Noise-resistant Landau-Zener sweeps from geometrical curves

Abstract

Landau-Zener physics is often exploited to generate quantum logic gates and to perform state initialization and readout. The quality of these operations can be degraded by noise fluctuations in the energy gap at the avoided crossing. We leverage a recently discovered correspondence between qubit evolution and space curves in three dimensions to design noise-robust Landau-Zener sweeps through an avoided crossing. In the case where the avoided crossing is purely noise-induced, we prove that operations based on monotonic sweeps cannot be robust to noise. Hence, we design families of phase gates based on non-monotonic drives that are error-robust up to second order. In the general case where there is an avoided crossing even in the absence of noise, we present a general technique for designing robust driving protocols that takes advantage of a relationship between the Landau-Zener problem and space curves of constant torsion.

13 pages, 11 figures; v3: final published version

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• Arbitrarily accurate composite pulses
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Cited by in corpus (10)

• Nonadiabatic Landau-Zener-Stückelberg-Majorana transitions, dynamics, and interference
• Designing dynamically corrected gates robust to multiple noise sources using geometric space curves
• Dynamically corrected gates in silicon singlet-triplet spin qubits
• Reverse engineering of one-qubit filter functions with dynamical invariants
• Designing globally optimal entangling gates using geometric space curves
• Robust population transfer of spin states by geometric formalism
• Quantum geometric protocols for fast high-fidelity adiabatic state transfer
• Quantum spectral analysis by continuous measurement of Landau-Zener transitions
• Hidden facts in Landau-Zener transitions revealed by the Riccati Equation
• An automated geometric space curve approach for designing dynamically corrected gates