Universal quantum computing with twist-free and temporally encoded lattice surgery

Abstract

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. Afterwards, we compute logical failure rates of a lattice surgery protocol for a biased circuit-level noise model. We then provide a new 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 runtimes 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 which is compatible with the other techniques mentioned above.

arXiv comment23 pages, 18 figures, comments welcome! V2 includes 2 added figures and fixed typos. V3 fixed a typo in Eq. (10)

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