



01739nas a2200121   4500008004100000245004000041210004000081260001300121520140700134100001701541700002201558856003701580       2024                        eng d00aError Correction in Dynamical Codes0 aError Correction in Dynamical Codes  c3/7/20243 a<p>We ask what is the general framework for a quantum error correcting code that is defined by a sequence of measurements. Recently, there has been much interest in Floquet codes and space-time codes. In this work, we define and study the distance of a dynamical code. This is a subtle concept and difficult to determine: At any given time, the system will be in a subspace which forms a quantum error-correcting code with a given distance, but the full error correction capability of that code may not be available due to the schedule of measurements associated with the code. We address this challenge by developing an algorithm that tracks information we have learned about the error syndromes through the protocol and put that together to determine the distance of a dynamical code, in a non-fault-tolerant context. We use the tools developed for the algorithm to analyze the initialization and masking properties of a generic Floquet code. Further, we look at properties of dynamical codes under the constraint of geometric locality with a view to understand whether the fundamental limitations on logical gates and code parameters imposed by geometric locality for traditional codes can be surpassed in the dynamical paradigm. We find that codes with a limited number of long range connectivity will not allow non-Clifford gates to be implemented with finite depth circuits in the 2D setting.</p>1 aFu, Xiaozhen1 aGottesman, Daniel  uhttps://arxiv.org/abs/2403.04163