The core principle of QEC is to flag physical errors while not destabilizing the underlying logical quantum information. QEC circuits contain measurements that can localize physical errors to a "detecting region", containing a few qubits over a few QEC cycles. In other words, when an error is flagged, the detecting region specifies where and when that error could have occured. By combining many overlapping detecting regions, we can narrow down the location of physical errors and prevent any impact on the logical quantum information. In standard surface code circuits, these detecting regions form a square tiling.
Error correction circuits deform these detecting regions in spacetime. In the standard code, the detecting region tiling always returns to its starting point. In dynamic codes, the tiling of detecting regions changes each cycle. As expanded upon below, we demonstrated three new circuits featuring this periodic re-tiling of the detecting regions: hexagonal, walking, and iSWAP. Each of these three circuits solves a unique challenge in QEC: hexagonal circuits reduce the number of couplers, walking circuits limit non-computation errors, and iSWAP circuits allow use of non-standard two-qubit entangling gates. Together, these demonstrations open the door to a variety of dynamic circuits, including those that avoid dropouts.
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