A possible building block for a scalable quantum computer has recently beendemonstrated [M. Mariantoni et al., Science 334, 61 (2011)]. This architectureconsists of superconducting qubits capacitively coupled both to individualmemory resonators as well as a common bus. In this work we study a naturalprimitive entangling gate for this and related resonator-based architectures,which consists of a CZ operation between a qubit and the bus. The CZ gate isimplemented with the aid of the non-computational qubit |2> state [F. W.Strauch et al., Phys. Rev. Lett. 91, 167005 (2003)]. Assuming phase or transmonqubits with 300 MHz anharmonicity, we show that by using only low frequencyqubit-bias control it is possible to implement the qubit-bus CZ gate with 99.9%(99.99%) fidelity in about 17ns (23ns) with a realistic two-parameter pulseprofile, plus two auxiliary z rotations. The fidelity measure we refer to hereis a state-averaged intrinsic process fidelity, which does not include anyeffects of noise or decoherence. These results apply to a multi-qubit devicethat includes strongly coupled memory resonators. We investigate theperformance of the qubit-bus CZ gate as a function of qubit anharmonicity,indentify the dominant intrinsic error mechanism and derive an associatedfidelity estimator, quantify the pulse shape sensitivity and precisionrequirements, simulate qubit-qubit CZ gates that are mediated by the busresonator, and also attempt a global optimization of system parametersincluding resonator frequencies and couplings. Our results are relevant for awide range of superconducting hardware designs that incorporate resonators andsuggest that it should be possible to demonstrate a 99.9% CZ gate with existingtransmon qubits, which would constitute an important step towards thedevelopment of an error-corrected superconducting quantum computer.
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