Experimental Demonstration of High-Fidelity Logical Magic States from Code Switching

Preparation of high-fidelity logical magic states has remained as a necessary but daunting step towards building a large-scale fault-tolerant quantum computer. One approach is to fault-tolerantly prepare a magic state in one code and then switch to another, a method known as code switching. We experimentally demonstrate this protocol on an ion-trap quantum processor, yielding a logical magic state encoded in an error-correcting code with state-of-the-art logical fidelity. Our experiment is based on the first demonstration of code switching between color codes, from the fifteen-qubit quantum Reed-Muller code to the seven-qubit Steane code. We prepare an encoded magic state in the Steane code with 82.58% probability, with an infidelity of at most <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>5.1</a:mn><a:mo stretchy="false">(</a:mo><a:mn>2.7</a:mn><a:mo stretchy="false">)</a:mo><a:mo>×</a:mo><a:msup><a:mn>10</a:mn><a:mrow><a:mo>−</a:mo><a:mn>4</a:mn></a:mrow></a:msup></a:math>. The reported infidelity is lower than the leading infidelity of the physical operations utilized in the protocol by a factor of at least 2.7, indicating the quantum processor is below the pseudothreshold. Furthermore, we create two copies of the magic state in the same quantum processor and perform a logical Bell basis measurement for a sample-efficient certification of the encoded magic state. The high-fidelity magic state can be combined with the already-demonstrated fault-tolerant Clifford gates, state preparation, and measurement of the 2D color code, completing a universal set of fault-tolerant computational primitives with logical error rates equal or better than the physical two-qubit error rate.