Spacetime circuit code[1–3] 

Qubit stabilizer code used to correct faults in Clifford circuits, i.e., circuits up made of Clifford gates and Pauli measurements. The code utilizes redundancy in the measurement outcomes of a circuit to correct circuit faults, which correspond to Pauli errors of the code.

The structure of the Clifford circuit yields correlations between the circuit's possible measurement outcomes. The set of outcomes can be made into a classical binary linear code called the outcome code [3; Corr. 2]. The spacetime circuit code is defined such that its error syndromes can be backpropagated to obtain the parity checks of the outcome code. In other words, both codes have the same set of parity check outcomes.

More technically, given an \([m,k]\) outcome code associated with an \(n\)-qubit circuit of depth \(\Delta\) with \(m\) measurements and \(2^k\) outcomes, the corresponding spacetime circuit code is an \([[ n (\Delta + 1), n (\Delta + 1) - (m - k) ]]\) code [3; Thm. 2].

The spacetime circuit code is the stabilizer code corresponding to the subsystem codes of earlier works [1,2], which dealt with specific families of Clifford circuits. The general case was developed in Ref. [3].

Many features of the spacetime circuit formalism can be understood through ZX calculus [4].