Low-overhead spacetime-code checks for deeper circuits

Determine whether deeper one-dimensional doped Clifford circuits admit low-overhead spacetime-code checks with sufficiently large detecting regions and suitable stabilizer-compatible doping locations under the connectivity and scheduling constraints of the target hardware architecture.

Background

The paper shows that increasing the circuit depth raises the tensor-network simulation cost approximately as 2^{\lceil d/2\rceil}, but also increases the number of physical CZ gates and therefore the accumulated experimental error. Deeper circuits must consequently be evaluated not only for classical simulation hardness but also for whether their error-detection mechanisms remain effective.

The IBM doped Clifford experiment uses spacetime-code postselection to detect errors. For deeper circuits, the unresolved issue is whether comparable low-overhead checks can be designed while maintaining sufficiently large detecting regions and appropriate locations for non-Clifford doping, given the connectivity and gate-scheduling limitations of the target hardware.