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 stabilizers of a code. A set of scheduling rules is typically imposed on the order of gates to ensure that the circuit can be rearranged into an equivalent circuit that can be easily seen to measure the stabilizers. In this work, we ask what would happen if we break these rules and instead use circuit schedules that we describe as tangled. We find that tangling schedules generates long-range entanglement not accessible using nearest-neighbor two-qubit gates. Our tangled-schedule method provides 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.