Department of Physics, ETH Zurich, CH-8093 Zurich, Switzerland.
Nature. 2011 Dec 14;481(7380):170-2. doi: 10.1038/nature10713.
The Toffoli gate is a three-quantum-bit (three-qubit) operation that inverts the state of a target qubit conditioned on the state of two control qubits. It makes universal reversible classical computation possible and, together with a Hadamard gate, forms a universal set of gates in quantum computation. It is also a key element in quantum error correction schemes. The Toffoli gate has been implemented in nuclear magnetic resonance, linear optics and ion trap systems. Experiments with superconducting qubits have also shown significant progress recently: two-qubit algorithms and two-qubit process tomography have been implemented, three-qubit entangled states have been prepared, first steps towards quantum teleportation have been taken and work on quantum computing architectures has been done. Implementation of the Toffoli gate with only single- and two-qubit gates requires six controlled-NOT gates and ten single-qubit operations, and has not been realized in any system owing to current limits on coherence. Here we implement a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator. By exploiting the third energy level of the transmon qubits, we have significantly reduced the number of elementary gates needed for the implementation of the Toffoli gate, relative to that required in theoretical proposals using only two-level systems. Using full process tomography and Monte Carlo process certification, we completely characterize the Toffoli gate acting on three independent qubits, measuring a fidelity of 68.5 ± 0.5 per cent. A similar approach to realizing characteristic features of a Toffoli-class gate has been demonstrated with two qubits and a resonator and achieved a limited characterization considering only the phase fidelity. Our results reinforce the potential of macroscopic superconducting qubits for the implementation of complex quantum operations with the possibility of quantum error correction.
托弗里门(Toffoli)门是一种三量子比特(three-qubit)操作,它根据两个控制量子比特的状态反转目标量子比特的状态。它使通用可逆经典计算成为可能,并且与 Hadamard 门一起,构成了量子计算中的通用门集。它也是量子纠错方案的关键元素。托弗里门已在核磁共振、线性光学和离子阱系统中实现。最近,超导量子比特的实验也取得了重大进展:已经实现了两量子比特算法和两量子比特过程层析成像,制备了三量子比特纠缠态,迈出了量子隐形传态的第一步,并开展了量子计算架构的工作。由于当前相干性的限制,仅使用单量子比特和双量子比特门实现托弗里门需要六个受控非门和十个单量子比特操作,尚未在任何系统中实现。在这里,我们使用耦合到微波谐振器的三个超导超导量子比特实现了托弗里门。通过利用超导量子比特的第三能级,我们相对于仅使用两能级系统的理论方案,显著减少了实现托弗里门所需的基本门数量。通过使用完整的过程层析成像和蒙特卡罗过程认证,我们完全表征了作用于三个独立量子比特的托弗里门,测量的保真度为 68.5±0.5%。类似的方法已经在使用两个量子比特和一个谐振器的情况下实现了托弗里门类门的特征,并且仅考虑相位保真度,就已经实现了有限的特征描述。我们的结果增强了宏观超导量子比特在实现复杂量子操作的潜力,并且有可能进行量子纠错。