Reproduce “Spacetime codes of Clifford circuits” on OpenResearch

About this paper

Nicolas Delfosse, Adam Paetznick

A circuit-centric framework is presented for fault detection and correction in any Clifford circuit through the introduction of "outcome codes" and "spacetime codes". This methodology automates the design of fault tolerance mechanisms by formally reducing circuit fault correction to a standard stabilizer code decoding problem, thereby enabling the use of existing efficient LDPC decoders.

Key insights

• The set of all possible measurement outcome bit-strings in a Clifford circuit constitutes a linear code (the "outcome code"), for which checks can be efficiently computed in polynomial time.
• A "spacetime code," a stabilizer code, can be directly constructed from the checks of the outcome code, generalizing previous circuit-to-code transformations to arbitrary Clifford circuits including those with intermediate and multi-qubit measurements.
• The back-accumulator, describing backward fault propagation, is the adjoint of the accumulator (forward fault propagation) with respect to the Pauli commutator, providing a unified mathematical foundation for fault propagation.

Summary by alphaXiv.