Conditions allowing error correction in driven qubits

Abstract

We consider a qubit that is driven along its logical $z$ axis, with noise along the $z$ axis in the driving field $\Omega$ proportional to some function $f(\Omega )$, as well as noise along the logical $x$ axis. We establish that whether or not errors due to both types of noise can be canceled out, even approximately, depends on the explicit functional form of $f(\Omega )$ by considering a power-law form, $f(\Omega )\propto {\Omega }^k$. In particular, we show that such cancellation is impossible for $k=0$, $1$, or any even integer. However, any other odd integer value of $k$ besides $1$ does permit cancellation; in fact, we show that both types of errors can be corrected with a sequence of four square pulses of equal duration. We provide sets of parameters that correct for errors for various rotations and evaluate the error, measured by the infidelity, for the corrected rotations versus the naïve rotations, i.e., the operations that, in the complete absence of noise, would produce the desired rotations (in this case a single pulse of appropriate duration and magnitude). We also consider a train of four trapezoidal pulses, which take into account the fact that there will be, in real experimental systems, a finite rise time, again providing parameters for error-corrected rotations that employ such pulse sequences. Our dynamical decoupling error correction scheme works for any qubit platform as long as the errors are quasistatic.

arXiv comment9+$\epsilon$ pages, 6 figures, 5 tables. Added discussion of realistic values of noise parameters in the case of a semiconductor-based singlet-triplet spin qubit. Clarified some definitions of terms. Now published in Phys. Rev. B; this is the published version

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Cited by in corpus (7)

• Geometric formalism for constructing arbitrary single-qubit dynamically corrected gates
• Doubly geometric quantum control
• Geometrical Formalism for Dynamically Corrected Gates in Multiqubit Systems
• Analytically parameterized solutions for robust quantum control using smooth pulses
• Noise-resistant Landau-Zener sweeps from geometrical curves
• Quantum optimal control in quantum technologies. Strategic report on current status, visions and goals for research in Europe
• Fidelity of a sequence of SWAP operations on a spin chain