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Implementation of a Toffoli Gate with Superconducting Circuits
Arkady Fedorov, Lars Steffen, Matthias Baur, M. P. da Silva, Andreas Wallraff
TL;DR
The paper demonstrates a Toffoli gate with three superconducting transmon qubits by exploiting the transmon’s third energy level to reduce implementation complexity and gate time. Full process tomography and Monte Carlo certification characterize the gate, yielding a fidelity of 68.5 ± 0.5%.
Problem
Implementing a Toffoli gate efficiently matters because existing two-level-system proposals require multiple elementary gates and the gate is relevant to quantum error correction.
Method
The authors use three transmon qubits coupled to a microwave resonator, exploiting the |2⟩ level through qubit-qutrit π-SWAP and 3π-SWAP operations, and characterize the process with tomography and Monte Carlo certification.
Results
68.5 ± 0.5% process fidelity was obtained using Monte Carlo process certification, alongside 70 ± 3% direct and 69% maximum-likelihood process-tomography estimates.
Takeaways & Limitations
Using additional transmon energy levels reduces total gate time and indicates a path toward practical quantum error correction as circuit coherence times improve.
Abstract
from arXiv · showhide
The quantum Toffoli gate allows universal reversible classical computation. It is also an important primitive in many quantum circuits and quantum error correction schemes. Here we demonstrate the realization of a Toffoli gate with three superconducting transmon qubits coupled to a microwave resonator. By exploiting the third energy level of the transmon qubit, the number of elementary gates needed for the implementation of the Toffoli gate, as well as the total gate time can be reduced significantly in comparison to theoretical proposals using two-level systems only. We characterize the performance of the gate by full process tomography and Monte Carlo process certification. The gate fidelity is found to be $68.5\pm0.5$%.