Stabilizer measurement decoding using additional edges to identify errors caused by cross-talk

A method, comprising:

• receiving a syndrome measurement history for syndrome measurements of a surface code comprising qubits implemented using mechanical resonators, wherein multiplexed control circuits control respective sets of the mechanical resonators;
• determining edges between syndrome measurements for respective ones of the qubits of the surface code for, or across, one or more rounds of the syndrome measurements, wherein the determined edges are selected from a group of supported edges comprising:
• two-dimensional cross-edges that identify correlated errors arising from spurious photon dissipation processes of a given one of the multiplexed control circuits that leads to cross-talk between storage modes of a given respective set of the mechanical resonators controlled by the given one of the multiplexed control circuits;
• and
• three-dimensional additional space-time correlated edges that identify space time errors arising from spurious photon dissipation processes of the given one or another given one of the multiplexed control circuits that leads to cross-talk between storage modes of a given respective set of the mechanical resonators controlled by the given multiplexed control circuit;
• determining weightings for the respective types of edges;
• and
• applying a minimum weight perfect matching (MWPM) to the weighted edges to decode the syndrome measurement history for the surface code.

A non-transitory, computer-readable medium, storing program instructions, that when executed on or across one or more processors, cause the one or more processors to:

• receive a syndrome measurement history for syndrome measurements of a surface code comprising qubits implemented using mechanical resonators, wherein multiplexed control circuits control respective sets of the mechanical resonators;
• determine edges between syndrome measurements for respective ones of the qubits of the surface code for, or across, one or more rounds of the syndrome measurements, wherein the determined edges are selected from a group of supported edges comprising:
• two-dimensional cross-edges that identify correlated errors arising from spurious photon dissipation processes of a given one of the multiplexed control circuits that leads to cross-talk between storage modes of a given respective set of the mechanical resonators controlled by the given one of the multiplexed control circuits;
• and
• three-dimensional additional space-time correlated edges that identify space time errors arising from spurious photon dissipation processes of the given one or another given one of the multiplexed control circuits that leads to cross-talk between storage modes of a given respective set of the mechanical resonators controlled by the given multiplexed control circuit;
• determine weightings for the respective types of edges;
• and
• apply a minimum weight perfect matching (MWPM) to the weighted edges to decode the syndrome measurement history for the surface code.