Abstract
Experimental implementation of the surface code will be a significant milestone for quantum computing. We develop a circuit and a decoder targeted for near-term implementation of a distance-3 surface code. We simulate the code under amplitude and phase damping and compare the threshold to a Pauli-twirl approximation. We find that the approximation yields a pessimistic threshold estimate. From numerical Monte Carlo simulations, we identify the gate and measurement speeds required to achieve reliable error correction. For superconductor devices, a qubit encoded in a 17-qubit surface code demonstrates a lower error rate than an unencoded qubit assuming gate times of 5–40 ns and times of at least 1–2 . If ns, the difference is significant and can be experimentally measured, allowing near-term implementation and verification of a small surface code. For ion trap devices, gates times of 1 and ms admit measurable differences in error rate.
8 More- Received 13 June 2014
DOI:https://doi.org/10.1103/PhysRevA.90.062320
©2014 American Physical Society