Noise-resistant Landau-Zener sweeps from geometrical curves

Fei Zhuang1, Junkai Zeng1,2, Sophia E. Economou1, and Edwin Barnes1

1Department of Physics, Virginia Tech, Blacksburg, Virginia 24061, USA
2Shenzhen Institute of Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China

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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.

The Landau-Zener problem is one of the oldest and most famous examples of quantum dynamics. When a system is swept through an avoided crossing in the energy spectrum, it can end up in many different possible states depending on the size of the energy gap and the sweeping rate. In the context of quantum information processing, this physics is often exploited to implement quantum logic gates and to perform state initialization and readout. Noise fluctuations in the energy gap can degrade the quality of these operations.

We show that noise errors can be mitigated by carefully modulating the sweeping rate. We leverage a recently discovered connection between qubit evolution and space curves in three dimensions to find sweeping rate profiles that dynamically suppress errors. We present a general procedure for finding such profiles by first constructing closed curves that satisfy certain constraints.

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