Fig. 3: A “dressed” QIRB circuit layer.

The bulk of a QIRB circuit consists of a sequence of “dressed” layers \(\{{\tilde{L}}_{i}\}\), each composed of three sublayers: (i) li,1, (ii) li,2, and (iii) li,3. The middle sublayer, li,2 is an Ω-distributed circuit layer, while the other two sublayers are specially crafted. Ideally, the state of the processor before the dressed layer \({\tilde{L}}_{i}\) is stabilized by the Pauli si−1. The first sublayer, li,1 is designed to rotate the state of the processor into an eigenstate of \({s}^{{{{\rm{pre}}}}}\), whose support, \({s}_{{{{\rm{meas}}}}}^{{{{\rm{pre}}}}}\), on the measured qubits in li,2 is a tensor-product of Pauli-Z and I operators. Likewise, li,3 is designed to (ideally) rotate the post-measurement state of the processor into an eigenstate of si, whose support on the measured qubits in li,2 is a uniform randomly chosen m-qubit Pauli operator, \({s}_{{{{\rm{meas}}}}}^{i}\).