High-fidelity and robust quantum gates for superconducting transmon qubits: Against intrinsic errors and decoherence noise

To realize practical quantum computation, the ability to precisely control qubit systems is a prerequisite. To increase the reliable circuit depth on noisy intermediate-scale quantum (NISQ) computing devices, or achieve the ultimate goal of error-corrected fault-tolerant quantum computation, constructing high-fidelity and robust quantum gates to meet the stringent computing requirements (beyond the fault-tolerant error threshold) is an important and timely issue. Besides, as the size of the quantum processors scales up, the cross-talk effects from the neighboring qubits will get worse, and the gate robustness against the noises, the uncertainties of system parameters, and the imprecise pulse calibrations will become more important. The simple or intuitive control pulses implemented in experiments, which often do not take these factors into accounts, could not achieve very accurate gates. On the other hand, optimal control methods have the potential ability to construct high-fidelity and robust quantum gates tackling these multiple issues simultaneously. We apply the robust control method [1,2] to construct smooth optimal control pulses to increase the gate fidelity and enlarge the robust window against noises and system parameter uncertainties for superconducting transmon qubits. The two-qubit CZ gate infidelity of the superconducting transmon qubits with characterized noises of the fast dephasing T_φ,1 contributed from the energy relaxation T₁ and from the white noise potentially due to the room temperature control electronics (RTCE), and noise of the slow dephasing T_φ,2 contributed from the flux noise (1/f noise) from the experiment [3], can be suppressed to ~4.7×10^-4, limited by the energy relaxation time T₁ = 30 μs. If T₁ is increased to 360 μs, the infidelity can be further reduced to .≤ 10^-4.

References

[1] C.-H. Huang and H.-S. Goan, Phys. Rev. A 95, 062325 (2017).

[2] C.-H. Huang, C.-H. Yang, C.-C. Chen, A. S. Dzurak, and H.-S. Goan, Phys. Rev. A 99, 042310 (2019).

[3] R. Barends, et al., Nature 508, 500 (2014).