In this talk, I will discuss a general formalism for detecting and correcting faults in a Clifford circuit. The scheme is based on the observation that the set of all possible outcome bit-strings of a Clifford circuit is a linear code, which we call the outcome code. From the outcome code we construct a corresponding stabilizer code, the spacetime code. Our construction extends the circuit-to-code construction of Bacon, Flammia, Harrow and Shi, revisited recently by Gottesman. With this correspondence, we reduce the problem of correcting faults in a circuit to the well-studied problem of correcting errors in a stabilizer code.
Based on joint work with Adam Paetznick.
https://arxiv.org/abs/2304.05943
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