Tangling schedules eases hardware connectivity requirements for quantum error correction

Error corrected quantum computers have the potential to change the way we solve computational problems. Quantum error correction involves repeated rounds of carefully scheduled gates to measure the stabilisers of the code. A set of scheduling rules are typically imposed on the the order of gates to ensure the circuit can be rearranged into an equivalent circuit that can be easily seen to measure the stabilisers. In this work, we ask what if we break these rules and instead use tangled schedules circuits. We find that tangling schedules can generate long-range entanglement not accessible using nearest neighbour two-qubit gates. Our tangled schedules provide a new tool for building quantum error correction circuits and we explore applications to design new architectures for fault-tolerant quantum computers. Notably, we show that for the widely used Pauli-based model of computation (achieved by lattice surgery) this access to longer range entanglement can reduce the device connectivity requirements, without compromising on circuit depth.