We present a detailed error analysis of a Rydberg blockade mediated controlled-NOT quantum gate between two neutral atoms as demonstrated recently in Phys. Rev. Lett. 104, 010503 (2010) and Phys. Rev. A 82, 030306 (2010). Numerical solutions of a mas
ter 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 $^{87}$Rb or Cs atoms. The relation between the process fidelity and the gate error probability used in calculations of fault tolerance thresholds is discussed.
We demonstrate trapping and quantum state control of single Cesium atoms in a 532 nm wavelength bottle beam trap. The three dimensional trap is formed by crossing two unit charge vortex beams. Single atoms are loaded with 50% probability directly fro
m a magneto-optical trap. We achieve a trapping lifetime of up to 6 s, and demonstrate fast Rabi oscillations with a coherence time of $T_2sim 43 pm 9rm ms$.
Long range Rydberg blockade interactions have the potential for efficient implementation of quantum gates between multiple atoms. Here we present and analyze a protocol for implementation of a $k$-atom controlled NOT (C$_k$NOT) neutral atom gate. Thi
s gate can be implemented using sequential or simultaneous addressing of the control atoms which requires only $2k+3$ or 5 Rydberg $pi$ pulses respectively. A detailed error analysis relevant for implementations based on alkali atom Rydberg states is provided which shows that gate errors less than 10% are possible for $k=35$.
We demonstrate the first deterministic entanglement of two individually addressed neutral atoms using a Rydberg blockade mediated controlled-NOT gate. Parity oscillation measurements reveal an entanglement fidelity of $F=0.58pm0.04$, which is above t
he entanglement threshold of $F=0.5$, without any correction for atom loss, and $F=0.71pm0.05$ after correcting for background collisional losses. The fidelity results are shown to be in good agreement with a detailed error model.
We present the first demonstration of a CNOT gate using neutral atoms. Our implementation of the CNOT uses Rydberg blockade interactions between neutral atoms held in optical traps separated by >8 murm m. We measure CNOT fidelities of F=0.73 and 0.72
using two different gate protocols, and show by measurement of parity oscillations that the gate can be used to generate two-atom states with fidelity at the threshold for entanglement. We anticipate that the long range nature of the Rydberg interaction will be attractive for future extensions of this work to multi-qubit systems.
