Implementing the surface code using time-dynamic circuits (Part 1)

Quantum Error Correction (QEC) below the surface code threshold has been realized using repeated application of circuits that measure stabilizers. These circuits can be understood using the concept of detecting regions, which track stabilizers as they are deformed by the circuit. Recently, using these detecting regions for circuit design, new families of surface code circuits have been proposed that allow for tradeoffs in hardware, such as the use of iSWAP gates instead of CZ gates, the periodic exchange of data and measure qubits, and operation of the surface code on a hexagonal lattice. In the first part of this two-part talk, we introduce these circuits and discuss their realization on state-of-the-art superconducting hardware.