Low overhead quantum computation using lattice surgery
Abstract
When calculating the overhead of a quantum algorithm made faulttolerant using the surface code, many previous works have used defects and braids for logical qubit storage and state distillation. In this work, we show that lattice surgery reduces the storage overhead by over a factor of 4, and the distillation overhead by nearly a factor of 5, making it possible to run algorithms with $10^8$ T gates using only $3.7\times 10^5$ physical qubits capable of executing gates with error $p\sim 10^{3}$. These numbers strongly suggest that defects and braids in the surface code should be deprecated in favor of lattice surgery.
 Publication:

arXiv eprints
 Pub Date:
 August 2018
 arXiv:
 arXiv:1808.06709
 Bibcode:
 2018arXiv180806709F
 Keywords:

 Quantum Physics
 EPrint:
 15 pages, 26 figures, download source for algorithm overhead calculation spreadsheet and SketchUp 3D model of twolevel state distillation. V2: Source actually contains spreadsheet and no unnecessary files. Spreadsheet and model in anc/ directory in source. V3: minor bug fixed in spreadsheet, runtimes now slightly longer. V4: minor bug fixed in logical Hadamard