Snakes on a Plane: mobile, low dimensional logical qubits on a 2D surface

Abstract: Recent demonstrations indicate that silicon-spin QPUs will be able to shuttle physical qubits rapidly and with high fidelity - a desirable feature for maximising logical connectivity, supporting new codes, and routing around damage. However it may seem that shuttling at the logical level is unwise: static defects in the device may 'scratch' a logical qubit as it passes, causing correlated errors to which the code is highly vulnerable. Here we explore an architecture where logical qubits are 1D strings ('snakes') which can be moved freely over a planar latticework. Possible scratch events are inferred via monitor qubits and the complimentary gap; if deemed a risk, remarkably the shuttle process can be undone in a way that negates any corruption. Interaction between logical snakes is facilitated by a semi-transversal method. We obtain encouraging estimates for the tolerable levels of shuttling-related imperfections.