Realization of three-qubit quantum error correction with superconducting circuits

A controlled-controlled NOT, or Toffoli, gate is used to develop a fast, high-fidelity, three-qubit error correction protocol with the potential to correct arbitrary single-qubit errors. Quantum computing on the right track Efforts to harness the power of quantum computers are complicated by the fact that they are more prone to errors than classical computers. Such errors can be detected and corrected without affecting computational capability by using quantum error-correcting codes, the simplest of which are three-qubit codes. This paper reports the implementation of three-qubit quantum error correction using superconducting circuits. Phase- and bit-flip errors are corrected with high fidelity using a Toffoli gate, a logic gate that makes universal reversible classical computation possible. The work serves to establish the conceptual components of a more complex device that could correct arbitrary single-qubit errors. Quantum computers could be used to solve certain problems exponentially faster than classical computers, but are challenging to build because of their increased susceptibility to errors. However, it is possible to detect and correct errors without destroying coherence, by using quantum error correcting codes 1 . The simplest of these are three-quantum-bit (three-qubit) codes, which map a one-qubit state to an entangled three-qubit state; they can correct any single phase-flip or bit-flip error on one of the three qubits, depending on the code used 2 . Here we demonstrate such phase- and bit-flip error correcting codes in a superconducting circuit. We encode a quantum state 3 , 4 , induce errors on the qubits and decode the error syndrome—a quantum state indicating which error has occurred—by reversing the encoding process. This syndrome is then used as the input to a three-qubit gate that corrects the primary qubit if it was flipped. As the code can recover from a single error on any qubit, the fidelity of this process should decrease only quadratically with error probability. We implement the correcting three-qubit gate (known as a conditional-conditional NOT, or Toffoli, gate) in 63 nanoseconds, using an interaction with the third excited state of a single qubit. We find 85 ± 1 per cent fidelity to the expected classical action of this gate, and 78 ± 1 per cent fidelity to the ideal quantum process matrix. Using this gate, we perform a single pass of both quantum bit- and phase-flip error correction and demonstrate the predicted first-orde