyd and Ben Baragiola, RMIT