Inplace Access to the Surface Code Y Basis
Craig Gidney
Abstract
In this paper, I cut the cost of Y basis measurement and initialization in the surface code by nearly an order of magnitude. Fusing twist defects diagonally across the surface code patch reaches the Y basis in <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo fence="false" stretchy="false">&#x230A;</mml:mo><mml:mi>d</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>/</mml:mo></mml:mrow><mml:mn>2</mml:mn><mml:mo fence="false" stretchy="false">&#x230B;</mml:mo><mml:mo>+</mml:mo><mml:mn>2</mml:mn></mml:math> rounds, without leaving the bounding box of the patch and without reducing the code distance. I use Monte Carlo sampling to benchmark the performance of the construction under circuit noise, and to analyze the distribution of logical errors. Cheap inplace Y basis measurement reduces the cost of S gates and magic state factories, and unlocks Pauli measurement tomography of surface code qubits on space-limited hardware.