Understanding logical channels graphically: a case study with the XYZ ruby code

Title: Understanding logical channels graphically: a case study with the XYZ ruby code

Speaker: Julio Carlos Magdalena De La Fuente, PhD candidate, Freie Universtät Berlin

Abstract:

Finding quantum error-correcting (QEC) protocols constitutes one of the biggest challenges in developing a fault-tolerant quantum computer. To devise these protocols, one typically considers subspaces in which to encode logical states to protect the logical information against the noise happening naturally on a device. Recently, a new dynamical perspective emerged in which time-dynamics are also taken into account. This allows for a more flexible design of error-correcting protocols since the logical encoding is allowed to change over time. Specifically, circuits take a center stage and the analysis of errors on that circuits constitutes a non-trivial but important task when devising and understanding error-correcting protocols.

In my talk, I will present a graphical tool to analyse Clifford circuits with respect to their error-correcting properties based on a tensor-network representation of the circuits. Using these methods, I present a new “Floquet code”, a protocol based on periodic measurements of (non-commuting) low-weight Pauli operators which we call the XYZ ruby code. In our formalism many aspects of QEC analysis can be unified and I will argue that it offers a helpful perspective beyond the circuit-based error-correction. Specifically, the tensor-network representation makes an explicit connection to fault-tolerant measurement-based error-correction schemes.