The surface code with a twist
Theodore J. Yoder1 and Isaac H. Kim2
1Department of Physics, Massachusetts Institute of Technology
2IBM, Thomas J. Watson Research Center
Published: 2017-04-25, volume 1, page 2
Doi: https://doi.org/10.22331/q-2017-04-25-2
Citation: Quantum 1, 2 (2017).
The surface code is one of the most successful approaches to topological quantum error-correction. It boasts the smallest known syndrome extraction circuits and correspondingly largest thresholds. Defect-based logical encodings of a new variety called twists have made it possible to implement the full Clifford group without state distillation. Here we investigate a patch-based encoding involving a modified twist. In our modified formulation, the resulting codes, called triangle codes for the shape of their planar layout, have only weight-four checks and relatively simple syndrome extraction circuits that maintain a high, near surface-code-level threshold. They also use 25% fewer physical qubits per logical qubit than the surface code. Moreover, benefiting from the twist, we can implement all Clifford gates by lattice surgery without the need for state distillation. By a surgical transformation to the surface code, we also develop a scheme of doing all Clifford gates on surface code patches in an atypical planar layout, though with less qubit efficiency than the triangle code. Finally, we remark that logical qubits encoded in triangle codes are naturally amenable to logical tomography, and the smallest triangle code can demonstrate high-pseudothreshold fault-tolerance to depolarizing noise using just 13 physical qubits.
Featured image: The distance 7 triangle code uses 37 qubits (black dots) with Z-type stabilizer plaquettes (blue), X-type plaquettes (red), and mixed-type plaquettes (half-blue, half-red). Overlaid on the code are arrows indicating the order in which ancillas (gray) couple to the data to extract the syndrome.
@article{Yoder2017surfacecodetwist, doi = {10.22331/q-2017-04-25-2}, url = {https://doi.org/10.22331/q-2017-04-25-2}, title = {The surface code with a twist}, author = {Yoder, Theodore J. and Kim, Isaac H.}, journal = {{Quantum}}, issn = {2521-327X}, publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}}, volume = {1}, pages = {2}, month = apr, year = {2017} }
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