We demonstrate how to use lattice surgery to enact a universal set of fault-tolerant quantum operations with color codes. Along the way, we also improve existing surface-code lattice-surgery methods. Lattice-surgery methods use fewer qubits and the same time or less than associated defect-braiding methods. Furthermore, per code distance, color-code lattice surgery uses approximately half the qubits and the same time or less than surface-code lattice surgery. Color-code lattice surgery can also implement the Hadamard and phase gates in a single transversal step---much faster than surface-code lattice surgery can. Against uncorrelated circuit-level depolarizing noise, color-code lattice surgery uses fewer qubits to achieve the same degree of fault-tolerant error suppression as surface-code lattice surgery when the noise rate is low enough and the error suppression demand is high enough.
@article{arxiv.1407.5103,
title = {Quantum computing by color-code lattice surgery},
author = {Andrew J. Landahl and Ciaran Ryan-Anderson},
journal= {arXiv preprint arXiv:1407.5103},
year = {2014}
}
Comments
13 pages, 19 figures. Video of talk on paper at http://pirsa.org/14070006