In order to achieve the high-fidelity quantum control needed for a broadrange of quantum information technologies, reducing the effects of noise andsystem inhomogeneities is an essential task. It is well known that a system canbe decoupled from noise or made insensitive to inhomogeneous dephasingdynamically by using carefully designed pulse sequences based on square ordelta-function waveforms such as Hahn spin echo or CPMG. However, such idealpulses are often challenging to implement experimentally with high fidelity.Here, we uncover a new geometrical framework for visualizing all possibledriving fields, which enables one to generate an unlimited number of smooth,experimentally feasible pulses that perform dynamical decoupling or dynamicallycorrected gates to arbitrarily high order. We demonstrate that this scheme cansignificantly enhance the fidelity of single-qubit operations in the presenceof noise and when realistic limitations on pulse rise times and amplitudes aretaken into account.
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