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Bulletin of the American Physical Society

Fidelity analysis of a Rydberg blockade CNOT gate with simulated quantum process tomography

X.L. Zhang, Alexander Gill, L. Isenhower, Thad G Walker, Mark E. Saffman

Published Jun 6, 2012• 0 citations
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Abstract We have numerically simulated quantum tomography of single-qubit and two-qubit quantum gates with qubits represented by mesoscopic ensembles containing random numbers of atoms. Such ensembles of strongly interacting atoms in the regime of Rydberg blockade are known as Rydberg superatoms. The stimulated Raman adiabatic passage (STIRAP) in the regime of Rydberg blockade is used for determining Rydberg excitation in the ensemble, required for the storage of quantum information in the collective state of the atomic ensemble and implementation of two-qubit gates. The optimized shapes of the STIRAP pulses are used to achieve high fidelity of the population transfer. Our simulations confirm the validity and high fidelity of single-qubit and two-qubit gates with Rydberg superatoms.

arXiv:1601.07282•Journal of Physics B Atomic Molecular and Optical Physics•May 16, 2016•27 citations
We present a detailed error analysis of a Rydberg blockade mediated controlled-not quantum gate between two neutral atoms as demonstrated recently in Isenhower et al. [Phys. Rev. Lett. 104, 010503 (2010)] and Zhang et al. [Phys. Rev. A 82, 030306 (2010)]. Numerical solutions of a master equation for the gate dynamics, including all known sources of technical error, are shown to be in good agreement with experiments. The primary sources of gate error are identified and suggestions given for future improvements. We also present numerical simulations of quantum process tomography to find the intrinsic fidelity, neglecting technical errors, of a Rydberg blockade controlled phase gate. The gate fidelity is characterized using trace overlap and trace distance measures. We show that the trace distance is linearly sensitive to errors arising from the finite Rydberg blockade shift and introduce a modified pulse sequence which corrects the linear errors. Our analysis shows that the intrinsic gate error extracted from simulated quantum process tomography can be under 0.002 for specific states of 87{}^{87}87Rb or Cs atoms. The relation between the process fidelity and the gate error probability used in calculations of fault tolerance thresholds is discussed.
We propose and analyze the implementation of a two-qubit quantum gate using circular Rydberg states with maximum orbital angular momentum. The intrinsic quantum gate error is limited by the finite Rydberg lifetime and finite Rydberg blockade shift. Circular states have much longer radiative lifetimes than low orbital angular momentum states and are therefore candidates for high-fidelity gate operations. We analyze the dipole-dipole interaction of two circular state Rydberg atoms and present numerical simulations of quantum process tomography to find the intrinsic fidelity of a Rydberg blockade-controlled phase gate. Our analysis shows that the intrinsic gate error can be less than $9\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}$ for circular Cs atoms in a cryogenic environment.
Abstract We have numerically simulated quantum tomography of single-qubit and two-qubit quantum gates with qubits represented by mesoscopic ensembles containing random numbers of atoms. Such ensembles of strongly interacting atoms in the regime of Rydberg blockade are known as Rydberg superatoms. The stimulated Raman adiabatic passage (STIRAP) in the regime of Rydberg blockade is used for determining Rydberg excitation in the ensemble, required for the storage of quantum information in the collective state of the atomic ensemble and implementation of two-qubit gates. The optimized shapes of the STIRAP pulses are used to achieve high fidelity of the population transfer. Our simulations confirm the validity and high fidelity of single-qubit and two-qubit gates with Rydberg superatoms.