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

TL;DR

This paper introduces twist-free and temporally encoded lattice surgery protocols for universal quantum computing, along with a decoder and optimized layouts, to improve efficiency and error correction in topological quantum codes.

Contribution

It presents a novel twist-free lattice surgery method, a decoder for spacelike and timelike errors, and a temporally encoded protocol to reduce quantum computation costs.

Findings

Decoder corrects spacelike and timelike errors effectively.

Twist-free protocol simplifies lattice surgery by removing twist defects.

Temporal encoding reduces runtimes and space-time costs.

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.