Implementation of a Toffoli gate with superconducting circuits


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 computation1 possible and, together with a Hadamard gate2, forms a universal set of gates in quantum computation. It is also a key element in quantum error correction schemes3,4,5,6,7. The Toffoli gate has been implemented in nuclear magnetic resonance3, linear optics8 and ion trap systems9. Experiments with superconducting qubits have also shown significant progress recently: two-qubit algorithms10 and two-qubit process tomography have been implemented11, three-qubit entangled states have been prepared12,13, first steps towards quantum teleportation have been taken14 and work on quantum computing architectures has been done15. Implementation of the Toffoli gate with only single- and two-qubit gates requires six controlled-NOT gates and ten single-qubit operations16, 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 approach15 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 correction17.

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Figure 1: Circuit diagram of the Toffoli gate.
Figure 2: Truth table of the Toffoli gate.
Figure 3: Process tomography of the Toffoli gate.


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We thank S. Filipp, A. Blais for useful discussions and K. Pakrouski for his contributions in early stages of the experimental work. This work was supported by the Swiss National Science Foundation, the EU IP SOLID and ETH Zurich.

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A.F. developed the scheme to realize the Toffoli gate. L.S., A.F. and M.B. carried out the experiments and analysed the data. L.S. designed and fabricated the superconducting resonator. A.F. and M.B. designed and fabricated the qubits. M.P.d.S. provided general theoretical support and specific advice on using Monte Carlo process certification. A.F., L.S., M.B. and A.W. contributed to setting up and maintaining the experiment. A.F., A.W. and L.S. wrote the manuscript. All authors commented on the manuscript. A.W. supervised the project.

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Correspondence to A. Fedorov or A. Wallraff.

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The authors declare no competing financial interests.

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Fedorov, A., Steffen, L., Baur, M. et al. Implementation of a Toffoli gate with superconducting circuits. Nature 481, 170–172 (2012).

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