Quantum computers promise to solve certain problems exponentially faster thanpossible classically but are challenging to build because of their increasedsusceptibility to errors. Remarkably, however, it is possible to detect andcorrect errors without destroying coherence by using quantum error correctingcodes [1]. The simplest of these are the three-qubit codes, which map aone-qubit state to an entangled three-qubit state and can correct any singlephase-flip or bit-flip error of one of the three qubits, depending on the codeused [2]. Here we demonstrate both codes in a superconducting circuit byencoding a quantum state as previously shown [3,4], inducing errors on allthree qubits with some probability, and decoding the error syndrome byreversing the encoding process. This syndrome is then used as the input to athree-qubit gate which corrects the primary qubit if it was flipped. As thecode can recover from a single error on any qubit, the fidelity of this processshould decrease only quadratically with error probability. We implement thecorrecting three-qubit gate, known as a conditional-conditional NOT (CCNot) orToffoli gate, using an interaction with the third excited state of a singlequbit, in 63 ns. We find 85\pm1% fidelity to the expected classical action ofthis gate and 78\pm1% fidelity to the ideal quantum process matrix. Using it,we perform a single pass of both quantum bit- and phase-flip error correctionwith 76\pm0.5% process fidelity and demonstrate the predicted first-orderinsensitivity to errors. Concatenating these two codes and performing them on anine-qubit device would correct arbitrary single-qubit errors. When combinedwith recent advances in superconducting qubit coherence times [5,6], this maylead to scalable quantum technology.
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