Practical elimination of leakage in superconducting qubits by pulse shaping

In trying to develop high-fidelity control of superconducting and optical lattice devices, many techniques have been borrowed from the NMR literature, such as shaped, computer-generated, and composite pulses. However, unwanted coupling to higher energy levels cause simple spin state control to fail. We have shown that we can effectively remove any coupling to the third level in specifically phase and transmon qubits by adding a second control proportional to the derivative of the first along a rotation axis perpendicular to that of the first control. The 2-control strategy gives implementations with basic pulse-shaping as small as 4 pixels. Using realistic values of decoherence(5 $\mu$s), we find errors as small as $10^{-4}$ for such a 4ns pulse, about an order of magnitude better than using one quadrature. An easy to implement analytic formula can also be applied that handily improves on any existing single-control analog or pixelated pulse. These results demonstrate that experimental calibration and decoherence effects are the limiting factors in achieving high-fidelity quantum gates, and the focus of attention should be on these rather than on increasing the anharmonicity.