Code switching revisited: Low-overhead magic state preparation using color codes

We propose a protocol to prepare a high-fidelity magic state on a two-dimensional (2D) color code using a three-dimensional (3D) color code. Our method modifies the known code-switching protocol with (1) a recently discovered transversal gate between the 2D and the 3D code and (2) a judicious use of flag-based postselection. We numerically demonstrate that these modifications lead to a significant improvement in the fidelity of the magic state. For instance, subjected to a uniform circuit-level noise of <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:msup><a:mn>10</a:mn><a:mrow><a:mo>−</a:mo><a:mn>3</a:mn></a:mrow></a:msup></a:math> (excluding idling noise), our code-switching protocol yields a magic state encoded in the distance-3 2D color code with a logical infidelity of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mn>4.6</b:mn><b:mo>×</b:mo><b:msup><b:mn>10</b:mn><b:mrow><b:mo>−</b:mo><b:mn>5</b:mn></b:mrow></b:msup><b:mo>±</b:mo><b:mn>1.6</b:mn><b:mo>×</b:mo><b:msup><b:mn>10</b:mn><b:mrow><b:mo>−</b:mo><b:mn>5</b:mn></b:mrow></b:msup></b:mrow></b:math> (quantified by an error-corrected logical state tomography) with an <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mrow><c:mn>84</c:mn><c:mo>%</c:mo></c:mrow></c:math> of acceptance rate. Used in conjunction with a postselection approach, extrapolation from a polynomial fit suggests a fidelity improvement to <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mn>5.1</d:mn><d:mo>×</d:mo><d:msup><d:mn>10</d:mn><d:mrow><d:mo>−</d:mo><d:mn>7</d:mn></d:mrow></d:msup></d:mrow></d:math> for the same code. Our protocol is aimed for architectures that allow nonlocal connectivity and should be readily implementable in near-term devices. Finally, we also present a simulation technique akin to an extended stabilizer simulator which effectively incorporates the non-Clifford <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>T</e:mi></e:math> gate, that permits to simulate the protocol without resorting to a resource intensive state-vector simulation.