Universal Quantum Computing with Twist-Free and Temporally Encoded Lattice Surgery

Lattice-surgery protocols allow for the efficient implementation of universal gate sets with two-dimensional topological codes where qubits are constrained to interact with one another locally. In this work, we first introduce a decoder capable of correcting spacelike and timelike errors during lattice-surgery protocols. Subsequently, we compute the logical failure rates of a lattice-surgery protocol for a biased circuit-level noise model. We then provide a protocol for performing twist-free lattice surgery, where we avoid twist defects in the bulk of the lattice. Our twist-free protocol eliminates the extra circuit components and gate-scheduling complexities associated with the measurement of higher weight stabilizers when using twist defects. We also provide a protocol for temporally encoded lattice surgery that can be used to reduce both the run times and the total space-time costs of quantum algorithms. Lastly, we propose a layout for a quantum processor that is more efficient for rectangular surface codes exploiting noise bias and that is compatible with the other techniques mentioned above.